Financial modeling amit kumar singh

Module-I

INTRODUCTION

Financial Modeling using Excel

P a g e | 2

Contents

1.1 Objectives

1.2 Introduction to Financial Models

1.3 Steps in creating Financial Models

1.4 Application of Finance Functions in MS Excel

1.5 Capital Budgeting Functions in MS Excel

1.6 Bond Mathematics in MS Excel

1.7 Creating a Dynamic Model in MS Excel

1.7.1 Valuation of Option Contract

1.7.2 Bankruptcy of a Firm

1.8 Summary

1.9 Questions to discuss

1.10 References

1.1 Objective of Financial Modeling using MS Excel

By the end of this Module, you should be able to:

Definition of Financial Modeling

Steps need to take care before creating dynamic Models in Excel

Solving the cases on Capital Budgeting, Bond Mathematics etc in MS Excel

Understanding Complex Financial Models like Binomial Tree, Black Scholes Merton

Model in MS Excel


P a g e | 3

A financial model is a dynamic research based mathematical application that helps to establish

relationship among different variables of financial problems. It helps in making projections. There

is a need to understand the relationship among variables in the form of independent variable and

dependent variables. While creating model there is need to create as much interdependencies as

possible. As more relationship can be established among variables the more useful the model will

become. Along with variables a model include parameter whose specifications is entered by user

The difference is that their values are expected to remain constant or change infrequently within

the context of the model. For example in calculation of Taxable Income, the tax rates and taxable

brackets are parameters because these variables have to be provided for the model to work, these

values are not expected to change frequently. The variables whose values are calculated by the

model are called calculated variable or dependent variable. Some of them may be intermediate

variables, calculated for use in other calculations. Others are of primary interest to the user and are

the output variables of the models.

1.3 Steps in Creating a Model

The Financial Models are created either by using Excel or VBA and a systematic approach is

required. A systematic approach always involves planning ahead and it is time consuming.. Excel

and VBA is a user based application tool which can be edited based on changing conditions. So

while working on financial model certain steps needs to be followed to get a systematic solution.

The following are the steps for creating model

Step 1: Structuring the definition of Problem

Step 2: Understanding the input and output variables of the Model

Step 3: Determine the application and feasibility of model

Step 4: Understanding the Financial and Mathematical Aspects of the Model

Step 5: Re-designing and updating the Model and working on its background application

Step 6: Testing the Model

Step 8: Protect the Model

Step 9: Document the Model

Step10: Updating the model whenever required


P a g e | 4

1.4 Application of Finance Functions in MS Excel

Some of the basis excel financial functions explained in this module are

FV

PV

PMT

IPMT

PPMT

1.4.1 FV Function

MS Excel is used to calculate the Future Value of money. The syntax for the FV function is:

Illustration 1: Mohit has deposited Rs 4000 in his saving bank account and he wishes to withdraw

the money after 4 years. The annual savings bank account rate of the bank is 4%. Compute the

amount of interest received by Mohit.

The interest rate can be calculated using the formula 𝐹𝑉 = 𝑃𝑉 × (1 + 𝑟𝑎𝑡𝑒)𝑛 in paper. In excel

the same can be calculated by using the FV function.

Figure 1.1 : Calculation of FV based on mathematical formula

When we write FV in MS Excel, then MS Excel will ask for rate=4%, nper = time = 4 year, PV=

-4000, PMT=0 (applies when annuity is there), type=0 (it’s for annuity concept, by default excel

always takes 0). Both the methods would yield answer of Rs 4679.43

FV(rate,nper,pv,fv,type)


P a g e | 5

Figure 1.2 : Calculation of FV based on FV formula in Excel

The answer obtained is negative in nature as this is bug in FV, PV calculation in MS Excel so

whenever we are using these function always put “-“over PV or FV value

1.4.2 PV Function

Similarly we can use the formula of PV to determine the present value of money. The syntax for

the PV function is

Illustration 2: Imagine after 8 year and 4 month Raj will get Rs 1 lakh from Sohan. Suppose the

interest rate in market is 8% p.a. So, the present value of the same can be determined by using PV

formula in Excel or manually by using 𝑃𝑉 =𝐹𝑉

(1+𝑟𝑎𝑡𝑒)𝑛

Figure 1.3 : Calculation of PV using mathematical formula

PV(rate,nper,pmt,fv,type

)


P a g e | 6

Using excel, PV is calculated as shown below:

Figure 1.4 : Calculation of PV using PV function in excel

Both the methods give the answer Rs 52672.04

1.4.3 RATE Function

The syntax for Rate function is

Rate can be calculated manually through mathematical formula as

((𝐹𝑉

𝑃𝑉)

1

𝑛− 1) × 100 = 𝑅𝑎𝑡𝑒%

Illustration 3: Ram has Rs 1000 with him and it will get double in 4 years as he has taken a NSC.

The return on investment is calculated as:

Figure 1.5 : Calculation of Rate using mathematical formula

The answer is 18.92%

RATE(nper,pmt,pv,fv,type,gue

ss)


P a g e | 7

Using excel, PV is calculated as shown below:

Figure 1.6 : Calculation of rate of return based on Rate formula in Excel

The answer is 19% (rounded off)

1.4.4 NPER Function

The syntax for NPER Function is given as:

Similarly, time period can be determined mathematically through log(

𝐹𝑉

𝑃𝑉)

log(1+𝑟%)= 𝑛𝑝𝑒𝑟. So, by using

NPER function.

Let us take the same illustration 3. The NPER function in excel is shown below:

Figure 1.7 : Calculation of period of investment based on nper formula in Excel

The NPER value is 4.13 i.e. approximately 4 years.

1.4.5 PMT Function

The PMT function returns the loan payment (principal plus interest) per period, assuming constant

payment amounts and a fixed interest rate. For example, determining the EMI of a loan. The syntax

for the PMT function is

NPER(rate,pmt,pv,fv,type)


P a g e | 8

Illustration 4: Raj has taken a loan of Rs 10,000 at the rate of 5% annually. The term of the loan

is 5 years. The monthly payment is Rs 229.34

Figure 1.8 : Understanding PMT formula in Excel

Now, since EMI calculation uses PV of annuity so we had kept FV=0 in PMT calculation.

1.4.6 IPMT AND PPMT Function

The IPMT function returns the interest part of a loan payment for a given period, assuming constant

payment amounts and a fixed interest rate. The syntax for the IPMT function is:

The PPMT function returns the principal part of a loan payment for a given period, assuming

constant payment amounts and a fixed interest rate. The syntax for PPMT function is given as:

PMT(rate,nper,pv,fv,type)

IPMT(rate,per,nper,pv,fv,type)

PPMT(rate,per,nper,pv,fv,type)


P a g e | 9

Illustration 5: Mathew has taken a loan of 4 lakhs at an interest rate of 13.25%. The loan is to be

paid in 8 equal installments. The equal installment is determined by using the PMT function. The

interest is calculated on the principal left with fixed rate of 13.25%.

Whenever installment is paid, it is always more than the interest which thereby reduce the principal

as extra is used to reduce the value of principal and thereby making the net principal = 0 at the end

of the period.

The Interest is computed using the IPMT function of excel.

In the given calculation of PPMT and IPMT function, we need to put 13.25%/8=rate, per=1 for 1st

period, 2= for 2nd period …….nper=8(total period), PV=4,00,000 (total loan value), fv=0,

type=0(annuity).

Figure 1.9 : Loan Amortization Schedule in Excel


P a g e | 10

The function using excel formula is shown in the screenshot below:

Figure 1.10 : Use of IPMT and PPMT formula in Excel during loan amortization

1.5 Capital Budgeting Functions in MS Excel

Net Present Value Function

NPV is the foremost criteria of Capital Budgeting technique to decide whether to accept or reject

a project where the estimation of future cash flow is done through Financial Modeling techniques

and then the same is discounted by WACC (Weightage Average --Cost of Capital) to determine

the present value of Cash Flow. If the sum total of cash inflows is more than the Initial Investment

or (∑ Initial Investment+ ∑PV of future Capital Expenditure) then the project is accepted otherwise

rejected.

Illustration 6: Suppose the Company XYZ is initiating a new project requiring an Initial

Investment of 50 lakh Rupees. Based on the riskiness of project, the proposition of funds raised

through debt and equity, individual cost and taxation rate the estimated WACC is 15%. The

expected life of project is 7 year. Expected Cash Flows from the project will be:-

Year Expected Cash Flows (in Rupees)

1 5 lakhs

2 5 lakhs

3 20 lakhs


P a g e | 11

4 8 lakhs

5 12 lakhs

6 5 lakhs

7 7 lakhs

Note- Expected Cash Flows can be Operating Cash Flow or Capital Free Flow or Free Cash Flow)

Now in order to calculate NPV manually or through Excel Formula the calculation will be done

on Excel Sheet as shown in the screenshot below.

Figure 1.11: Working on NPV Calculation

Like this PV of cash flows for individual years can be determined.


P a g e | 12

Figure 1.12 : Determining the sum of PV of cash flows in NPV calculation

As the NPV is negative, we have to reject the project

The syntax for the NPV function in excel is

NPV function is shown in the screenshot below

Figure 1.13 : Working of NPV formula in Excel

When we write =NPV() in excel it calculated the PV of cash flows from year 1 to …….n, since

initial investment happened on year 0 so it was put outside bracket where cash inflows are

represented with “+” sign where cash outflow with “-“ sign.

XNPV Function

When the NPV is calculated, the period of receivable of cash flows is assumed to be constant. In

reality it can be different. For uneven period cash flows, XNPV function is used.

NPV(rate,value 1, value 2,…)


P a g e | 13

The syntax for XNPV function is:

Illustration 7: The below table shows the cash flows for the following dates. The WACC is 14%.


27/6/2007 -70000

5/12/2008 12000

2/2/2009 15000

9/5/2011 18000

22/8/2012 21000

1/8/2014 26000

Figure 1.14 : Calculation of NPV of uncertain cash flows based on XNPV formula in Excel

IRR Function

IRR is the minimum return expected on an investment under the condition when ∑PV of future

cash flows=Initial Investment or at what discount rate NPV=0. To determine IRR manually, trial

and error method and Interpolation is appropriate while in excel IRR function is appropriate.

Excel tries to calculate the IRR value until the result is accurate within 0.00001%. If after 20 trials

it is not able to calculate the accurate value, it will show #NUM error. The syntax for IRR is:

XNPV(rates,values , dates)

IRR (values , guess)


P a g e | 14

Guess is the number that we guess is close to the result of IRR. If guess is omitted, it is assumed

to be 10%. Values are the array or reference to cells that contain number for which we want to

calculate the IRR. Values must contain at least one positive value and one negative value to

calculate the IRR. IRR uses the order of values to interpret the order of cash flows. Please make

sure that the sequence of outflows and inflows in logical, desired manner.

Illustration 8: For example a Capital Budgeting decision requires an initial investment of Rs

70,000 creating a useful life of 5 year generating cash flows of Rs 12,000, Rs 15,000, Rs 18,000,

Rs 21,000 and Rs 26,000 in 5 successive years.

Figure 1.15 Working on IRR in Excel

The IRR comes out to be 0.09.

In the example I have Guess as 15%, irrespective of whether we write guess or not there will be

no change in the final answer.

There are certain drawbacks in the IRR calculation as Internal Rate of Return assumes that the

cash flows from the project are reinvested at the IRR, also mathematical interpretation of IRR get

complicated whenever the series of cash outflows and inflows happens regularly. It leads to

Polynomial Equation creating multiple values of IRR which leads to confusion.

For Example, consider the following cash flows:


P a g e | 15

Year Future cash flows

0 -10,000

1 6,000

2 -2,000

3 14,000

Now, if we want to determine the IRR for this scenario, it can be represented as

10,000 = (6000

1 + 𝐼𝑅𝑅) − (

2000

(1 + 𝐼𝑅𝑅)2) + (

14000

(1 + 𝐼𝑅𝑅)3)

If we try to solve this Polynomial Equation, we will get multiple values of IRR. So, in any capital

investment decision if there are multiple cash outflows then it would be appropriate to use MIRR.

MIRR

MIRR Returns the internal rate of return where positive and negative cash flows are financed at

different rates. The syntax of MIRR is:

Here “values” represent the array of the project's cash flows, “finance_rate” is the relevant cost

of capital, and “reinvest_rate” is the rate of return at which the project's cash flows are expected

to be reinvested. Usually WACC= finance rate while reinvest rate can be any appropriate rate of

return depending on the avenues for the investment favourable.

Illustration 9: Consider an example where a company XYZ is evaluating a project that has the

following cash flow associated with it:

Year 0 1 2 3 4 5 6

Cash Flows -120 80 -20 60 80 -40 120

Here we assume finance rate = reinvest rate = cost of capital = 15%. In order to calculate the

MIRR, we have to determine the ∑ of PV of a cash outflows and ∑ FV of all cash inflows. Since

MIRR(values, finance_rate,reinvest_rate)


P a g e | 16

finance rate is used for discounting and reinvest rate for compounding, here both we assume as

same.

Year 0 1 2 3 4 5 6

Cash Flows -120 80 -20 60 80 -40 120

- 15.1228 = 20

(1+15%)2

-22.87 = 40

(1+15%)4

∑=120+15.1228+22.87=157.9928

Year 0 1 2 3 4 5 6

Cash Flows -120 80 -20 60 80 -40 120

= 120. (1 + 15%)0 = 120

= 80. (1 + 15%)5 = 160.91

60. (1 + 15%)3 = 91

= 80. (1 + 15%)2 = 106

∑ of FV of cash inflows= 477 million Rs

Figure 1.20 : Understanding MIRR calculation

Now, use the formula ∑FV of cash Inflows=∑ of PV of Cash Outflow. (1 + 𝑀𝐼𝑅𝑅)𝑛

477 = 158. (1 + 𝑀𝐼𝑅𝑅)𝑛


P a g e | 17

= (477

158) = (1 + 𝑀𝐼𝑅𝑅)𝑛

3.0189 = (1 + 𝑀𝐼𝑅𝑅)6

log(3.0189) = 6 log(1 + 𝑀𝐼𝑅𝑅)

0.47984 = 6 log(1 + 𝑀𝐼𝑅𝑅)

0.079974 = log(1 + 𝑀𝐼𝑅𝑅)

𝑎𝑛𝑡𝑖𝑙𝑜𝑔(. 079974) = 1 + 𝑀𝐼𝑅𝑅

1.20219 = 1 + 𝑀𝐼𝑅𝑅

𝑀𝐼𝑅𝑅 = 20.219%

The same calculation can be done on MS Excel by using MIRR function.

Figure 1.16: MIRR calculation in Excel

Whenever IRR is calculated we assume the future cash flows will occur after every regular interval

of time, in reality probability to get periodical cash inflow is very less, so in case of non periodical

cash flows XIRR function is used in MS Excel.

XIRR Function

XIRR function returns the internal rate of return for a schedule of cash flows that is not necessarily

periodic. The syntax for XIRR function is:

XIRR(values, dates,guess)


P a g e | 18

Illustration 10: The table below gives the cash flows for the respective dates


27/6/2007 -70000

5/12/2008 12000

2/2/2009 15000

9/5/2011 18000

22/8/2012 21000

1/8/2014 26000

Figure 1.17 : XIRR calculation in Excel

1.6 Bond Mathematics in MS Excel

Debt Instrument brings an obligation to the borrower to pay constant coupon at the regular interval

of time till its maturity. This makes the feature of coupon similar to annuity. So we can use

mathematical application of PV of annuity to solve the bond arithmetic. Coupon is always

calculated on the face value. Based on cash inflows (coupon+ face value), cash outflows (price)

the required rate of return can be determined which is determined as current yield and yield till

maturity (YTM).

Current Yield does not follow time value of money while YTM follows time value of money where

minimum return on investment on debt instrument is determined assuming the debt instrument is


P a g e | 19

holds till its maturity. The calculation of YTM is similar to IRR calculation. Price of the bond

fluctuates based on demand-supply, macroeconomics and microeconomics scenarios around the

issuer of debt instrument. Price at which the debt instruments trades in market is represented as

clean price while the adjustment of accrued interest on the clean price is called dirty price.

Accrued Interest is calculated based on day count convention following by different countries,

Price of the bond is inversely proportional to the YTM where the rate of change of change in price

with respect to change in YTM is determined through Duration. Duration can be Macaulay

Duration and Modified Duration. While the relationship between prices of bond with respect to

YTM is convex in nature instead of linear relationship, which is explained mathematics through

Convexity. Bond Arithmetic in Excel can be simply explained through this example.

Illustration11: Suppose a 12.5%, 6 year bond pays coupon annually matures at Rs 1000. The

YTM on this bond is 15%. Present Value of bond or Price of bond can be done manually through

PV of Annuity (Coupon) +PV of Face Value or in by using PV function in excel.

Coupon is always paid on Face Value. 12.5% on Rs 1000 will be Rs 125.


P a g e | 20

Figure 1.18 : Calculation of Price of bond mathematically in Excel

The same can be calculated by using PV function in MS Excel in one step.

Figure 1.19 : Calculation of Price of bond through PV formula in Excel

Here, rate=YTM, nper=life of bond, pmt=coupon value, fv=face value, type=0 (all case of

annuity), if we put we will price of bond =RS 905.387. Similarly for the same problem if we want

to determine YTM, we can use RATE function.

Figure 1.20 : Determining YTM of bond through RATE formula in Excel


P a g e | 21

Similarly the life of bond is determined through NPER function, value of coupon through PMT

function, For Face Value of Bond we can use FV function.

Now in reality when the bond is trading on Exchange the price at which it is trading is called Clean

Price which can be determined through discounting of Cash Flows. This is determined on actual

basis by using PRICE function in MS Excel. The syntax for PRICE function is

Here settlement date = date on which the bond is sought to be valued

maturity date = date on which the bonds matures

rate = rate at which coupon is paid

Yld=required rate for valuation

Redemption = the redemption value of bond

Frequency = number of coupon in a year

Basis = day count convention to be used.

Illustration 12: In order to value the 11.75% 2016 bond, maturing on April 16, 2016, and on 06th

July, 2014, using day count convention of 30/360 and the required yield of 15% where the coupon

is paid semi annually.

Therefore price function is given as:

= price(16/04/2016,06/07/2014,0.1175,0.15,100,2,4)

When we are writing Date it should in Date format, so better use =DATE function in MS Excel.

Price(settlement, maturity, rate, yld, redemption, frequency, basis)


P a g e | 22

Figure 1.21 : Use of PRICE function in Excel

So, the price comes Rs 95.03. This is the clean price. Now when adjustment of accrued interest is

made on it we will get dirty price. To determine Accrued Interest we need help of Day Count

Convention. There are four popular Day Count Conventions:-

Day Count Conventions Description

30/360 This convention considers each month including February as

having 30 days and year consisting of 360 days.

Actual/360 This convention counts the actual number of days in a month,

but uses 360 as the number of days in a year.

Actual/Actual This convention uses the actual days in the month and the

actual number of days in a year.

Actual/365 This convention uses the actual number of days in a month and

365 days in a year.

When the trading of debt instruments happens, investors buy and sell debt instrument. Transaction

happens on dirty price where calculation of accrued interest is very important. There are certain

excel functions used to compute accrued interest.


P a g e | 23


P a g e | 24

Illustration 13: Consider a hypothetical bond having coupon rate of 9.5%. The bond will mature

on 23rd March 2016. Suppose the coupon is paid semi annually and it follows the day count

convention of 30/360 and we want to do valuation of bond on 06th July, 2014. Then to know the

various information regarding coupons we can use multiple functions in MS Excel.

In order to know the next coupon period COUPNCD function is used. The next coupon period

is 23rd September’14.

If we want to determine the previous coupon period which would be definitely be six month

old, i.e. 23rd September’14, the function COUPPCD is used.

Since in the day count convention we assume 360 days in a year. Therefore, if we want to

know how many days left for the next coupon date, COUPDAYSNC function is used.

Similarly in order to determine the number of days from the previous coupon to settlement

can be determined using COUPDAYBS function.

The below screenshot shows all the above four coupon functions:


P a g e | 25

Figure 1.22 : Use of various coupon functions in excel

ACCRINTM Function

Accrued Interest is the compensation the buyer needs to pay to seller over the current price of the

bond to compensate the time value of holding the bond beyond the last coupon date. ACCRINTM

function is used to compute accrued interest. The syntax for ACCRINTM is:

In order to calculate the Accrued Interest we need to know the Issue Date, First Coupon Payment

Date, Face Value, Frequency (the number of times the coupon is paid within in a year), Basis (Day

ACCRINTM( issue, settlement, rate, par, basis)


P a g e | 26

Count Convention), Calculation Method if it is true the MS Excel will calculate the interest from

Issue Date to Settlement Date and if it is false then MS Excel will calculate the interest from

Settlement Date to 1st Interest Date. In most of cases we need to put the Calculation Method as

True.

Illustration 14: Consider a hypothetical bond having coupon rate of 9.5%. The bond will mature

on 23rd March 2016. Suppose the coupon is paid semi annually and it follows the day count

convention of 30/360. We want to do valuation of bond on 06th July, 2014. It is assumed that the

coupons are all paid at maturity. The bond is issued on 13th May 2008 and the first coupon date is

15th May 2008. The face value of the bond is Rs 100

The ACCRINTM function is shown below:


P a g e | 27

Figure 1.23 : Example of Accrued Interest calculation

1.7 Creating a Dynamic Model

Financing Modeling is task of building an abstract representation of a financial decision making

situation. It is a mathematical model designed to represent a financial asset or a portfolio of a

business or a project or any other domain. A financial model starts with preparing a forecast for

the future performance of a firm by identifying historical data on Balance Sheet, Profit and Loss

Statement, Cash Flow Statement etc and then projecting on basis of this the future figures. It helps

an analyst to set assumptions, to analyze the performance and test the sensitivity of data based on

calculation and understanding the impact of change. While creating Financial Model in excel font

color is very important like all hard coded facts or constant is coded in blue color, all formulae

in black, all linkages across spreadsheet should be in green color, the negatives numbers are

represented with brackets. Numbers should be written with 1000 separator and number of

decimals to be represented with number depends on scope of research undergoing.

1.7.1 Model 1: Valuation of an Option Contract

Let us create a Financial Model to value an option contract under Black Scholes Merton Model.

Since Derivative Contract assumed to follow Lognormal Distribution pattern so here I use


P a g e | 28

NORMSDIST Function to determine the cumulative normal distribution value. Now the formula

for Non Dividend Paying Stock under Black Scholes Merton Model is

𝑑1 =𝑙𝑛 (

𝑆𝐾) + (𝑟 +

𝜎2

2 ) 𝑡

𝜎√𝑡

𝑑2 = 𝑑1 − 𝜎√𝑡

Premium of a call option

𝑪 = 𝑺 × 𝑵(𝒅𝟏) − 𝑵(𝒅𝟐) × 𝑲𝒆−𝒓𝒕

Premium on a Put Option

𝑷 = 𝑵 × (−𝒅𝟐)𝑲𝒆−𝒓𝒕 − 𝑺 × 𝑵(𝒅𝟏)

Assume a stock called DLF trading in market at Rs 221.70 on 17 July 2014. Option data for the

stock is available below. Consider a strike price of Rs 230. It is OTM call option and ITM put

option. As per the data, premium on call option is Rs 5.40 and premium on put option is Rs 12.20.

Through Black Scholes Merton Model it will be determined whether the premium is overvalued

or undervalued. ICICI Bank FD Rates is taken as risk free interest for 90 days which is 8.5% per

annum. Standard Deviation is determined by last 3 month historical data. It is 3.724%.

Figure 1.24 : Historical 1 day value of a stock-DLF


P a g e | 29

Figure 1.25 : Historical option data of DLF at different strike prices

Figure 1.26 : Risk free interest rate in the market at varying periods


P a g e | 30

Figure 1.27 : Calculation of Standard Deviation

Formula for Black Scholes Merton Model is already discussed. In MS Excel a Dynamic Model

can be created for the valuation of Option contract.


P a g e | 31

Figure 1.38 : Calculation of option premium based on Black Scholes Model

According to this Model the price at the which trading in market is under valued.

1.7.2 Model-2 Bankruptcy of a Company

Altman Z Score Model was published in 1968 through which it can be determined the probability

that the firm can be bankrupt within 2 years. The Z Score is the linear combination of five ratios

weighted by coefficients.

The original Z score Model is :-

Z=1.2T1+1.4T2+3.3T3+0.6T4+0.99T5

Where T1=Working Capital/Total Assets. Measures the liquid assets in relation to size of

company.

T2=Retained Earning/Total Assets. Measures the profitability that reflects in the company age and

earning power.

T3=EBIT/Total Assets. Measures the Operating Efficiency apart from tax and and leveraging

factors. It recognizes operating earnings as being important to long-term viability.


P a g e | 32

T4=Market Value of Equity / Book Value of Total Liabilities. Adds market dimension that can

show up security price fluctuation

T5=Sales/ Total Assets. Standard measure for total asset turnover (varies greatly from industry to

industry).

Companies with Z score value less than 1.22 is in Distress Zone, while those above 2.9 are in safe

zone.

Figure 1.39 : Accounting Information required for Z-score calculation


P a g e | 33

Figure 1.40 : Calculation under Altman-Z score Model

1.8 Summary

1. A Financial Model is dynamic mathematical tool created to understand the relationship

among the variables of a financial problems so that it can help to answer “what if” questions

or make projections.

2. Models include dependent variables and independent variables. The variables whose

values are calculated by the model are called calculated variable or dependent variable.

Models are always created to observe how the values of the output variable will change

with changes in values of one or more independent variables.

3. Models include a independent variable called parameter who are independent variable

whose values are provided by creator or user of Model

4. Steps to construct a Financial Model are as follows:-


P a g e | 34

Define the structure of Problem

Define the input and output variables of the Model

Decide who will use the Model and how often

Understanding the Financial and Mathematical Aspects of the Model

Design the Model and create the spreadsheet

Testing, protecting and documenting the model

5. Application of Finance Function in MS Excel

FV Formula- It returns the future value of single set of cash flow or series of cash flows in

the form of annuity

PV formula-It returns the present value of single set of cash flow or series of cash flows in

the form of annuity

PMT formula-It determines the annuity value from future value or present value of cash

flow

IPMT formula- Use in loan amortization schedule to determine the interest period on period

basis on the decreasing principal

PPMT formula- use to determine extra principal paid over the interest because of constant

EMI in a loan amortization schedule

NPV formula- It determines the net present value of investment by deducting the PV of

Cash Outlay on the present value of cash inflows

IRR= It determines the minimum return on investment considering at a rate at which initial

investment would become equal to sum of present value of cash inflows

MIRR formula- It works when IRR results into multiple solutions. Finance Rate and

Reinvestment Rate implied here. Finance rate is used for the multiple cash outlay value to

determine the present value while Reinvestment rate is used for determining the sum total

of future value of cash inflows

XNPV formula-This calculates the NPV of series of uncertain cash flows

XIRR formula-This calculates the IRR of uncertain cash flows

6. Debt Instrument is a financial instrument in which borrower raise funds for a fixed duration

of time from lender whereby paying interest (coupon) after every regular interval of time

and on maturity pays Face Value.


P a g e | 35

7. Price of Bond can be determined through PV formula while YTM can be determined

through Rate formula, Coupon can be determined through PMT formula and Face Value

through FV formula.

8. Similarly along with PV formula for determining Price, in MS Excel “Price” formula can

be used.

Here Settlement Date=day on which bond is sought to be valued

Maturity date=day on which bond will mature

Rate=rate at which coupon is paid

Redemption is the redemption value of bond

Frequency is the number of coupon in a year

Basis=day count convention to be used

9. Since bonds are trading in market at clean price while at settlement dirty price is

determined, where dirty price=clean price+ accrued interest

10. Accrued Interest in MS Excel is determined through “=ACCRINTM” or “=ACCRINT”

formula

11. ACCRINT is use for coupon paying bond while ACCRINTM is used for zero coupon bond

paying face value at maturity

12. Clean Price is determined through demand and supply mechanism. Along with that changes

in Interest Rate, Government policies towards debt instrument, Inflation rate changes

impact the bond price

13.


P a g e | 36

14. Coupdays function- Return the number of days in a coupon period that contain the

settlement date

15. Coupnum function- Return the number of coupon payable between the settlement date and

maturity date

16. Coupdaysnc function- Return the number of days from the settlement date to next coupon

date

17. Couppcd function- the previous coupon date before the settlement date

18. Coupncd function- Return the coupon date after the settlement date

19. Dynamic Model in MS Excel-Valuation of Option

Normsdist function is used in MS Excel to represent lognormal distribution

Valuation of Option Contract is done through Black Scholes Merton Model and Binomial

Tree Model

For Black Scholes Model, d1 and d2 is determined initially for which N(d1) and N(d2) is

determined through NORMSDIST function in MS Excel or Cumulative Normal

Distribution Table can be used

Based on N(d1) and N(d2) values, premium on call option and premium on put option will

be determined and same can be check through put call parity

Binomial Tree Model is represented as one step Binomial Tree, two step Binomial Tree or

three step Binomial Tree depending upon the volatility.

u=proportionate increase in price of underlying or d=proportionate decrease in price of

underlying is determined through formula, 𝑢 = 𝑒𝜎∗𝑡 and d= 𝑒−𝜎∗𝑡

e=euler number in MS Excel is represented with =exp function

20. Bankruptcy of a firm-Altmann Z-score Model

Altmann Z-score Model talks about possibility of a firm get bankrupt within 2 years.

Z=1.2T1+1.4T2+3.3T3+0.6T4+0.99T5

where T1=Working Capital/Total Assets. Measures the liquid assets in relation to size of

company.


P a g e | 37

T2==Retained Earning/Total Assets. Measures the profitability that reflects in the

company age and earning power.

T3=Measures the Operating Efficiency apart from tax and and leveraging factors. It

recognizes operating earnings as being important to long-term viability.

T4=Market Value of Equity / Book Value of Total Liabilities. Adds market dimension that

can show up security price fluctuation

T5=Sales/ Total Assets. Standard measure for total asset turnover (varies greatly from

industry to industry).

1.10 Questions to Discuss

Two Marks Questions

1. What is Financial Model?

2. Define the properties of Financial Model?

3. What are the steps taken to create a Financial Model?

4. What is the application of NORMSDIST in MS Excel?

5. Explain COUPDAYBS function?

6. Explain COUPDAYSNC function?

7. Explain COUPNCD function?

8. Explain COUPNUM function?

9. Explain COUPPCD function?

Five Marks Questions

1. What is the application of day count convention in Bond Mathematics?

2. What are the steps taken to create a Financial Model?

3. What are the application of finance functions in MS Excel?

4. With example explain FV function in MS Excel with and without PMT function?

5. What are the difference between NPV and XNPV function in MS Excel?

6. What are the difference between IRR and XIRR function in MS Excel?

7. How different is calculation of NPV and IRR in MS Excel ?


P a g e | 38

8. How price and ytm of bond is calculated in MS Excel?

Ten Marks Questions

1. With example, define loan amortization schedule using IPMT, PPMT, PMT, Goal Seek?

2. Explain Bond Mathematics in MS Excel using price, ytm, coupon based formulaes,

mduration, accrued interest?

1.10 References:

Khan MY, Jain PK(2008) Financial Management 3rd Edition Mc Graw Hill Publication-

New Delhi

Pandey I.M (2003) Financial Management, Vikas Publishing House-New Delhi

Tija S. J (2004) Building Financial Models- A guide to creating and interpreting

Financial Statements

Beninga S. (2008) Financial Modeling-3rd Edition

Damodaran A. (2008) -Damodaran on Valuation, Wiley Finance-USA

Fabozzi J.F (2008) The Handbook of Fixed Income Securities-8th Edition

Hull C.J (1997)-Options, Futures and Other Derivatives-6th Edition

Websites:

Fixed Income Securities, Understanding trading on debt instruments- last retrieved on

18/11/2014 from http://www.moneycontrol.com/fixed-income/

Financial Modeling-Financial Functions in Excel- last retrieved on 18/11/2014 from-

http://www.excel-easy.com/functions/financial-functions.html

Financial Modeling-Financial Functions in Excel- last retrieved on 18/11/2014 from

http://office.microsoft.com/en-in/excel-help/financial-functions-reference-

HP010342519.aspx

Option Pricing Model, Black Scholes Merton Model on Option Valuation- last retrieved on

18/11/2014 from- http://mitsloan.mit.edu/newsroom/2013-black-scholes-merton.php

http://www.moneycontrol.com/fixed-income/

http://www.excel-easy.com/functions/financial-functions.html

http://office.microsoft.com/en-in/excel-help/financial-functions-reference-HP010342519.aspx

http://office.microsoft.com/en-in/excel-help/financial-functions-reference-HP010342519.aspx

http://mitsloan.mit.edu/newsroom/2013-black-scholes-merton.php


P a g e | 39

Video Links:wc

Amir Parmar, (14 October 2013) Microsoft Excel Financial Functions - viewed on

18/11/2014-http://www.youtube.com/watch?v=-6ERqkxlcFY

Hun Kim (15 Feb 2013) Financial Formula PMT function (Calculate Loan Payments)-

viewed on 18/11/2014 http://www.youtube.com/watch?v=WiVU5qeX48Q

Paul Wilmott (21 Feb 2011)-Bond Maths- viewed on 18/11/2014-on Quantitative

Finance-http://www.youtube.com/watch?v=lrRJ70N2Nhc

http://www.youtube.com/watch?v=-6ERqkxlcFY

http://www.youtube.com/watch?v=WiVU5qeX48Q

http://www.youtube.com/watch?v=lrRJ70N2Nhc


P a g e | 40

Module II: Sensitivity Analysis Using Excel.


P a g e | 41

Module II: Sensitivity Analysis Using Excel.

Contents

2.1 Objectives-Sensitivity Analysis using MS Excel

2.2 Introduction to Sensitivity Analysis

2.2.1 Understanding one way data table

2.2.2 Understanding two way data table

2.2.3 Understanding Goal Seek

2.3 Scenario Manager Function using MS Ex

2.4 Application of MS Solver

2.5 Summary


2.7 References

2.1 Objective-Sensitivity Analysis using MS Excel


Understand the significance of Sensitivity Analysis

What IF Analysis using MS Excel-Goal Seek

What IF Analysis using Excel-one way data table

What IF Analysis using Excel-two way data table

Financial Planning Application using Data Table

Analyzing different scenarios using Scenario Manager

Analyzing Mathematical Constraint scenario using Solver


P a g e | 42

2.2 Introduction to Sensitivity Analysis

Sensitivity Analysis is the study of how the uncertainty or deviation in the output of mathematical

model can impacts the different sources of uncertainty in the inputs. The main goal is to gain

insight to find out which assumptions are critical. The process involves various ways of changing

input variables of the model to see the impact on output variables.

In order to understand Sensitivity Analysis we will take an example.

Illustration-1: Suppose Amit want to start a Juice Shop. Before opening the shop suppose he is

curious to analyze how is his profits, Revenue, Variable Costs will depend on the price he will

charge and the unit cost. Most Worksheet Models contain assumptions about certain parameters

or inputs to the model. In this example also inputs includes

a. The price for which glass of juice will be sold

b. The variable cost of producing 1 glass of juice

c. The sensitivity of demand for juice to the price changed

d. The annual fixed cost of running a juice shop

Based on the input assumptions, he can compute the output of interest. In this example, the output

will include:-

a. Annual Profit

b. Annual Revenue

c. Annual Variable Cost

Despite enough research, assumptions about the input values can have errors. For example, the

best guess about the variable cost of producing 1 glass of juice might be Rs 6 but it is possible that

the assumptions can have errors. Sensitivity Analysis determines how a spreadsheet’s output vary

in response to the change in its inputs. For example he want to know if he will change the profit

then how much it will affect the yearly profit, revenue and variable cost. Data Table in MS Excel

will help to find the sensitivity. With a one-way data table, he can determine how changing input


P a g e | 43

will change any number of outputs. With a two-way data table, he can determine how changing

two inputs will change a single output.

Figure 2.1: Example to explain the working of data table

Now suppose he want to know how change in price for example from Rs 12 through Rs 26 in Rs

1 increments affect the annual profits, revenue and variable cost. Because here changing only 1

input, one way data table can solve this problem. In order to set one way data table, he will have

to begin by listing input values in a column.

Representation of one way data table will be like this.


P a g e | 44

Figure 2.2: Data formatting in data table

In order to work on Data Table whole rectangular area will be selected and then Data tab under it

what if analysis then if data table is selected a window will open asking for Row input cells and

column input cells. Enter the data which is independent variable here in this case (Price) of

mentioned in the statement. Price which is mentioned in the statement is Rs 20 per glass. Select

the cell for that and press OK.


P a g e | 45

Figure 2.3: One way Data Table


P a g e | 46

Figure 2.4: Outcome on data table

Now I can measure the sensitivity of change in the price of juice (independent variable), its impact

on Profit, Contribution, Revenue, Variable Cost (dependent variables). If we notice initial column

is creating confusion as after calculation it is showing duplication so we should edit it. If I try to

delete it then whole data will become zero.


P a g e | 47

Figure 2.5: Impact of change on data table

Appropriate solution can be remove the formulas within each cell through Paste Special Value

after copying them so what we can do that go the irrelevant cell, go to format cell or CTRL+1,

then custom then inside that click on General, then under Type write within “ “.

So one by one if Amit go the each cell and then go to format cell and then inside that under Name,

Custom and after clicking General then if I write in Type-“Profit”, then for other cell, “Revenue”,

then for other cell “Variable Cost” and like this then I will get my data table as


P a g e | 48

Figure 2.6: Data Table

Till now he has changed one variable and see its impact on different dependent variables. Now he

will change two variables Price and Demand and then he will see it impact on Profits.

Figure 2.7: Two way data table-initiation

For this he will use two way data table. For putting random data following any pattern he can use

Fill function under HOME ribbon.


P a g e | 49

Figure 2.8: Adding number in series

Now the objective is to see the impact on profit by changing two variables called demand and price

per unit. For this the first thing what he need to put here is the data of profit at the top end of data

table mentioned under this case.


P a g e | 50

Figure 2.9: Data arrangement under two way data table

Then copy the whole rectangular data, go to Data>>What If Analysis>>Data Table


P a g e | 51

Figure 2.10: Working under two way data table


P a g e | 52

Figure 2.11: Outcome under two way data table

Data mentioned in the row is demand and in column is price per unit, while in row input cell he

would put demand mentioned and in column input cell he put price per unit as mentioned in the

case which he created at the beginning of session about Cost Sheet of Amit Juice Company.

By seeing in this excel sheet he can understand and prove mathematically how the profit get

impacted by the change in demand and price together.


P a g e | 53

Illustration-2: Another parameter which we can use in Sensitivity Analysis is Goal Seek which

help to find the breakeven point. Suppose Amit want to know that how much glasses of juice can

he sell so that he get back my investment. Goal Seek feature in MS Excel enables us to compute a

value for the worksheet input such that it matches with the goal being specified. Goal Seek is used

in finance to determine discount rate or compounding rate in Capital Budgeting, Bond Arithmetic

etc. Suppose in the same example Amit want to know how many juices should he sell in a year so

that he get break even. Consider the same example again,

Figure 2.12: Break-even calculation through Goal Seek

In order to determine the break even he will go to Data>>What If Analysis>>Goal Seek. A

dialogue box will open where in Set cell, he will chose the cell having profit data. At breakeven

the profit would be zero, so in option: To value, put value=0. Please chose the cell having demand

in option ”by changing cells”. Then press OK.


P a g e | 54

Figure 2.13: Break-even calculation through Goal Seek

Illustration 3: Goal Seek can also help in Financial Planning. Suppose he want to buy a house in

Bangalore and he is considering based on his Financial Strength how much price of house can he

afford in Bangalore. He have a liquid cash of 5 lakh Rupees which he can give for down payment.

He is thinking to take 15 year loan from bank for the remaining periods. As next month is his

wedding so probably after 15 year he will have to plan for his child education. Interest rate on

home loan is 14.25% per annum. By considering all the constraints and his financial obligation

suppose he can pay an EMI of Rs 8000 to the bank for 15 years. Now the question arises, which

will be price range of 2 BHK house which should he start searching. For this he will use Goal Seek

in MS Excel.


P a g e | 55

Figure 2.14: Financial Planning calculation through Goal Seek

Amount of loan would be Price of house-Down Payment. Since of House cell he kept blank so the

Amount of loan is showing -5 lakh Rupees. Monthly Payment can be calculated by PMT function.

Now, the value of Monthly payment will be calculated below and the total interest paid=(EMIx180

periods)-loan value.


P a g e | 56

Figure 2.15: EMI-part of Financial Planning calculation through PMT

It will come -6742.50. But my commitment to pay is Rs 8000 per month. Now I can use Goal Seek

to determine the price of house. MS Excel command to go Goal Seek is Data>>What if

Analysis>>Goal Seek. In Goal Seek under set cell if amit would select Monthly Payment cell , to

value=8000 and by changing cell, in that cell=price of loan. Goal Seek will give the outcome.


P a g e | 57


In set cell he put cell that containing Monthly Payment data, To value he can put Rs 8000 which

is his ability to pay every month. By changing the cell having empty data of price of car, then press

OK.

Figure 2.17: Result-Financial Planning calculation through Goal Seek


P a g e | 58


This mean under the given financial condition, he can afford to buy a house of Rs 10 lakh 93

thousand Rupees. Interest rate is very high because of which the value of Rs 8000 per month spread

over 15 years turns to be only Rs 5.93 lakh only. By using one way data table he can analyze the

same situation where he can see the impact of Interest Rate on the Price of House.

Figure 2.19: Financial Planning calculation through Data Table


P a g e | 59

Figure 2.20: Financial Planning calculation through two way data table

2.3 Scenario Manager Function in MS Excel

Scenario Manager in MS Excel helps us to see different perspective of a same event at same

moment instead of changing frame of reference one by one. Consider an example of NPV

calculation.

Imagine Sonal Sharma is the financial manager of Hindustan Seva Product limited (HSPL). HSPL

is considering to set up a plant at Indore. The project staff has developed the following cash flow

forecast for the plant.


P a g e | 60

Figure 2.21: Basic data for Scenario Manager

Now, under this condition suppose Sonal want to know the NPV of the project. She is considering

a WACC of 13%. NPV is the net present value of the project which is determined by ∑PV of Cash

Inflows-Initial Investment. ∑PV of Investment is determined by PV of annuity of net cash inflows

of Rs 50 million. PV of annuity is determined by PV function in MS Excel.

=Rs 271.3122 million.

NPV=271.3122-250=Rs 21.3122 million.

Figure 2.22: NPV calculation for Scenario Manager

Now she wants to analyze these data under three scenarios, impacting it effect on NPV.

Figure 2.23: Different scenario for Scenario Manager

Instead of observing them individually through Scenario Manager Sonal can observe all three

behavior at one moment. Before working on Scenario Manager naming of cells should be done as

it will help during working.


P a g e | 61

Figure 2.24: Naming a cell

Spacing is not allowed during naming, space between the words is to be connected by underscore.

If we do not put underscore then MS Excel would show error.

Figure 2.25: Error while naming cells

In order to start working on Scenario Manager, first select all the required cells, then go to

Data<<What If Analysis<<Scenario Manager<<Add<<Mention the name of Scenario( suppose it


P a g e | 62

Pessimistic) When clicked on Add, the window will come which will ask for adding scenario,

mention the name of scenario and put necessary comments and then press ok.

Figure 2.26: Scenario Manager building

Now a dialogue box will open which will ask for necessary entry to be made for the particular

scenario.

Figure 2.27: Scenario building for Scenario Manager-working on scenario


P a g e | 63

Like this fill the data for each scenario. So, created 3 scenario as mentioned by requirement of

Sonal.

Figure 2.28 building for Scenario Manager-observing scenarios

Now by going to any scenario, just click on show, it will highlight the required scenario. To see

all of them together, click on Summary. After clicking on Summary, the Excel will ask for the

destination for the scenario summary. For that highlight a cell where summary need to be

presented. Result cell will be the cell on the impact need to be felt. In this case the result cell will

be the cell on NPV.


P a g e | 64

Figure 2.29: Scenario building for Scenario Manager-result

The result will be like this.


P a g e | 65

Figure 2.30: Scenario building for Scenario Manager-result

2.4 Solver in MS Excel

Optimizing values in an Excel spreadsheet to meet a given objective can be a tough process.

Fortunately, Microsoft Office, solver, a numerical optimization add-in is there to assist in this task.

To install Solver in a system, please go to File Command (MS Excel 2010, MS Excel 2013) or

Office Ribbon button in MS Excel 2007, there go to Excel Options, then Add-Ins and there install

Solver. It will get highlight under Data command in MS Excel.


P a g e | 66

Figure 2.31: Finding Solver in MS Excel

Once we have Solver we can talk about Optimization. Let try to understand the application of

Solver by taking an example. Assume there is company called Galaxy Limited manufacturing two

toy models-Spider Man and Krrish. The Manager of the company want to maximize the production

per dozen per week. Profit on 1 dozen of Spider Man per week is 8$ while the profit on Krrish per

week per dozen is 5$. During production the following constraint are faced by Management.

Constraints are:-

a. Resources are limited to 1000 pounds of plastic as a raw material.

b. 40 hour of production time per week

c. Total production in a week cannot exceed 700 dozens

d. Number of dozens of Spider Man cannot exceed the number of dozens of Krrish by 350

Necessary input considerations are- Spider Man requires 2 pounds of plastic and 3 minute of labor

per dozen while Krrish require 1 pound of plastic and 4 minute of labor per dozen.


P a g e | 67

While solving problems on Linear Programming, first thing what need to define is decision

variables. Here considering the cases, 2 decision variables can be defined X and Y,

Where, X= weekly production level of Spider Man in dozens,

Y=weekly production level of Krrish in dozens.

Objective of any firm is to maximize the profit or minimize the costs. Since in this case the per

dozen profit is mentioned for both products so objective function would be defined as

Objective Function will be= Max=8X + 5Y (Weekly profit)

Constraint can be written mathematically subject to

2X + 1Y<=1000 (Plastic)

3X + 4Y<=2400 (Production Time)

X + Y <= 700 (Total production)

X -Y <=350 (Mix)

Where non negativity restriction are Xj> = 0, j = 1,2 (Non negativity)

This is Linear Programming Approach. This can be solved by Graphical method or by Simplex

Method. In MS Excel this can be solved by Solver function. Consider any value of X and Y, here

in MS Excel assumed value of X=2, Y=1.


P a g e | 68

Figure 2.32: LPP working in MS Excel

By considering the value of X=2, Y=1, write all the equations in some particular cell.

Figure 2.33: Putting constraint under LPP Model

Once written all the equations in a cell, open a Solver from Data in MS Excel. Once Solver get

open, set the objective of a cell as maxima, if cost was mentioned then minima have to get select.

Then in option in Solver where to insert changing cells, select the cells where assumed values of

X and Y was put, then select all constraints specifying limitation.


P a g e | 69

Figure 2.34: Adding constraint in MS Excel-Solver


P a g e | 70

Figure 2.35: Data Entry in MS Excel-Solver

Once all details get filled then click on Solve. Click on ok. The optimal solution can be generated.


P a g e | 71

Figure 2.36: Solver-result

Figure 2.37: Framework of LPP Model

2.5 Summary


P a g e | 72

1. Sensitivity Analysis is the study of how the uncertainty or deviation in the output of

mathematical model can impacts the different sources of uncertainty in the inputs

2. The process involves various ways of changing input variables of the model to see the

impact on output variables.

3. Sensitivity Analysis can be done with Goal Seek, Solver, Scenario Manager, Data Table

4. Goal Seek helps to understand the relationship between input variables with the output

variable where one input variable can be change and it impact on final outcome can be

realized

5. For observing the change in multiple inputs on the output variable, Solver is used where

the sum total of all change on the final value can be realized

6. By defining the value of output variable the impact on any input variable can be observe

through Goal Seek

7. MS Solver is available in Data tab in MS Excel. If not visible it can be install through Excel

Add-ins available in Excel Options

8. Through Solver objective function can be define and it can be set to any optimal value or

maximal or minimal. When the objective is the maximization of profit or revenue, it is set

at maxima while when the objective is minimization of cost, it is set at minimal

9. Objective function is define in the term of decision variable and on which constraint are

written with non negativity restriction. Constraints are mentioned with inequality

10. MS Solver solves scenario mentioned in Linear Programming format which can be solve

mathematically through Graphical Method or through Simplex Method. Graphical Method

can only work for 2 decision variable while through Solver multiple variables can be solved

11. Suppose I want to buy a house in Bangalore but keeping all my constraint and obligation

want to find out what would be the price of house I should look in market to buy. In order

to find the answer of this question I can use Goal Seek or Solver. Mathematically I can

solve this situation by keeping price of house as x then I will find out how much loan I can

take from bank, depending upon my down payment as loan taken=x-down payment.


P a g e | 73

Considering the time period and rate of loan financing the EMI can be determined through

Present Value of Annuity calculation

12. In MS Excel the same can be solved where in price of house any number can be taken

which MS Excel will automatically adjust when Goal Seek command is applied. x cannot

be considered as in MS Excel because in MS Excel x is consider as a character and any

mathematical calculation cannot be performed later on. EMI can be determined in MS

Excel through PMT function. Then Goal Seek can be applied by equating the value of EMI

at x price of loan to desired value of EMI

13.

14. Through Goal Seek and Solver relationship between decision variables and objective

variable can be establish while in order to understand the impact on objective variable with

a change of one particular variable again and again can be observe simultaneously by using

data table.

15. Data table helps to see the impact of volatility in one decision variable on the outcome.

Data table can be one way data table or two way data table. In one way data table impact

of one decision variable on the output is observe while in two way data table, two variables

changing horizontally and vertically can be observe simultaneously.

16.


P a g e | 74

17.

18. Scenario Manager in MS Excel helps us to see different perspective of a same event at

same moment instead of changing frame of reference one by one.

19. In order to start working on Scenario Manager, select the cells on which this application

want to apply, then in data tab<<what-if analysis<<scenario manager can be selected, then

click on add and mention different scenarios

20.


Two Marks Questions

1. What is Sensitivity Analysis?

2. How data table helps in what-if analysis?

3. How data can be edited inside data table?

4. What is the difference between one way data table and two way data table?


P a g e | 75

5. What is Goal Seek?

6. What is Scenario Manager?

7. What is Solver?


1. How Financial Planning can be discussed through data table and goal seek?

2. Explain the application of Scenario Manager in MS Excel?

3. How Linear Programming problems can be solved in MS Excel?

Ten Marks Questions

1. A paper mill produces two grades of paper namely x and y. Because of raw material

restrictions, it cannot produce more than 400 tons of grade x and 300 tons of grade y in

a week. There are 160 production hours in a week. It requires 0.2 and 0.4 hours to

produce a ton of products x and y respectively with a corresponding profit of RS 200

and Rs 500 per ton. Formulate the above as LPP to maximize the profit and find the

optimum product mix. Solve this through Solver.

2. A furniture company manufactures desks and chairs. There are four departments

namely carpentry, upholstery, painting and varnishing with capacities as given below:

Assuming that raw material are available in adequate quantities and the manufacturer

wishes to know how many desks and chairs he should produce. He enjoys a good


P a g e | 76

market share and contribution from desk is Rs 40 and from chair is Rs 25. Solve it

through Solver.

2.7 References

1. Pandey I.M (2003) Financial Management, Vikas Publishing House-New Delhi

2. Tija S. J (2004) Building Financial Models- A guide to creating and interpreting

Financial Statements

3. Beninga S. (2008) Financial Modeling-3rd Edition

Websites:

1. What If Analysis in Excel-Understanding the use of Goal Seek, Solver, Scenario

Manager- last retrieved on 18/11/2014 from http://www.excel-easy.com/data-

analysis/what-if-analysis.html

2. What If Analysis in Excel-Use of data table, Goal Seek, Scenarios- last retrieved on

18/11/2014 from-http://office.microsoft.com/en-in/excel-help/introduction-to-what-

if-analysis-HA010243164.aspx

Video Links:

1. Codible (25 Aug 2012) How to use Excel Data Table for Financial Planning-

viewed on 18/11/2014- https://www.youtube.com/watch?v=Wcmd0jO1Ngs

2. Aldo Mencaraglia (17 June 2012) How to use Goal Seek Function in Excel-

viewed on 18/11/2014- http://www.youtube.com/watch?v=fcKCUDyF73Y

3. Danny Rocks (21 September 2012) How to use Solver tool in MS Excel-

viewed on 18/11/2014-http://www.youtube.com/watch?v=K4QkLA3sT1o

4. Piyesh Shah (28 Nov 2012) Linear Programming with Excel Solver- viewed on

18/11/2014 https://www.youtube.com/watch?v=RicajFzoenk

http://www.excel-easy.com/data-analysis/what-if-analysis.html

http://www.excel-easy.com/data-analysis/what-if-analysis.html

http://office.microsoft.com/en-in/excel-help/introduction-to-what-if-analysis-HA010243164.aspx

http://office.microsoft.com/en-in/excel-help/introduction-to-what-if-analysis-HA010243164.aspx

https://www.youtube.com/watch?v=Wcmd0jO1Ngs

http://www.youtube.com/watch?v=fcKCUDyF73Y

http://www.youtube.com/watch?v=K4QkLA3sT1o

https://www.youtube.com/watch?v=RicajFzoenk


P a g e | 77

Module III: Simulation Using Excel.


P a g e | 78

Module III: Simulation Using Excel.

Contents

3.1 Objectives-Simulation using MS Excel

3.2 Introduction to Simulation

3.2.1 Application of Rand(), Rand between, Random Number Generation

3.3 Monte Carlo Simulation using Excel-Determination of Pi

3.4 Simulation of Brownian Motion

3.5 Monte Carlo Simulation-Stock-TCS

3.6 Summary

3.7 Questions to discuss

3.8 Problems to Practice

3.9 References

3.1 Objective-Simulation


Understand the importance of simulation

Application of Random Number in Statistics, Finance

Working on Random Number to understand the derivation of Pi, Brownian Motion

Application of Historical Price concept in conjunction with What If Analysis to understand

the derivation of stock prediction.


P a g e | 79

3.2 Introduction-SIMULATION

Prediction of uncertainty around a decision is very important. Either consider a smallest decision

of where to send kid for studies or big decision like what specialization should I chose after class

X, possibility of outcome is very tough to determine as outcome of every decision depends on lots

of factors. Now consider the decision of investment on Stock Market where objective is to predict

the next movement on a stock or a market where investors use Technical Analysis, Fundamental

Analysis or to observe the movement in Derivative Market. There are numerous tools and software

but predicting market is impossible as it depends on multiple scenario and predicting scenario may

be possible but the probability that each scenario that will impact the next movement is impossible.

Investment Banks around the world use to work on Algorithmic Trading where software in order

to calculate the impact of mood or sentiment of trader analyze the Facebook, Twitter and other

social networking sites. Like this multiple cases Simulation Model helps a lot. In order to work on

Simulation Model which would be replica of situation need to be create. Then testing this model

under multiple cases leads to the possibility of different outcomes.

Simulation is done in Excel using Random Numbers. Rand() is the function which can determine

the Random Numbers between 0 to 1.

Suppose the objective is to determine 10 Random Numbers between 10,000 to 25,000 then Rand

between function can be used. It will randomly generate a number between the given condition.

Every time any changes be made in the worksheet where Randbetween or Rand command is used,

MS Excel will generate a random number. In order to make the number generated constant or free

from formula, paste special+value can be done or a combination short cut keys (Alt+E+S+V)


P a g e | 80

Figure 3.1: Showing Rand between function in MS Excel

Random Numbers with specific conditions can be generated by Random Number Generation

present in Data Analysis under Data Ribbon. If not installed then go to File (MS Excel 2010-2013)

or Office ribbon button in MS Excel 2007 and then Excel Options then Add Ins then Analysis took

pack then under Manage. Click on Go,

Figure 3.2: Installing Analysis Tool Pack

A window will open.


P a g e | 81

Figure 3.3: Add-Ins-Analysis Took Pack

Select Analysis Tool Pak and Solver Add-In and press ok. Then it get visible under Data Analysis.

Figure 3.4: Data Analysis


P a g e | 82

Click on Random Number Generation under Data Analysis to generate Random Numbers

specifying conditions.

Figure 3.5: Random Number Generation-MS Excel

Under this Random Number Generation Window, based on the objective the number of variables

and number of Random Numbers can be inserted under specifying the conditions under Normal,

Binomial, Bernoulli, Poisson, Discrete. If click on Normal Distribution, then mean and standard

deviation of required distribution need to be specify, where for Binomial p-value, while for

Binomial distribution p-value and number of trails etc. Then Output Option can be specified where

the result can be generated in new worksheet or in same worksheet. For example if I like to create

Normal Distribution pattern of 5 variables under that 10 Random Numbers each having mean of

66 and standard deviation of 70 then the output would be like this.


P a g e | 83

Figure 3.6: Normal Distribution-Data Analysis

Let try to create a Simulation Model for Amit Hotel which is near Bangalore International Airport,

which has 40 rooms available for boarding but it can make booking up to 45. On any given day

the hotel does not have bookings less than 36 nor more than 45. Each of the bookings have the

equal probability of occurrence. Hotel also has to accommodate passengers who had the

cancellation at the airport. The cancellation at the airport has the distribution as follows:-

Now the average number of booking on any given day can be calculated as Total Booking=Hotel

Booking+ Cancellations. And in order to determine the percentage of day when the hotel is

overbooked can be determined as by summing up the total number of days when hotel is

overbooked and dividing it by total number of days used in simulation. As the simulation can be

done on MS Excel so let highlight the assumptions mathematically. Then lower limit and upper


P a g e | 84

limit can be specified. Lower limit for number of reservation of 36 would be 0 while the upper

limit would be cumulative frequency. Like this others lower and upper limits for other variables

can be figure out.

Figure 3.7: Working on Business Simulation-Hotel Example

Like this, Figure for cancellation Figure can also be determined.


Once the data of Reservation and Cancellation is present then Simulation Model can be generated.

In order to work on Simulation Model, let assume the total number of days. Suppose I have taken

14 days. More the number of days taken more accurate answer can be generated. Then a random

number is allotted to each days by using RAND() function. Then relationship between the random

number generated with associated Reservation Figure can be determined by using VLOOKUP

function of MS Excel.


P a g e | 85


Once the Reservation based on Random Numbers is generated then in similar manner Cancellation

can also be determined by using Vlookup function. Once the Cancellation is determined, then total

reservation can be determined by adding reservation with cancellation.


P a g e | 86


Like this by changing Random numbers different scenario can be generated. In order to determine

the number the days the Hotel get overbooked, IF function can be used.


P a g e | 87



P a g e | 88


3.3 Monte Carlo Simulation- Determination of Pi(π)

Rand () is the function through which it can be determined Random Variables between 0 to 1. In

order to determine the value between -1 to +1, the formula can be =1-2 x Rand (). In MS Excel if

this formula is used, it will generate random numbers between -1 to +1. Plot this representation of

1000 variables in x-y scatter diagram. Rectangular representation can be obtained having

length=breadth=2.


P a g e | 89

Figure 3.13: Determination of Pi: Monte Carlo Simulation

Now Pi (π)=(circumference of circle)/(diameter of circle), now values of random variables can be

used to set up the equation of circle. Equation of circle=𝑥2 + 𝑦2 = 𝑟2. Here consider a circle which

is imposed over the rectangle having a radius of 1. So, the equation will be 𝑥2 + 𝑦2 = 1. Now

consider (x,y) is any point on the circle, where mid point of circle is (0,0) whose values can be

determined by considering random variables. Then by using IF function coordinates of circles can

be defined, like abscissa or ordinate of associated x or y value, where only those points are selected

which are within the circle while rest by using IF command made 0.


P a g e | 90

Figure 3.14: Calculation of Pi-Random Variables

Now the area of circle and area of rectangle can be determined by using IF function. Area of circle

is determined by points which are below circle horizon, while all the point are on the part of area

of rectangle. Area of circle is determined by counting the total number of points satisfying the

condition of Equation of Circle. So, value of π=𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒

𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 where it is multiplied by 4 as

rectangle being Standard rectangle having area of 4 . Value so obtained is 3.132 which is make

more realistic if more data is taken.

3.4 Simulation of Brownian Motion

Brownian Motion is the random motion of the particle suspended in the fluid resulting from the

collision with the quick atoms or molecules in a gas or liquid where the relative velocity of particle

is directly proportional to square root of temperature. The application of Brownian Motion is

relevant study of Random Walk Hypothesis on Stocks.


P a g e | 91

In order to work on Brownian Motion in MS Excel Rand () is used where to derive the value

between -1 to +1 , the formula which is used is 1-2 x Rand (). Suppose there are two variables

called x and y. Relative change is x and y is measured as dx and dy where both imagine at point

0. Then through Simulation their relative change can be determined where each step the change

will be, 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑥𝑡ℎ 𝑠𝑡𝑒𝑝 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 (𝑥 − 1)𝑡ℎ 𝑡𝑒𝑟𝑚 +

𝑑𝑥( 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑥𝑡ℎ 𝑠𝑡𝑒𝑝). Based on the outcome obtained, the result can be plotted in

xy scatter diagram.

Figure 3.15: Working on Brownian Motion

Since the mechanism works on Random Variables, so my clicking enter the whole mechanism can

be changed and the output will be


P a g e | 92

Figure 3.16: Simulation of Variables in Brownian Motion

This led the foundation of Random Walk Hypothesis which state that future movement of stocks

can never be identified. Although Albert Einstein study on Particle Theory can help to study this

movement. Now the concept of Brownian Motion can be applied on multiple particles together.

Suppose there are 100 particles, each at moment, t=0 showing a position assume as (0,0) while

with the time period will show Random Walk Hypothesis which can be measured through

Simulation by using Rand () function where movement of each particle at each step will follow

the formula, 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑥𝑡ℎ 𝑠𝑡𝑒𝑝 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 (𝑥 − 1)𝑡ℎ 𝑡𝑒𝑟𝑚 +

𝑑𝑥( 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑥𝑡ℎ 𝑠𝑡𝑒𝑝). After the movement at each time period when scatter diagram

is plotted, the moment of randomness can be observed.


P a g e | 93

Figure 3.17: Showing Brownian Motion at different time periods


P a g e | 94

Figure 3.18: Diagram Representation-Showing Brownian Motion at different time periods

3.5 Monte Carlo Simulation-Stock-TCS

Monte Carlo Simulation can be applied on Stock Market. Considering the return 3 month time

period of TCS, average return and standard deviation can be determined and on applying Monte

Carlo Simulation different possibility of the value of money thinking for investment can be

determined. Assume Salman Khan looking for investment planned to put Rs 1 lakh upfront on

TCS, the best IT stock. Every year he is planning to put Rs 100,000. Historical data about TCS

can be downloaded from www.nseindia.com. Then average return and standard deviation of return

is calculated, then assuming the return on stock follows normal distribution pattern, by using

norminv and rand() formula in excel, the random return is determined and then on based on random

return determined the ending value of investment is determined.

http://www.nseindia.com/


P a g e | 95

Figure 3.18: Working on Monte Carlo Simulation-TCS

After determination of random return , the value of investment at the end of year is determined.

Figure 3.19: Working on Monte Carlo Simulation-TCS


P a g e | 96

By following 1 simulation model , at the end of 25 year if initially Salman Khan start with 1 lakh

Rs and every year if he put annuity of 100000 Rs he will get 24, 23, 945 Rs. By using Data Figure,

multiple scenario can be run together to get better understanding of given experiment.


P a g e | 97

Figure 3.20: Using Data Figure on working on Monte Carlo Simulation-TCS


P a g e | 98

Figure 3.21: Simulation Iteration-TCS

Once the outcome come , based on the input the data can be summarized in the form of Median,

Average, Percentile etc.


P a g e | 99

Figure 3.22: Outcome of Simulation Model on TCS

5% percentile here means that there is 95% chance that at the end of 25 year if I continue investing

1 lakh rupees every year starting 1 lakh rupees now on a stock called TCS there is 95% chance

that I get value more than 23, 99,202 Rs at the end of 25 years.

Statistical Information about the return of the stock can be determined by using Descriptive

Statistics function available in Data Analysis.


P a g e | 100

Figure 3.23: Statistical Analysis on TCS after Monte Carlo Simulation


P a g e | 101

Input Range would be the total return figure about the stock, summary statistics would give all

required information.

Figure 3.24: Outcome-Statistical Analysis on TCS after Monte Carlo Simulation

Returns are negatively skewed and distribution is platykurtic. Normal Distribution can be plotted

by using Data Analysis-Histogram.

Figure 3.25: Data Analysis-Analysis Tool Pak


P a g e | 102

Figure 3.26: Working under Histogram

Input Range would be the return on the stock while in Output Option Cumulative Percentage

should be selected.

Figure 3.27: Outcome-Histogram of Data Analysis


P a g e | 103

Now a graph can be plotted signifying the normal distribution pattern keeping Cumulative

distribution data on x-axis and Frequency is y-axis.

Figure 3.28: Frequency Distribution-Normal Distribution

Similarly the logic of Monte Carlo can be applied on pricing of stock to identify the likely price

of the stock in future. Consider the same stock –TCS. Price of stock as per 27th August 2014 is Rs

2549.55. 3 month volatility is 1.4189%. Daily Volatility can be determined ==3 𝑚𝑜𝑛𝑡ℎ 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑦

√90.

Daily Volatility would be 0.15%. Likely future price will be determined by using NORMINV

function in MS Excel.


P a g e | 104

Figure 3.29: Use of Norminv function to calculate the return

According to Random Walk Hypothesis, the expected change per day is to be 0 where probability

is determined through RAND().


P a g e | 105

Figure 3.30: Average return on stock based on Simulation

One Simulation Model cannot help, by using Data Figure multiple models can be created then it

analyzing them makes sense.

Each outcome of price is the simulated outcome of change after 1000 days. Then Statistical

analysis can be done on this by determining the average, Median, Standard Deviation, Percentile

on these stock price change.


P a g e | 106

3.6 Summary

1. Simulation is the imitation of the operation of a real-world process or system over time.

2. Simulation can be tested on a model which represent key characteristics or behavior of

selected physical or abstract system or process.

3. Simulation can be used to show the eventual real effects of alternative conditions and

courses of action. Simulation is also used when the real system cannot be engaged, because

it may not be accessible, or it may be dangerous or unaccepFigure to engage, or it is being

designed but not yet built, or it may simply not exist.

4. To work on Simulation, we need Random Numbers. Random Numbers can be generated

by using Rand(), Randbetween and through Random Number Generation. Rand() generates

random numbers between 0 and 1. Randbetween creates random numbers between any two

specified limit.

5.

6. Monte Carlo Simulation let us to see all possible outcomes of a decision and work on

accessing the risks, so that better decision making situation can be create for the outcome.

7. Monte Carlo performs risk analysis by building models of possible outcomes by

substituting a range of values-probability distribution, it then calculates results over and

over each time using different sets of random variables.

8. Pi value can be determine through Monte Carlo Simulation. Rand() generates a value

between 0 and 1, if a function = 1 − 2 × 𝑅𝑎𝑛𝑑( ) 𝑖𝑠 𝑢𝑠𝑒𝑑, we will get a random number


P a g e | 107

between -1 to +1. If more than 1000 random numbers are generated by using this formula

for two variables and if it is plotted on scatter diagram, a rectangular representation arises

9. Pi= (𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒)/(𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒), now values of random variables

can be use to set the equation of circle. Equation of circle=𝑥2 + 𝑦2 = 𝑟2. Let try to impose

a circle over the rectangle having radius=1. The rectangular representation obtained by 1-

2*Rand() is having length=breath=2

10.

11. Circle can be imposed over rectangular random representation by using IF function in MS

Excel. As we know the equation of circle=𝑥2 + 𝑦2 = 𝑟2. Consider a point inside the circle

having coordinate (x,y) where distance of this point from centre (0,0) so, the given equation

is 𝑥2 + 𝑦2 = 1

12. Area for the region for which the values less than 1 is considered when 𝑥2 + 𝑦2 < 1, that

value would not be considered turn to be 0. (𝑥2 + 𝑦2 > 1)

13. Value of π=𝑎𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒

𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 where it is multiplied by 4 as rectangle being Standard

rectangle having area of 4 . Value so obtained is 3.132 which is make more realistic if more

data is taken.

14. Brownian Motion is the random motion of the particle suspended in the fluid resulting from

the collision with the quick atoms or molecules in a gas or liquid where the relative velocity

of particle is directly proportional to square root of temperature. The application of

Brownian Motion is relevant study of Random Walk Hypothesis on Stocks.


P a g e | 108

15. In order to work on Brownian Motion in MS Excel Rand () is used where to derive the

value between -1 to +1 , the formula which is used is 1-2 x Rand ().

16. Suppose there are two variables called x and y. Relative change is x and y is measured as

dx and dy where both imagine at point 0. Then through Simulation their relative change

can be determined where each step the change will be, 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑥𝑡ℎ 𝑠𝑡𝑒𝑝 =

𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 (𝑥 − 1)𝑡ℎ 𝑡𝑒𝑟𝑚 + 𝑑𝑥( 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑎𝑡 𝑥𝑡ℎ 𝑠𝑡𝑒𝑝)

17. In order to work on Monte Carlo Simulation on Stocks, NORMINV function is used.

NORMINV function in MS Excel will generate cumulative normal distribution value for a

data having specified mean and standard deviation under certain probability factor.

18. Probability factor will be here generated through RAND() which will generate a random

number between 0 to 1. Daily Mean=0, Daily standard

deviation=𝑛−𝑝𝑒𝑟𝑖𝑜𝑑 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

√𝑛

19. Random Return on the stock can be calculated by NORMINV function. Each day

movement on the stock will be calculate by formula=

ℎ𝑖𝑠𝑡𝑜𝑟𝑖𝑐𝑎𝑙 𝑝𝑟𝑖𝑐𝑒 × (1 + 𝑛𝑜𝑟𝑚𝑖𝑛𝑣(𝑟𝑎𝑛𝑑( ), 0, (𝑛 − 𝑝𝑒𝑟𝑖𝑜𝑑 𝜎

√𝑛))

20. Once the movement is created and it average can be taken. Then through one way data

Figure similar values can be created which helps to analyze under multiple scenario.


Two Marks Questions

1. What is Simulation?

2. How Simulation helps in business decision making?

3. How Rand() works?


4. Using Monte Carlo Simulation, demonstrate the calculation of Pi?


P a g e | 109

5. Using Monte Carlo Simulation, demonstrate the Brownian Motion?

6. How Monte Carlo Simulation can be done in MS Excel? Explain with an example?

7. Explain all random number generation tools with examples?

Ten Marks Questions

1. Demonstrate the application of Monte Carlo Simulation on a stock with the statistical tools

calculating the VaR at 95% confidence interval


1. To generate a number between -1 and 1, which formula can be used

a. Rand()

b. 1 − 2 × 𝑅𝑎𝑛𝑑()

c. 2 − 3 × 𝑅𝑎𝑛𝑑()

d. 1 + 2 × −𝑅𝑎𝑛𝑑( )

2. What formula is used to determine daily volatility from annual volatility?

a. 𝑎𝑛𝑛𝑢𝑎𝑙 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦

√252

b. (𝑎𝑛𝑛𝑢𝑎𝑙 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦) × √252

c. (𝑎𝑛𝑛𝑢𝑎𝑙 𝑣𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦) + √252

d. None of These

3. To put a random number between 0 and 1 which function can be used?

a. Rand()

b. Randbetween

c. Random Number Generation

d. All of them

4. Normal Distribution Pattern can be in the form of……………………………….

a. Leptokurtic

b. MesoKurtic

c. Platykurtic


P a g e | 110

d. All of These

5. Descriptive Statistics of a data can be determined through ……………………….

a. Data Figure c. Solver

b. Data Analysis d. Goal Seek

6. To observe the Brownian Motion on a stock to justify the Random Walk Hypothesis,

which statistical representation help?

a. Histogram

b. Scatter Diagram

c. Line Graph

d. Candle Stick Model

7. What is the short cut key to remove formulaes from worked excel document?

a. Ctrl+C, Alt+E+S+V

b. Ctrl+C, Alt+E+S+F

c. Ctrl+C, Alt+E+S+T

d. Ctrl+C, Alt+E+S+N

8. What is the syntax for the VLOOKUP() function?

a. Vlookup(lookup_value,range_lookup,col_index_num, Figure_array)

b. Vlookup(lookup_value, col_index_num, Figure_array,range_lookup,)

c. Vlookup(lookup_value, Figure_array range_lookup,col_index_num,)

d. Vlookup(lookup_value,Figure_array1,Figure_array2,range_lookup)

9. To use the vlookup function, in the Figure, which column should the lookup_value be

located in?

a. In the left most column

b. In the right most column

c. In the middle column

d. Anywhere

10. To make the content inside the data Figure static so that the change in content in that

cell does not impact the content of other cells. What should we do?

a. Format cell>>Custom>>#,###

b. Format cell>>Custom>>General


P a g e | 111

c. Format cell>>Custom>>0,000,0000

d. Format cell>>Custom>>#,##,0.00(Red)(#,00,#)

Answers

1-a, 2-a, 3-a, 4-d, 5-b, 6-b, 7-a, 8-c, 9-a, 10-b

3.9 References

1. Building Financial Models- A guide to creating and interpreting Financial Statements-

John S.TJIA

2. Pandey I. M, (2003) Financial Management, Vikas Publishing House – New Delhi

3. Financial Modeling-Simon Benninga

Websites:

1. Introduction to Monte Carlo Simulation- http://office.microsoft.com/en-in/excel-

help/introduction-to-monte-carlo-simulation-HA001111893.aspx

2. Random Number in Excel-

http://spreadsheets.about.com/od/excelfunctions/qt/080218_randbetw.htm

Video Links:

1. Monte Carlo Simulation in Excel-Dr Gerard Verschuuren-

http://www.youtube.com/watch?v=UeGncSFijUM

2. Basic Monte Carlo Simulation of a Stock Portfolio-

http://www.youtube.com/watch?v=Q5Fw2IRMjPQ

3. Random Number Generation in MS Excel-Dr Salimian-

http://www.youtube.com/watch?v=rBEMr6CyK7g

http://office.microsoft.com/en-in/excel-help/introduction-to-monte-carlo-simulation-HA001111893.aspx

http://office.microsoft.com/en-in/excel-help/introduction-to-monte-carlo-simulation-HA001111893.aspx

http://www.youtube.com/watch?v=UeGncSFijUM

http://www.youtube.com/watch?v=Q5Fw2IRMjPQ


P a g e | 112

Module IV: Accounting in Excel


P a g e | 113

Module IV: Accounting in Excel

Contents

4.1 Objectives-Excel in Accounting

4.2 Introduction of Accounting

4.2.1 Understanding Income Statement, Balance Sheet, Cash Flow Statement

4.3 Common Size Financial Statement

4.4 Income Statement Forecasting-TCS-2015

4.5 Balance Sheet Forecasting-TCS-2015

4.6 Analysis of Financial Statement

4.6.1 Margin Ratios-Gross Profit Margin, Operating Profit Margin, Net Profit Margin

4.6.2 Capital Gearing Ratio-Interest Coverage Ratio, PBT/Interest, Debt/Equity Ratio

4.6.3 Price Earning Ratio, Price Book Value Ratio

4.6.4 Return on Investment, Return on Equity

4.7 Summary

4.8 Questions to Practice

4.9 Problems for Practice

4.10 References

4.1 Objective of Excel in Accounting


Framework of construction of Financial Statement in MS Excel


P a g e | 114

Establish the trend of financial figure movement of Y on Y basis

Analyze Financial Statement through MS Excel

Forecast Financial Statement based on trend analysis

Excel in Accounting

4.2 Introduction of Accounting

Accounting is the language of business which measures the business economic performance. It is

the part of the information system of a business enterprise. It provides financial information

concerning the activities of an enterprise to a diverse group of people such as shareholders,

managers, creditors, tax authorities etc. On the basis of purpose the accounting is used, accounting

is used, it is divided into three parts-financial accounting, cost accounting and management

accounting. Financial Accounting is mainly concerned with recording business transactions in the

book of account for the purpose of presenting final accounts to management, shareholders and tax

authorities etc. Cost Accounting is the techniques and processes of ascertaining costs. Management

accounting focuses on the measurement, analysis and reporting of information for internal use by

management.

Income Statement or Profit and Loss statement is the financial statement of company show

company’s revenue and expenses during a particular period. It indicates how revenues get

transformed into net income. It is the summary of how business incurs its revenue and expenses

through both operating and non operating activities.

Balance Sheet is the snapshot of company financial condition. A standard balance sheet has three

parts-assets, liabilities, ownership equity. Total Asset in a balance sheet is equal to liabilities plus

owner’s equity. Assets can be Current Asset- Cash and cash equivalent, Account Receivable, Pre-

paid Expenses. Non Current Asset-Property, Plant and Equipment, Investment Property like Real

Estates, Intangible Assets, Biological Assets. Liabilities include Account Payable, Provision for

warrants, Financial Liabilities like Promissory Notes and Corporate Bonds, Deferred Tax

Liabilities and Deferred Tax Assets, Unearned Revenue for the services paid by customers but not

yet provided. Equity includes issued capital and reserves attributable to equity holder of parent


P a g e | 115

company, non controlling interest in equity. Following disclosures can be allowed- number of

shares authorized, issued, fully paid, par value of shares, Reconciliation of share value at the

beginning and end of period, shares reserved for issuance under options and contracts etc.

Cash Flow Statement is the financial statement that shows how changes in balance sheet accounts

and income affect cash and cash equivalent and it can be studied under operating, financial and

investing activities. Cash Flow Statement concerned with the flow of cash in and out of business.

Balance Sheet and Profit and Loss Statement reflects accrual basis accounting used by firms while

Cash Flow Statement which reflects liquidity of company talks about cash and cash equivalent.

Cash flow statement under operating activities includes receipt from the sale of goods and services,

Interest receipt, receipt and payable to employee/supplier. In order to determine cash flow from

operating activities, the following enteries are adjusted to net profit like non cash expenses like

depreciation and amortization, deferred tax, dividend received, any gain or loss associated with

sale of non current asset. Cash Flow from investing activities includes purchase or sale of an asset

like land, building, marketable securities etc , loans made to suppliers or received from customers,

payment related to mergers and acquisitions. While cash flow from financial activities includes

inflow of cash from investors such as banks and shareholders, as well as outflows of cash to

shareholders when dividend is paid, sale or repurchase of company’s stock, payment of dividend

tax, repayment of debt principal including capital lease.

4.3 Common Size Financial Statement

Common Size Financial Statements usually involve the balance sheet and the income statement.

It is simply created to display the line items on a statement as a percentage of one selected or

common figure. Creating common size financial statements makes it easier to analyze a company

over time and compare it with peers. Using common size financial statements helps investors to

spot trends that raw financial statement may not uncover. The common figure for a common size

balance sheet analysis is total assets. Instead of total assets sum of total liabilities and shareholder

equity which is the Capital Employed can also be taken as a common figure in the balance sheet

analysis. The common size strategy from the balance sheet leads insight into firm capital structure

and compare it with rivals. An investor by looking figures analyze and then on that basis conclude

about prospect of company. It is important to add short-term and long-term debt together and


P a g e | 116

compare this amount to total cash on hand in the current assets section. It lets the investor know

how much of a cash cushion is available, or if a firm is dependent on the markets to refinance debt

when it comes due.

The common figure for Income Statement is top line sales. For cash flow items are also expressed

in term of % sales. This can give insight into number of cash flow items including Capital

Expenditure as a percentage of revenue. Debt issuance is another important figure in proportion to

the amount of annual sales. In order to work on Common Size Balance Sheet in Excel Template I

have considered the stock TCS. Mentioned below is the Standalone Balance Sheet of TCS

comparing the financial figures from 2010 to 2014


P a g e | 117

Figure-4.1 Historical Balance Sheet value of TCS

Here, Total Liabilities=Total Debt+ Net Worth

And Net Worth=Total Share Capital+ Capital Reserve+ Revaluation Reserve

Where Total Share Capital= Equity Share Capital+ Share Application Money+ Preference Share

Capital


P a g e | 118

Figure-4.2 Common Size Balance Sheet value of TCS in term of Capital Employed


P a g e | 119

Figure-4.3 Historical Balance Sheet value of TCS

Here, Total Current Assets=Inventories+ Sundry Debtors + Cash and Bank Balance

Total CA, Loans & Advances= Total CA+ Loans & Advances+ Fixed Deposits

Net Current Assets=Total Current Assets-Total CL & Provisions


P a g e | 120

Figure-4.4: Common Size Balance Sheet value of TCS in term of Total Assets


P a g e | 121

Similarly the similar representation can be done for Profit and Loss Statement.


P a g e | 122

Figure-4.6: Common Size P&L value of TCS in term of % of sales


P a g e | 123

In order to work on forecasting, the first step is to identify the next year total income which is the

sum of Net Sales+ Other Income + Stock Adjustments. I assume Stock adjustments and Excise

Duty will remain zero for next year also as they are 0 from last 2 years. If stock adjustments and

Excise Duty arise also they will not impact the forecasting outcome as such as their values very

less. So the next year movement in Total Income will depend on movement of Net Sales and Other

Income. I assume geometric mean to track the movement .

Figure-4.6: Measuring the growth in sales

Figure-4.7: Measuring the growth in sales


P a g e | 124

Next Year Net sales will be probably== 64,672.93 𝑥 (1 + 29.4312%) = 83,742.47399

crores. In order to work on Other Income I considered only last 3 year data as after 2011 there was

significant change in the source of other income and I believe this change will increase in

compounding.

Figure-4.8: Measuring the growth in sales (CAGR Model)

So, the total income for March 2015=3680.7475+ 83, 742.47399=87,423.22145 Crore.

Figure-4.9: Calculation of total income

On the basis of this other accounting figures can be determined. I will take simple average for that.


P a g e | 125

Figure-4.10: Calculating the average of P & L items

Now each Category inputs can be estimated on the basis of % age of total income. Total Income

is already determined.

4.4 Income Statement Forecasting-TCS-March 2015


P a g e | 126


P a g e | 127


P a g e | 128

Figure-4.11: Forecasted FY 2015 accounting data of P&L

4.5 Financial Forecasting-Balance Sheet-TCS

In a Balance Sheet, ∑ of Total Assets= ∑ of total Liabilities, Geometric Mean or Arithmetic Mean

can be used to determine the average of previous movement and on the basis of this, next

movement can be determined.

Figure-4.12: Calculation of CAGR of total liabilities

I assume that the company is not issuing any Preference Share , there Is no revaluation reserve.

Changes can be observed in Equity Share Capital and in Capital Reserve.


P a g e | 129


P a g e | 130

Figure-4.13: Forecasted FY 2015 accounting data of Balance Sheet

Final Consolidated outcome for forecasting is:-


P a g e | 131

Figure-4.14: Forecasted FY 2015 accounting data of Balance Sheet

4.6 Analysis of Financial Statement

Financial Statement Analysis is an important tool to understand the nature the historical

performance by a company. Let understand the company through the perspective of profitability

decision undertaken.

Figure-4.15: Analyzing the calculation of Profit Margin


P a g e | 132

There is no as such differential in movement between Operating Profit Margin and Net Profit

Margin. The differential factor between two is the interest which does not move up significantly

showing company debt value does not change significantly. To prove this historical value of

interest can be taken from P & L account and long term debt can be taken from Balance Sheet.

Figure-4.16: Graph between long term debt and Interest

Since there is there is as such not much differential between operating profit margin and net profit

margin so the factors which leads to volatility in gross profit margin can be analyzed.


P a g e | 133

Figure-4.17: Impact of COGS on Gross Profit

Under Cost of Good Sold, the 4 factors are included:-

1. Raw Material

2. Power and Fuel Cost

3. Employee Cost

4. Other Manufacturing Expenses

Power and Fuel Cost is not significant, probably other three are more significant.

Figure-4.18: Component of COGS

Employee Cost is most important cost factor impacting COGS maximum. Gradually the impact of

non direct expenses can also be highlighted.


P a g e | 134

Liquidity position of the TCS is in better shape as highlight by their Current Ratio and Quick Ratio.

Figure-4.19: Liquidity Ratio across periods

Figure-4.20: Calculation of % of non direct expenses of total expenses

Non Direct Expenses plays a pivotal role in the costing pattern of TCS. Now Debt/Equity Ratio

can be analyzed.


P a g e | 135

Figure-4.21: debt by equity ratio

Similarly, Interest Coverage Ratio can be determined to see the contribution of debt on the profit.

Figure-4.22: Interest Coverage Ratio calculation

Now if I compare Debt/Equity Ratio with PBT/Interest ratio


P a g e | 136

Figure-4.23: Comparison of PBT/Interest and Debt/Equity

Debt/Equity Ratio is keep on increasing while PBT/Interest is volatile where concept on leverage

states that if Return on Investment>Rate of Interest then EPS, ROE goes up significantly. In order

to see the impact of leverage on Return on Investment let find out the relationship.

Figure-4.24: Analyzing ROA, ROE with Rate of Interest

Since always ROI>Rate of interest always so EPS goes up significantly


P a g e | 137

Now, in order to work on Price to Earning Ratio and Price to Book Value ratio, forecasting of the

likely price of TCS stock for March 2015 can be done assuming the growth rate followed in past

will show the similar movement in future.

Figure-4.25: Comparison of PE ratio with Price to Book Value Ratio

If I compare PE ratio with Price to Book Value ratio it seems TCS is too much over valued but

average annual growth rate of 30% justifies this over valuation.


P a g e | 138

4.7 Summary

1. Accounting is the language of business which measures the business economic

performance. It provides financial information concerning the activities of an enterprise to

a diverse group of people such as shareholders, managers, creditors, tax authorities etc

2. Balance Sheet is the snapshot of company financial condition. Standard balance sheet has

three parts-assets, liabilities, ownership equity.

3. Assets can be Current Asset- Cash and cash equivalent, Account Receivable, Pre-paid

Expenses. Non Current Asset-Property, Plant and Equipment, Investment Property like

Real Estates, Intangible Assets, Biological Assets. Liabilities include Account Payable,

Provision for warrants, Financial Liabilities like Promissory Notes and Corporate Bonds,

Deferred Tax Liabilities and Deferred Tax Assets

4. Cash Flow Statement is the financial statement that shows how changes in balance sheet

accounts and income affect cash and cash equivalent and it can be studied under operating,

financial and investing activities

5. Balance Sheet and Profit and Loss Statement reflects accrual basis accounting used by

firms while Cash Flow Statement which reflects liquidity of company talks about cash and

cash equivalent.

6. Cash flow statement under operating activities includes receipt from the sale of goods and

services, Interest receipt, receipt and payable to employee/supplier.

7. Cash flow from financial activities includes inflow of cash from investors such as banks

and shareholders, as well as outflows of cash to shareholders when dividend is paid, sale

or repurchase of company’s stock, payment of dividend tax, repayment of debt principal

including capital lease.

8. Common Size Financial Statement are simply created to display the line items on a

statement as a percentage of one selected or common figure.

9. Using common size financial statements helps investors to spot trends that raw financial

statement may not uncover.

10. The common figure for a common size balance sheet analysis is total assets or Capital

Employed while for Income Statement is Net Sales.


P a g e | 139

11.

12. In order to start working on forecasting of Financial Figures, estimation of next year Total

Liabilities is important

13. Estimation of Total Liabilities is done through Geometric Mean or through Arithmetic

Mean

14. Once the Total Liabilities is estimated, other financial figures can be determined as already

other financial figures were represented as %

15.


P a g e | 140

16. Like the steps followed to calculate Total Liabilities in Source of Funds in Balance Sheet

similarly Net Sales in Profit and Loss statement, Total Assets in Application of Funds is

estimated

17. Through % of net sales or through % of total assets or % of total liabilities other items in

different years can be estimated, then average of them can be done to get a cumulative

figure which when multiplied with forecasted figure mentioned in above point can create

new estimated financial figure.

18. Once all required financial figures is determined, then the forecasted financial statement

can be complete by following basic accounting principles like at last total assets should be

equal to total liabilities, Total Current Assets=Inventories+ Sundry Debtors + Cash and

Bank Balance, Total CA, Loans & Advances= Total CA+ Loans & Advances+ Fixed

Deposits, Net Current Assets=Total Current Assets-Total CL & Provisions

19. Financial Statement Analysis is an important tool to understand the nature the historical

performance by a company. It is process of reviewing and analyzing a company’s financial

statement. It is a process of identifying the financial strengths and weakness of the firm by

establishing the relationships between the items of the balance sheet and the profit and loss

statement

20. Ratio is defined as “ the indicated quotient of two mathematical expressions” , in financial

analysis, a ratio is used as a benchmark for evaluating the financial position and

performance of a firm. Basically all financial ratios are divided into four important

categories:-

a. Liquidity Ratios

b. Leverage Ratios

c. Activity Ratios

d. Profitability Ratios

21. Liquidity Ratio measures the firm’s ability to meet current obligations. Leverage Ratio

shows the proportions of debt and equity in financing the firm’s assets. Activity Ratio

reflects the firm’s efficiency in utilizing its asset. Profitability ratios measures the overall

performance and effectiveness of firm. Liquidity Ratio consist of Current ratio, quick ratio,


P a g e | 141

cash ratio, net working capital ratio. Leverage ratio includes debt ratio debt-equity ratio,

interest coverage ratio. Activity Ratio includes Inventory turnover ratio, Debtor turnover

ratio, Asset Turnover ratio, Current asset turnover ratio, working capital turnover ratio.

Profitability ratio includes gross profit margin, net profit margin, return on investment,

return on equity, price earning ratio


Two Marks Questions

1. What is Accountancy?

2. Why Accountancy is considered as a language of business?

3. What is Balance Sheet?

4. What is Profit and Loss statement?

5. What is the difference between Cash Flow Statement and Fund Flow Statement?

6. What is Common Size Financial Statement?

7. What is difference between ROI and ROE?


1. Explain with steps the process of Financial Forecasting?

2. What is the need of analysis on Financial Statement? How it will help in decision making

before investment in market?

3. How the projection of Income Statement can be done?

4. What interpretation can be observe after looking at leverage ratios of a company?

5. Explain the relevance of Du-Point Analysis?


P a g e | 142

Ten Marks Questions

1. What is Fundamental Analysis? How understanding of Financial Statement help in

Investment decision? What are the tools helps in understanding the financial figures?

Explain with an example?


1. Which among is not the part of liquidity ratio?

a. Current Ratio c. Quick Ratio

b. Activity Turnover Ratio d. Net working capital ratio

2. Which factor create differential in operating profit margin and net profit margin?

a. Change in Interest Rate

b. Change in Sales and administrative expenses

c. Change in Non cash expenses

d. Change in Net Working Capital

3. Which item is not the part of cost of good sold?

a. Raw Material

b. Sales and Administrative Expenses

c. Power and Fuel Cost

d. Employee Cost

4. If the company share price falls, then its P/E ratio and dividend yield will………………..

a. PE ratio and dividend yield both decreases

b. PE ratio decreases, dividend yield no change

c. PE ratio decreases, dividend yield increases

d. Both PE ratio and dividend yield inceases

5. What is the shortcut key of working on Filter?

a. Alt+d+f+f c. Alt+e+f+f

b. Alt+d+e+f d. Alt+f+e+f

6. Net Worth of a company is …………………………

a. Total Share Capital+ Capital Reserve+ Revaluation Reserve


P a g e | 143

b. Total Share Capital+ Capital Reserve

c. Capital Reserve+ Revaluation Reserve

d. None of These

7. Which of the following statements are true in relation to common size statement analysis?

a. It examines the changes over time

b. It may concentrate on gross margin percentage

c. It concentrates on different geographic segments of production

d. It may concentrate on relative size of current assets

8. Which ratios is not use to access the capital gearing of an enterprise?

a. Debt Ratio

b. Long term debt to assets ratio

c. Interest coverage ratio

d. Debt to equity ratio

9. Which of the following are not long term solvency ratio?

a. ROI

b. Interest Coverage Ratio

c. Debt Ratio

d. Long term debt to assets ratio

10. Which of the following is true?

a. An unlevered enterprise has ROE higher than ROTA

b. The more an enterprise relies on debt the more control it has on its finance

c. When the enterprise has a ROE greater than its interest rate, ROTA exceeds ROE

d. None of these

Answers

1-b, 2-a, 3-b, 4-c, 5-a, 6-a, 7-a, 8-b, 9-a, 10-c

4.10 References


P a g e | 144

1. Khan MY Jain PK(2008) Financial Management 3rd Edition Mc Graw Hill Publication-

New Delhi

2. Pandey I.M (2003) Financial Management, Vikas Publishing House-New Delhi

3. Building Financial Models- A guide to creating and interpreting Financial Statements-

John S Tjia

4. Financial Modeling-Simon Benninga

Websites:

1. Financial Forecast Analysis- http://office.microsoft.com/en-in/templates/financial-

forecast-analysis-8-years-TC101877397.aspx

2. How to forecast the Income Statement-

http://financialmodelingtutorial.com/how-to-forecast-income-statement/

3. Analysis of Financial Statement- http://www.slideshare.net/MohdAadil/analysis-of-

financial-statements-12201127

Video Links:

1. Forecasting Financial Statements-Shav Van

http://www.youtube.com/watch?v=hRqchLs4mUc

2. Forecasting Financial Statements-Prakash Kumar-

http://www.youtube.com/watch?v=CXwwjBiWPS0

3. Analysis of Financial Statements- https://www.youtube.com/watch?v=x6dd0IHuC98

http://office.microsoft.com/en-in/templates/financial-forecast-analysis-8-years-TC101877397.aspx

http://office.microsoft.com/en-in/templates/financial-forecast-analysis-8-years-TC101877397.aspx

http://financialmodelingtutorial.com/how-to-forecast-income-statement/

http://www.youtube.com/watch?v=hRqchLs4mUc

https://www.youtube.com/watch?v=x6dd0IHuC98


P a g e | 145

Module V: Excel in Valuation and Portfolio Theory


P a g e | 146

Module V: Excel in Valuation and Portfolio Theory

Contents

5.1 Objectives-Excel in Valuation and Portfolio Theory

5.2 Business Valuation

5.2.1 Approaches on Business Valuation

5.2.2 Discussion on Project Cash Flow

5.2.3 Discussion on Discounted Cash Flow Valuation

5.3 Detailed discussion on FCFE and FCFF items

5.4 Projection of Income Statement

5.5 Understanding Terminal Value of Cash Inflow

5.6 Financial Model-Corporate Valuation

5.7 Risk Analysis on Corporate Valuation

5.8 Excel in Portfolio Management

5.9 Technical Analysis on stock

5.10 Portfolio Optimization using MS Excel-Solver

5.11 Summary

5.12 Question for Practice

5.13 Problems for Practice

5.14 References


P a g e | 147

5.1 Objective-Excel in Valuation and Portfolio Theory


Understand why Business Valuation is so important

What are the different approaches follows to do Business Valuation?

What are the factors on which Project Cash Flows depends?

What are different sources of Project Cash Flows?

How to develop financial models for Corporate Valuation?

Understand different forms of risks involved in Corporate valuation decisions

Represent Portfolio Management applications in MS Excel

5.2 Business Valuation

Business valuation is a series of procedures used to anticipate the economic value of an owner’s

interest in a business. Valuation is used by firm, their professionals to determine the price they are

willing to pay or receive to effect a sale of a business. The technique of hypothetical conditions

based on assumption that the business will continue forever in its current form (going concern).

Valuation is used by Insiders of a firm like CEO, CFO, Operating Manager to identify

opportunities and it help them in decision making. It is used by Investors like Hedge Funds/Pension

Funds, Insurance Company, Retail Investor before investment or to find out appropriate


P a g e | 148

investment opportunity, it is used by Consultants like Investment Bank, Credit Rating Agencies,

Brokerage House to suggest/recommending their investors the ideal source/avenue for investment.

Valuation help firm during Merger and Acquisition, work on defensive strategies against hostile

takeover, assisting during listing, subsequent offering and de-listing etc.

Approaches of Valuation can be:-

1. Macro Analysis

2. Strategic Analysis

3. Retrospective/ Prospective Analysis

Macro Analysis-

Monetary Policy- Process by which government, Central Bank, Monetary Authority of

country controls the supply of money, availability of money

Fiscal Policy- Government policy that attempt to influence the direction of economy

through the changes in Government taxes, Fiscal allowances

Stages of Business Cycle- Recovery, Early Expansion, Late Expansion, Early Recession,

late Recession

Strategic Analysis-

Industry Life Cycle-Pioneering, Rapid Growth, Mature Growth, Stabilization and Market

Maturity, Deceleration of growth and decline

Porter’s Five Forces- Rivalry among the existing competitors, Threat of new entrant,

Threat of Substitute products, Bargaining Power of Buyers, Bargaining power of Supplier

Retrospective Analysis-

Financial Statement Analysis of Company

Understanding the accounting policies-conservative/aggressive


P a g e | 149

Ratio Analysis of the Company-Liquidity, Operating, Risk and Growth

Ratio Comparison with other companies in the industry/sector

Companies for investment can be growth companies, defensive companies, cyclical companies

and speculative companies. Growth Company is where the management has the ability to

consistently select investments or projects which earn higher returns than required by their risk.

Defensive Companies have earnings that are relatively insensitive to downturn in economy.

Cyclinal Companies tends to follow the business cycle. Speculative Companies have assets that

are risky but the assets are potential to generate very large earnings. Valuation is done on

Enterprise scale or of Equity. For Enterprise valuation, valuation of debt is included.

Value of firm is determined by four factors-it capacity to generate cash flows from assets in place,

the expected growth rate of these cash flows, the length of time it will take the firm to reach stable

growth, and the cost of Capital. In discounted cash flow valuation, estimation of value of asset is

determined by discounting back the expected cash flows on the asset at the rate that reflects the

riskiness. In a sense the intrinsic value of an asset is determined. The value of any asset is a function

of the cash flows generated by that asset, the life of asset, the expected growth in the cash flows,

the riskiness associated with them. In other word, it is present value of the expected cash flows on

the asset. Value of Asset==∑𝑃𝑉 𝑜𝑓 𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠

(1+𝑊𝐴𝐶𝐶)𝑛

Free Cash Flow to the Firm=EBIT(1-tax%)+Depreciation-Capital Expenditure-∆ in Noncash

Working Capital.

Discounted Cash Flow analysis show us the expected value of business by the reference to future

cash flows. Discounted cash flow analysis involves estimating the present value of future cash

flows that business being valued is expected to generate. DCF analysis requires high quality

historic and projected financial information on the business. The quality of financial information

is crucial to DCF valuation-“garbage in…..garbage out”.

The particular information required will depend on the nature of company being valued but at the

most basic level, detailed assumptions over the projected period are required for:

Turnover

Operating Margins


P a g e | 150

Interest Charges

Taxation Charges

Depreciation Charges

Capital Expenditure

Working Capital Movements

There is danger of over generalizing in preparing cash flow forecasts-assuming a constant growth

rate after first couple of years. It is important to question the forecast and consider all cyclical,

industry specific and other general or macroeconomic influences. Rather than discounting the cash

flows indefinitely into the future, a terminal value based on company long term growth rate

(perpetual growth rate methodology) or a multiple of final year earnings or cash flows ( exit

multiple methodology), is usually assumed after a period of say five to ten years. The terminal

value represent a high proportion of the overall valuation of business (particularly in a company

pursuing long term growth and investing heavily during the forecast period).

A DCF valuation is only as accurate as the assumptions/ key sensitiveness underlying it and it is

easiest way to establish a margin of error as a principal assumption.

In theory, the choice of discount rate or assessment of internal rate of return will depend critically

on the cost of debt and market risk premium in the country of target, the share price volatility of

the target and the level of debt of an optimal capital structure. However a purchaser would have to

consider other issues, such as his funding cost and value of business to it.


P a g e | 151

Figure 5.1: Discussion on Cash Flows and different ways to understand

DCF valuation focuses on the cash flows generated by one part of the business – the Operating

Assets.

A business generates cash through its daily operations of supplying and selling goods or services.

Some of the cash has to go back into the business to renew fixed assets and support working capital.

If the business is doing well, it should generate cash over and above these requirements. Any extra

cash is free to go to the debt and equity holders. The extra cash is known as Free Cash Flows.

Formulas of FCFF are as per below.

FCFF = NI + D&A – change in WC + Interest * (1-tax rate) – Capex

Projections Project free cash flows over the forecast period (5 - ) 10 years Project enough years to provide for achieving a normalized cash flows

Terminal Value Trading multiples of terminal year Net Profit, EBITDA, EBIT Trading multiples of (terminal year + 1) Net Profit, EBITDA, EBIT “Perpetuity value” of cash flows after terminal year

Discount Rate

Present Value

WACC of companies in similar businesses to reflect the relative risk Cost of Equity using CAPM Model

Determine a range of values for the enterprise by discounting the projected free cash flows and terminal values to the present

Adjustments Adjust valuations for all assets & liabilities not accounted for in projections Incremental shares are calculated using treasury stock method

Sensitivity Analysis DCF is sensitive to changes in growth rate & margin assumptions Sensitivity with respect to terminal value and discount rate


P a g e | 152

FCFF = EBITDA * (1- tax rate) + (D&A * tax rate) – change in WC – Capex

Project Cash Flows depends on:-

Industry cycle and competitive structure (operating margins)

Economic cycle

Known significant events

Useful life of asset (e.g. oil well, mine)

Comfort of forecaster

Length of any competitive advantage

Allow enough time to reach a normalised or mature level of cash flows which assumes

constant growth and/or capital needs into perpetuity

While projections become less reliable the further out they go, it may be necessary to go

out up to 10 years or more in order to reach a normalized level of free cash flow.

Sources of Project Cash Flows

The free cash flows from a business can be projected using information about the industry in which

a business operates and information specific to the business. A variety of sources can be used, such

as research reports, S&P industry surveys, industry journals and manuals, and other miscellaneous

sources. DCF analysis is an attempt to look at the company’s pure operating results free and clear

of extraordinary items, discontinued operations, onetime charges, etc. It is also extremely

important to look at the historical performance of a company or business (margins, growth) to

understand how future cash flows relate to past performance. A company’s FCFF represents the

return available to both sources of its capital; debt lenders and equity investors. Free cash flows

there reflects the cash generated by the assets of a business, irrespective of how such assets are

financed.

In summary, DCF projections should be based on:

Historical Performance

Company or Management Projections

Industry Estimates


P a g e | 153

Industry data

Macroeconomic data

5.3 Detailed Explanation of FCFF line items

• Net Income- Net income is taken directly from the Income statement. It represents the

income available to shareholder’s after taxes, depreciation, amortization, interest expenses

and the payment to preferred dividends

Non-cash items Adjustment to Net Income

Depreciation Addition

Amortization Addition

Losses Addition

Gains Subtraction

Restructuring charges

(expense)

Addition

Reversal of restructuring reserve (in Subtraction

Amortization of bond discount Addition

Amortization of bond premium Subtraction

Deferred taxes Addition

• After tax interest- Since interest is tax deductible, after-tax interest is added back to the net

income. Interest cost is a cash flow to one of the stakeholder’s of the firm (debt holders)

and hence, it forms a part of FCFF.

• Non Cash Charges- Non Cash Charges includes items that affect net income but do not

involve the payment of cash. Some of the most common non cash items are listed below.

a. Capital Expenditure- Investment in fixed assets is the cash outflow required for the

company to maintain and grow its operations. It is possible that a company acquires

assets without expending cash by using stock or debt . Analyst should review the


P a g e | 154

footnotes, as these asset acquisitions may not have used cash in the past, but may affect

the forecast of future FCFF .

b. Change in Working Capital- The working capital changes that affect FCFF are items

such as Inventories, Accounts Receivables and Accounts Payable. This definition of

working capital excludes cash and cash equivalents and short-term debt (notes payable

and the current portion of long term debt payable). Do not include non-operating

current assets and liabilities, e.g. dividends payable etc.

Example of FCFF and FCFE

Consider the Balance Sheet and Profit & Loss Statement of XYZ Company over two year time

period.


P a g e | 155

Solution= Determination of Change in Net Working Capital= Change in A/C Payable+ Change

in A/C Receivable+ Change in Inventory.=(90-45)+(120-90)+(60-60)=75


P a g e | 156

Then Capital Expenditure =Gross Property, Plant & Equipment-Accumulated Depreciation-

Depreciation

Capital Expenditure=(1200+900)-(570+420)-150=300

Net Borrowing=Change in short term debt + Change in long term debt=(60-30)+(342-300)=72

Then FCFF through EBIT formula will be=EBIT* (1- tax rate) +D – change in WC – Capex

=

FCFF=285*(1-30%)+150-75-300=-25.5

While FCFF through EBITDA formula would be =

FCFF = EBITDA * (1- tax rate) + (D&A * tax rate) – change in WC – Capex

=FCFF=435*(1-30%)+150*30%-75-300=-25.5


P a g e | 157

While FCFE=FCFF-Interest Expenses*(1-tax rate)+Net Borrowing

FCFE=-25.5-45*(1-30%)+72=15

5.4 Projection of Income Statement

Project the operating results and free cash flows of a business as discussed over the forecast period

(typically 5 to 10 years). Project forward enough years to achieve a ‘normalised’ (ex-growth) or

‘mature’ level of cash flows prior to deriving a terminal value. Note that while projections become

less reliable further out, it may still be necessary to go out up to 10 years or more in order to reach

normalised levels. You should be careful to ensure that, for a cyclical business, you should end the

forecast period at a mid point in the cycle. Furthermore, if the company you are forecasting is

expected to have a competitive advantage, your period should be of sufficient length to capture the

entire period of the competitive advantage. A simplified DCF can be created which projects only

the items in the FCFF formula. However, a more rigorous approach pulls such results from a fully

integrated three-statement model. In forecasting future cash flows, you should be aware of the

sensitivity of cash flow streams over the forecast period. The traditional method of discounting

cash flows assumes that cash flows occur at the end of each annual period. It may sometimes be

more accurate to forecast cash flows on the assumption that they fall evenly throughout the years.

5.5 Terminal Value

Terminal Value estimates the perpetuity growth rate and exit multiples of the business at the end

of the forecast period, assuming a normalized level of cash flows. Since DCF analysis is based on

a limited forecast period, a terminal value must be used to capture the value of the company at the

end of the period. The terminal value is added to the cash flow of the final year of the projections

and then discounted to the present day along with all other cash flows.

Terminal values can be calculated based on two methodologies:

Perpetuity value

Exit multiple.


P a g e | 158

Figure 5.2: Series of cash flows with terminal Cash Flows

Terminal Value Calculations-Perpetuity Growth Method

Perpetuity value of normalized terminal cash flow - This approach calculates the value of the

business on the assumption that it will operate into perpetuity. Two perpetuity formulae can be

utilized, both of which should be shown in a DCF analysis. The first method is growing perpetuity,

which is a preferred method. A growing perpetuity assumes that growth of the business will

continue and that the necessary new capital will return more than its cost. Growth requires capital

spending, and thus a growing perpetuity begins with free cash flow rather than EBIT (1 – tax rate).

𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 = (𝐹𝐶𝐹𝐹𝑛 + 1

𝑊𝐴𝐶𝐶% − 𝑔𝑟𝑜𝑤𝑡ℎ%)

n is the final year of the projection period, and g is the nominal growth rate expected into

perpetuity. The nominal growth rate is generally the inflation rate component of the discount plus

an expected real growth (or minus a deflation) in the business. A reasonable range for perpetuity

growth is the nominal GDP growth rate of the country. Under no growth Perpetuity environment,

assumes that a company earns its cost of capital on all new investments into perpetuity. As such,

the level of investment growth is irrelevant because such growth does not affect the value (i.e. the

growth rate is zero and Capital Expenditure is equal to depreciation and amortization). Such a

methodology is appropriate in industries in which competition is expected to eliminate excess

returns, thus driving asset returns to the cost of capital.


𝑊𝐴𝐶𝐶%)

17 24 24 31 53 89 102 110

425

0

100

200

300

400

500

2008 2009 2010 2011 2012 2013 2014 2015 2016 Annual cashflow Terminal Value

Cash Flows (Rs mn)

Terminal Value


P a g e | 159

5.6 Financial Model-Corporate Valuation


P a g e | 160


P a g e | 161


P a g e | 162

Figure 5.3: Corporate Valuation


P a g e | 163

5.7 Risk Analysis in Corporate Valuation

Free cash flow is a very important concept; it focuses on the amount of cash that owners of a

business can consume without reducing the value of the business. It recognizes that a business

needs to invest in current and long-term assets in order to continue and grow its operations. Thus

free cash flow focuses on the ability of a business to generate cash flows beyond those needed to

invest in such assets as inventories, plant and equipment, advertising, labor, other cost of sales,

research and development, and the like. free cash flow being a primary objective of management

and analytical measurements, net income must too be studied as it can emit signals which cash

flow overlooks—but its usefulness is more of short-term significance. Valuation Risk is the

financial risk that an asset is over valued and it may not have an appropriate value than expected

and will yield less than when liquidated. Factor contributing to valuation risk is the incomplete

data, market instability, financial modeling uncertainties and poor data analysis. The risk can be

concern for investors, lenders, market regulators, and other people involved in financial markets.

To mitigate this risk it is important to provide transparency and ensure integrity and consistency

of data, models and processes used to process and report calculations within the valuations from

all participants.

DCF Projections-Reality Check

Confront sales growth assumptions with underlying market dynamics

1. Be skeptical of projected sales growth curves that look show dramatic improvements

versus recent actual performance

2. Does the increase in sales reflect a constant market share in an expanding market? If so,

why is the market expanding?

3. Does that assumption agree with industry projections?

4. If it is an expanding market, why will the company be able to maintain a constant market

share? Or does the increase reflect a rising market share in a stagnant market? If yes, why?

Are some firms leaving the industry? Why?


P a g e | 164

Check reasonableness of margins

1. Be clear on the actions or events needed to trigger improvements in margins (or reasons

for decreases in margins)

2. Are the margin levels consistent with the structure of competition in the industry?

3. Any risk of new entrants/substitute products that will drive margins down?

Capital Expenditures

1. Watch out for step-up of production capacity required as sales increase.

2. Is the Capex level sufficient to support the forecasted increase in sales?

3. Factor in the impact of industry trends on Capex (e.g., increased environmental

expenditures, technology changes, etc.)

5.8 Excel in Portfolio Management

Portfolio Management is all about managing different avenues of investment together so as to

maximize the return/risk ratio. It makes sense when ever portfolio is created the different avenues

should be negatively correlated. Degree of Correlation between two variable is measured by

coefficient of correlation. It have value from -1 to +1. For example coefficient of correlation

between two sector like Oil & Gas and FMCG can be determined by considering two stocks like

ONGC and ITC. 3 month historical data of ONGC and ITC is considered.


P a g e | 165

Figure 5.4: Coefficient of Correlation calculation in Excel

Figure 5.5: Coefficient of Determination Calculation


P a g e | 166

Now the nature of relationship of stocks-ITC and ONGC with respect to NIFTY is measured by

Beta which is the factor of Systematic Risk. Beta measures the degree of sensitiveness of relative

change in the price of stock with respect with market. Beta in MS Excel is calculated by slope

function.


P a g e | 167

Figure 5.6: Beta calculation in MS Excel


P a g e | 168

Figure 5.7: Security Market Line

5.9 Technical Analysis of Stocks

Consider a stock called DLF. Historical Price of DLF is taken from 07th May 2014 to 10th July

2014. For the given time period we can determine the Beta of the stock and can represent them in

the form of Candle Stick Charts. For reference on Candle Stick Model, refer www.

Stockcharts.com.


P a g e | 169

Figure 5.7: Historical price movement of DLF

The Candle Stick Representation will be done in MS Excel under Other Charts representation.


P a g e | 170

Figure 5.8: Candle Stick Movement of DLF

5.10 Portfolio Optimization Using MS Excel-Solver Function

Consider I want to create portfolio of 6 stocks. I chose each stock from one sector and the overall

calculation works on assumption of historical data of last 3 month. Suppose I chose the Sector IT,

Banking, Auto, Pharma, FMCG, Manufacturing and the stocks are TCS, SBI, Bajaj Auto, ITC,

Ranbaxy and RIL. Historical data of all companies are taken from www.nseindia.com.

Stocks Sector Return Standard Deviation

TCS IT 0.20163 1.670785

ITC FMCG 0.049662 1.47458776

Ranbaxy Pharma 0.30666 1.5720595564

RIL Manufacturing 0.058973 1.83723243

Bajaj Auto Auto 0.178989 1.679179

SBI Banking 0.2788444 2.3753188

Table 5.9: Description about stocks-part of portfolio

http://www.nseindia.com/


P a g e | 171

Figure 5.10: Average Return and Standard Deviation of different stocks

Now I will try to create variance covariance matrix. In order to work on Variance Covariance

matrix first I will determine excess return on each stock, which is equal is X=return-average return.

Then variance covariance matrix will be determined by = (1

𝑛) 𝑋𝑡 . 𝑋 where 𝑋𝑡 = 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑠𝑒 𝑜𝑛 𝑋.

MMULT function is used to multiply matrices. First, 𝑋𝑡 . 𝑋 will be determined

Figure 5.11: use of mmult to determine variance covariance matrix

Once we get 𝑋𝑡. 𝑋 then I will try to determine the value of (1

𝑛) ∗ (𝑋𝑡. 𝑋), here n=57. So, the

required value in MS Excel is determined by first selecting all the required (6x6) matrix, then using

the division formula, put the required equation and then ctrl+ shift+ enter.


P a g e | 172

Figure 5.12: use of mmult to determine variance covariance matrix


P a g e | 173

Figure 5.13: Working on variance covariance matrix


P a g e | 174

Figure 5.14: Variance covariance matrix

Now I will try to determine the coefficient of correlation among to understand the nature of relationship

between each stocks as covariance does not clarify the extent of relationship. Now

𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛(𝑥𝑦) = (𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒(𝑥𝑦)

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑥.𝑠𝑡𝑎𝑛𝑑𝑟𝑎𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑦)So, first I will

determine 𝜕. 𝜕𝑡. ∂=standard deviation.


P a g e | 175

Figure 5.15: Calculation of Standard Deviation Matrix

Figure 5.16: Calculation of Standard Deviation Matrix


P a g e | 176

Figure 5.17: Coefficient of Correlation matrix

By looking at the coefficient of correlation matrix, I can figure out the relationship between the

variables. Like TCS and RIL are negatively correlated so if I am thinking of 2 stock portfolio I

should include them together, like this I can find out other relationships.

Let talks about Portfolio Creation from six stocks under different cases and then I try to measure

the Return and Risk on the portfolio. Return on the portfolio is the ∑𝑅𝑖. 𝑊𝑖, where Wi=individual

weight and Ri=individual return or it can be determined by formula =

𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑠𝑒 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑚𝑎𝑡𝑟𝑖𝑥. 𝑟𝑒𝑡𝑢𝑟𝑛 𝑚𝑎𝑡𝑟𝑖𝑥

In a portfolio of equally weighted I took equal weight for each stock=(1/6)=16.66666%.. In MS

Excel return on a portfolio can be determined by using SUMPRODUCT function or MMULT

function.


P a g e | 177

Figure 5.18: Calculation of Return matrix

Standard Deviation of the portfolio will be determined by using the formula=


P a g e | 178

Figure 5.19: Calculation of standard deviation of portfolio matrix

Now by using solver I will try to find the what will be the weight of portfolio that will bring the maximum

return for the portfolio at the minimum risk where I put constraint

1. the standard deviation of portfolio should be less than or equal to the standard deviation of ITC

stock having minimal standard deviation among all stocks.

2. Total weight on the portfolio=1


P a g e | 179

Figure 5.20: Working on calculation of Sharpe Ratio


P a g e | 180

Figure 5.20: Working on calculation of Sharpe Ratio with Solver


P a g e | 181

Figure 5.21: Solver to determine optimal portfolio


P a g e | 182

Figure 5.22: Optimal portfolio

5.11 Summary

1. Business valuation is a series of procedures used to anticipate the economic value of an

owner’s interest in a business. Valuation is used by Insiders of a firm like CEO, CFO,

Operating Manager to identify opportunities and it help them in decision making. It is used

by Investors like Hedge Funds/Pension Funds, Insurance Company, Retail Investor before

investment or to find out appropriate investment opportunity, It is used by Consultants like

Investment Bank, Credit Rating Agencies, Brokerage House to suggest/recommending

their investors the ideal source/avenue for investment. Valuation help firm during Merger


P a g e | 183

and Acquisition, work on defensive strategies against hostile takeover, assisting during

listing, subsequent offering and de-listing etc.

2. Approaches of Business Valuation:-

a. Macro Analysis-

Monetary Policy- Process by which government, Central Bank, Monetary Authority of

country controls the supply of money, availability of money

Fiscal Policy- Government policy that attempt to influence the direction of economy

through the changes in Government taxes, Fiscal allowances

Stages of Business Cycle- Recovery, Early Expansion, Late Expansion, Early Recession,

late Recession

b. Strategic Analysis

Industry Life Cycle-Pioneering, Rapid Growth, Mature Growth, Stabilization and Market

Maturity, Deceleration of growth and decline

Porter’s Five Forces- Rivalry among the existing competitors, Threat of new entrant,

Threat of Substitute products, Bargaining Power of Buyers, Bargaining power of Supplier

c. Retrospective/ Prospective Analysis

Financial Statement Analysis of Company

Understanding the accounting policies-conservative/aggressive

Ratio Analysis of the Company-Liquidity, Operating, Risk and Growth

Ratio Comparison with other companies in the industry/sector

3. Value of firm is determined by four factors-it capacity to generate cash flows from assets

in place, the expected growth rate of these cash flows, the length of time it will take the

firm to reach stable growth, and the cost of Capital

Value of Asset==∑𝑃𝑉 𝑜𝑓 𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠

(1+𝑊𝐴𝐶𝐶)𝑛


P a g e | 184

Free Cash Flow to the Firm=EBIT(1-tax%)+Depreciation-Capital Expenditure-∆ in

Noncash Working Capital.

4. The free cash flows from a business can be projected using information about the industry

in which a business operates and information specific to the business. A variety of sources

can be used, such as research reports, S&P industry surveys, industry journals and manuals,

and other miscellaneous sources.

5. A Company’s FCFF represents the return available to both sources of its capital; debt

lenders and equity investors. Free cash flows there reflects the cash generated by the assets

of a business, irrespective of how such assets are financed.

6. While working on valuation-a two step or three step life cycle model can be anticipated

with an appropriate discount rate. Weightage Average cost of capital is use as a discount

rate where proper efforts has been put on determination of cost of equity and cost of debt

7. Project Cash Flows depends on:-

Industry cycle and competitive structure (operating margins)

Economic cycle

Known significant events

Useful life of asset (e.g. oil well, mine)

Comfort of forecaster

Length of any competitive advantage

Allow enough time to reach a normalised or mature level of cash flows which assumes

constant growth and/or capital needs into perpetuity

While projections become less reliable the further out they go, it may be necessary to go

out up to 10 years or more in order to reach a normalized level of free cash flow.

8. Discounted Cash Flow analysis show us the expected value of business by the reference to

future cash flows. Discounted cash flow analysis involves estimating the present value of

future cash flows that business being valued is expected to generate

9. Rather than discounting the cash flows indefinitely into the future, a terminal value based

on company long term growth rate (perpetual growth rate methodology) or a multiple of

final year earnings or cash flows ( exit multiple methodology), is usually assumed after a

period of say five to ten years.


P a g e | 185

10.

11. Perpetuity value of normalized terminal cash flow –


𝑊𝐴𝐶𝐶% − 𝑔𝑟𝑜𝑤𝑡ℎ%)

n is the final year of the projection period, and g is the nominal growth rate expected into

perpetuity. The nominal growth rate is generally the inflation rate component of the

discount plus an expected real growth (or minus a deflation) in the business.

12. Under no growth Perpetuity environment, assumes that a company earns its cost of capital

on all new investments into perpetuity. As such, the level of investment growth is irrelevant

because such growth does not affect the value (i.e. the growth rate is zero and Capital

Expenditure is equal to depreciation and amortization).

𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 = (𝐹𝐶𝐹𝐹𝑛+1

𝑊𝐴𝐶𝐶%)

13. Free cash flow is a very important concept; it focuses on the amount of cash that owners

of a business can consume without reducing the value of the business.

14. Free cash flow focuses on the ability of a business to generate cash flows beyond those

needed to invest in such assets as inventories, plant and equipment, advertising, labor, other

cost of sales, research and development

15. Valuation Risk is the financial risk that an asset is over valued and it may not have an

appropriate value than expected and will yield less than when liquidated.

16. Factor contributing to valuation risk is the incomplete data, market instability, financial

modeling uncertainties and poor data analysis.

17. Portfolio Management is all about managing different avenues of investment together so

as to maximize the return/risk ratio. It makes sense when ever portfolio is created the

different avenues should be negatively correlated. Coefficient of Correlation between two

17 24 24 31 53 89 102 110

425

0

100

200

300

400

500

2008 2009 2010 2011 2012 2013 2014 2015 2016 Annual cashflow Terminal Value

Cash Flows (Rs mn)

Terminal Value


P a g e | 186

variables-x and sy can be determined by correl function in MS Excel. Regression

Coefficient between two variables-x and y assuming x=independent variable and

y=dependent variable is determined by slope function. Beta is the factor which measures

the degree of sensitiveness of relative movement of a stock with respect to relative

movement in market is in MS Excel is determined by slope function

18. Technical Analysis on the stock can be done in MS Excel by using stock charts where line

graph, candle stick representation can be plotted with volume and without volume

19. Portfolio Optimization using Solver

Solver is the MS Excel based application used to maximize or minimize or finding an

optimal value of a given set of conditions. It is used in Operation Research to work on

Linear Programming Model

Maximumizition of Sharpe Ratio would be the objective under Solver

Variance-Covariance Matrix, Coefficient of Correlation Matrix can be determined through

mmult function in MS Excel

Portfolio standard deviation is determined by using formula =

𝑠𝑞𝑟𝑡(𝑊𝑡. ∑(𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 − 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒). 𝑊)

Return on a portfolio can be determined by using formula

= 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑠𝑒 𝑜𝑓 𝑤𝑒𝑖𝑔ℎ𝑡 𝑚𝑎𝑡𝑟𝑖𝑥. 𝑟𝑒𝑡𝑢𝑟𝑛 𝑚𝑎𝑡𝑟𝑖𝑥

Sharpe Ratio=(𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 𝑃𝑟𝑒𝑚𝑖𝑢𝑚)/(𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛)


Two Marks Questions

8. What is Business Valuation?

9. What is the need of Business Valuation?

10. What are the approaches of Business Valuation?

11. What is the difference between Free Cash Flow to Equity (FCFE) and Free Cash Flow to

Firm(FCFF)?

12. Explain Risk Analysis in Corporate Valuation?


P a g e | 187


8. How the terminal value of a firm can be determined?

9. How the beta of a stock can be calculated in MS Excel?

10. How representation of Candle Stick Model can be done in MS Excel?

11. How Variance Co-variance matrix can be generate in MS Excel?

12. What is the need of Portfolio Optimization?

13. Explain the application of MMULT function in MS Excel?

Ten Marks Questions

1. Considering certain number of stocks in a portfolio, how could portfolio optimization can

be done through MS Solver?


1. Beta of a stock can be determined by …………………. Formula in MS Excel

a. Correl

b. Covar

c. Slope

d. Std.p

2. Coefficient of Determination which measures the strength of straight line between the

return on stock with respect to return on market lies between………………….

a. 0 and 1

b. -1 to 1

c. Any positive integer

d. Any natural number

3. Sharpe Ratio is ……………………….

‘a. 𝐸𝑥𝑐𝑒𝑠𝑠 𝑅𝑒𝑡𝑢𝑟𝑛

𝑅𝑖𝑠𝑘 𝐹𝑟𝑒𝑒 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑅𝑒𝑡𝑢𝑟𝑛

‘b. 𝐸𝑥𝑐𝑒𝑠𝑠 𝑅𝑒𝑡𝑢𝑟𝑛

𝐵𝑒𝑡𝑎 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘


P a g e | 188

‘c. 𝐸𝑥𝑐𝑒𝑠𝑠 𝑅𝑒𝑡𝑢𝑟𝑛

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘

‘d. 𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘

𝐸𝑥𝑐𝑒𝑠𝑠 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑠𝑡𝑜𝑐𝑘

4. Which mathematical formula in MS Excel would help to find the expected return on a

stock where probabilities and probable return under that probability is mentioned

a. Mmult

b. Combin

c. Sumproduct

d. Concatenate

5. In matrix form, the formula of standard deviation is…………………..

a. √(𝑤𝑡). ∑((𝜎2) − 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒). 𝑤𝑡

b. √(𝑤𝑡). ∑((𝜎2) − 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒). 𝑤

c. √(𝑤𝑡). ∑((𝜎2) − 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒).

d. None of these

6. What is the relationship between Covariance xy with Coefficient of correlation xy?

a. (𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒(𝑥𝑦)

𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑥.𝑠𝑡𝑎𝑛𝑑𝑟𝑎𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛𝑦)

b. 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒(𝑥𝑦). 𝜎𝑥. 𝜎𝑦

c. 𝜎𝑥.𝜎𝑦

𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒(𝑥𝑦)

d. None of these

7. For matrix multiplication, which Excel formula is useds

a. Mmult


P a g e | 189

b. Combin

c. Sumproduct

d. Concatenate

8. In order to maximize the parameters under Sharpe Ratio, which MS Excel function can

be used

a. Goal Seek

b. Data Analysis

c. Data Table

d. Solver

9. Return on day to day basis of a stock can be determined by using formula

a. (𝑡𝑜𝑑𝑎𝑦 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒−𝑦𝑒𝑠𝑡𝑒𝑟𝑑𝑎𝑦 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒

𝑦𝑒𝑠𝑡𝑒𝑟𝑑𝑎𝑦 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒) × 100

b. 𝑙𝑜𝑔𝑒 (𝑡𝑜𝑑𝑎𝑦 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒

𝑦𝑒𝑠𝑡𝑒𝑟𝑑𝑎𝑦 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒) × 100

c. Both of these

d. None of these

10. What is the short cut for transposing array of data in MS Excel?

a. Ctrl+c, Alt+e+s+v+e

b. Ctrl+c, Alt+e+s+e

c. Both of these

d. None of these

Answers

1-c, 2-a, 3-c, 4-c, 5-b, 6-a, 7-a, 8-d, 9-a, 10-c

a. References:

1. Pandey I. M, (2003) Financial Management, Vikas Publishing House – New Delhi

2. Aswath Damodaran (2008)-Damodaran on Valuation, Wiley Finance-USA

3. Michael C Ehrhardt, Eugene Brigham (2008) Corporate Finance: A Focuseed Approach,

South-Western Publications-USA


P a g e | 190

4. Prasanna Chandra, (2008) Financial Management and Theory and Practice-Mc Graw Hill

Publications-New Delhi

Websites:

1. Analyze and Optimize Portfolio of Assets- http://in.mathworks.com/discovery/portfolio-

optimization.html?nocookie=true

2. Portfolio Optimization Problems-By Burns Statistics-

http://in.mathworks.com/discovery/portfolio-optimization.html?nocookie=true

3. Private Company Valuation- By Aswath Damodaran-

www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/pvt.pdf

Video Links:

1. Portfolio Optimization in Excel-By Colby Wright-

http://www.youtube.com/watch?v=FZyAXP4syD8

2. The Minimum Variance Portfolio and the Efficient Portfolio-

http://www.youtube.com/watch?v=S5VYM0lMb2Y

3. Valuation by Aswath Damodaran-

http://www.youtube.com/watch?v=K_36oYXYESU



http://www.stern.nyu.edu/~adamodar/pdfiles/eqnotes/pvt.pdf

http://www.youtube.com/watch?v=S5VYM0lMb2Y

http://www.youtube.com/watch?v=K_36oYXYESU


P a g e | 191


P a g e | 192

Data & Analytics

Financial modeling amit kumar singh