Valuation And Capital Budgeting

Discounted Cash Flow Valuation, Bond & Stock Valuation

(Chapter 4, Chapter 8 & Chapter 9)

Interest RateSimple Interest: Where interest is not reinvestedExample: Interest rate = 5% per annualPrincipal Amount = $1,000Lender (Creditor) will receive:the principal amount + interest payment after one year = $1,000 x 1.05 = $ 1,050Compound Interest: When cash is invested at compound rate, each

interest payment is reinvested.In above example, if the lender reinvests $ 1050 that is the principal

amount + interest payment for another one year at 5%, $1050 x 1.05 = $1,102.5 OR $ 1,000 x 1.05 x 1.05 =

$ 1,000 x (1.05)² = $ 1,000 x 1.1025 = $ 1,102.5Future Value = FV = C0 x (1+ r) T

Where C0 is the cash to be invested at date 0, r is the interest rate, and T is the number of periods over which the cash is invested.

Stated Annual Interest Rate&

Effective Annual Interest Rate• Stated Annual Interest Rate becomes meaningful only if the

compounding interval is given. For example, 10% semi-annual compounding = [1+ (0.10/2)]² = (1 + 0.05)² = (1.05)² = 1.1025

10% quarterly compounding = [1 + (0.10/4)]= [1 + 0.025] = 1.1038• Effected Annual Interest Rate is meaningful without a

compounding interval. For example, EAIR of 10.25% means that a $1 investment will be worth $ 1.1025 after one year.

Stated Annual Interest Rate &Effective Annual Interest Rate

Future Value with Compounding mT

FV = C0 (1 + r/m)r= stated interest rate, m = compounding interval, T= YearsExample: Harry Jones is investing $ 5,000 at a stated annual

interest rate of 12 % per year, compounded quarterly, for five years. What is his wealth at the end of five years?

Effective Annual Interest Rate = (1 + r/m) m - 1Example: EAIR = [1+(0.10/2)]² - 1 = (1+0.05)² - 1 = (1.05)² -1= 1.1025 – 1 = 0.1025= 10.25%

Continuous Compounding

C0 xWhere C0 is the initial investment r is the stated annual interest rate, and T is the number of years over which the investment runs. The “e” is a constant and is approximately equal to 2.718

Example: If you invest $ 1,000 at a continuously compounded at 10% for two years. What is the value of your wealth at the end of two years?

Net Present Value

Present Value of Investment=

C1/1+rC1 is cash flow at date 1

and r is the appropriate interest rate

It is also referred as discount rate (required rate)

Net Present ValueNPV = - C0 + C1/(1+r) + C2/(1+r)² +……. CT/ (1+ r)

T= - C0 +

Perpetuity: PV = C/rGrowing perpetuity: PV = C/(r-g)

Questions1. An investor is purchasing a British consol is entitled

to receive annual payments from British government forever. What is the price of a consol that pays $ 120 annually if the next payment occurs one year from today? The market interest rate is 15%.

2. In its most recent corporate report, RT Limited apologized to its stockholders for not paying dividends. The report states that management will pay a $ 1 dividend next year. That dividend will grow at 4% every year thereafter. If discount rate is 10%, how much are you willing to pay for a share of RT Limited?

Questions3. Barrett Pharma is considering a drug project that costs $

100,000 today and is expected to generate end-of year annual cash flow of $ 50,000 forever. At what discount rate would Barrett be indifferent between accepting or rejecting the project.

4. Assuming an interest rate of 10%, calculate the present value of the following streams of yearly payment:– $ 1,000 per year, forever, with the first payment one year

from today– $ 500 per year, forever, with the first payment two year

from today– $ 2,420 per year, forever, with the first payment three

year from today

Question

The Trojan Pizza Company is contemplating investing $ 1 million in four new outlets in New York. The firm’s CFO has estimated that the investment will pay out cash flows of $ 200,000 per year for nine years and nothing thereafter. The cash flows will occur at the end of each year and there will no cash flow after year 9. The CFO has determined that the appropriate discount rate for this investment is 15%. This is the rate of return that the firm can earn at comparable projects. Should the Trojan Pizza Company make the investments in the new outlets.

BONDS & STOCKSVALUATION

BondsA bond is a certificate showing that a borrow owes a

specific amount. In order to repay the money, the borrower has agreed to make interest and principal payments on designated dates.

• Pure Discount Bonds: It pays a single payment of amount “x” at a fixed future date.Maturity date: When the issuer makes the last payment.Expire: The bond is said to expire or mature on the date of its final payment.Face Value: The payment at maturity is termed the bond’s face value.

Bonds Value of Pure Discount Bond

PV = F /(1+ r) T

Example: Consider a bond with a face value of S 1,000,000 that matures in

20 years. Suppose the interest rate (the market interest rate) is 10%.

What will be its PV?

BondsLevel Coupon Bonds: The coupon payments

(interest payments) are made at regular times (six monthly) till maturity.The principal amount / denomination (Face Value) is paid at the maturity.

PV = C/(1+r) + C/(1+r)² +…….+ C /(1+ r) T + F/(1+ r) T Example: Consider a level coupon bond with theface value $ 1,000, coupon rate is 13% annually, coupon is paid every six months. The face value will be paid out four years from now. What is PV of the bond?

BondsTo solve this numerical, you have to find out the following:1. Coupon payment (C)?2. Number of coupon payments or number of

periods (T)?3. Discount Rate = r?4. The face value or the principal payment and at

what time?You can solve the numerical putting the values in the discount model as given or you can use annuity factor PV = C x + F/(1+ r) T

Annuity Factor for T = 8 & r=.05 is 6.463

BondsConsols: 1. They have no final maturity date.2. Never stop paying a coupon.Therefore a consol is a perpetuity.Valuation of a consol: PV = C/rExample: Consider a consol with yearly interestpayment of $ 50 and market interest rate is 10%

BondsInterest Rates & Bond Prices

If market interest rate goes up the bond prices come down and vice versa.Example: The interest rate is 10%. A two year

bond with a coupon rate of 10% and with coupon payment annually, Face value $1,000. What will be its price (PV)?

What if the interest rate is 12% then what willbe the price? And if the interest rate is 8% then What will be the price?What is Yield to Maturity?

BondsWhen the bond is said to sell at a discount that means it is selling below its face value. That is the coupon rate is below the market interest rate

When the bond is said to sell at a premium that means it is selling above its face value. That is the coupon rate is above the market interest rate

When the bond is said to sell at par that means it is selling at its face value. That is coupon rate is equal to the market interest rate

Common StocksValuation Models:1. Discount Model

P0 = Div1/(1+r) + Div2/(1+r)² +……. DivT/ (1+ r) T

2. Zero Growth = constant dividend flow = Perpetuity = P0 = Div /r

3. Constant Growth = Growing Perpetuity P0 = Div /(r-g)

Common StocksExample1:Suppose an investor is considering the purchase

of a share of Redko Mining Company. The stock will pay a $ 3 dividend a year from today. This dividend is expected to grow at 10% per year for the foreseeable future. The investor thinks that the required rate of return on this stock is 15%, given the assessment of the Redko Mining’s risk. What is the value of a share of Redko Mining Company’s stock?

Common StocksExample 2:Consider the stock of Electric Co. Limited. The

dividend for a share of stock a year from today will be $1.15. During the next four years, the dividend will grow at 15% per year. After that, growth will be equal to 10% percent per year. Calculate the present value of the stock if the required return is 15%.

Annuity: PV = C [ 1/r – 1/r(1+r

Growing Annuity: PV = [1/r-g – 1/r-g (1+g/1+r ]

Solution: Two – step process to discount these dividends.

Step 1: Calculate the net present value of dividends of the dividends growing at 15%, i.e., the present value at the end of each of the first five years.PV = Div1/1+r + Div2/(1+r)² + Div3/(1+r)³ + Div4/(1+r)⁴ + Div5/(1+r)⁵PV = 1.15/1.15 + 1.3225/1.3225 + 1.5209/1.5209 + 1.749/1.749 + 2.0114/2.0114 = 1+1+1+1+1 = $5

Common Stocks

Common StocksStep 2: growth rate (g2) = 10% = 0.10Dividend at the end of year 6 =

Div6 = 2.0114 (1.10) = 2.2125We can use growing perpetuity formula

to calculate the present value at year 5P5 = Div6/ r-g2 = 2.2125 / (0.15 – 0.10) = 2.2125 /0.05 = 44.25The present value of P5 at the end of year 0 is

PV = P5/(1+r)⁵ = 44.25 /(1.15)⁵= 44.25 / 2.0114 = 22

Add Step 1 + Step 2 = 5 + 22 = $27

Preferred Stock (Share)• Preferred Stock :

Preferred stock is stock that is issued by corporations and that provides the holder a fixed dividend in perpetuity just like consol.

Price=PV= Div/rPreferred stockholder has no voting rightPreferred stock is generally considered a hybrid instrument.Preferred Stock is senior (i.e. higher ranking) to common stock, but subordinate to bonds in terms of claim (or rights to its share of the assets of the company).

Common StocksGROWTH OPPORTUNITIES

A company with a level stream of earnings per share = EPS

The company pays all these earnings to stockholders as dividends

Earnings Per Share (EPS) = Dividend Per Share (Div)EPS = Div

Using the perpetuity formula to calculate the value of a share: EPS/r = Div/r

Where “r” is the required discount rate on the firm’s stock

Common StocksIf now a growth opportunity (capital budgeting

proposal) is available to the company. Suppose the company retains entire dividend at

date 1 in order to invest in the project.The net present value per share of the project at

date 0 is NPVGO = the net present value (per share) of the growth opportunity.

What is the price of a share of the stock at date 0 if the firm decides to take on the project at date 1?

Common StocksNPVGO will be added to the original stock price

EPS/r + NPVGO

Example: Sarro Limited expects to earn $1,000,000 per year in perpetuity if it takes no new investment opportunities. There are 100,000 shares of stock outstanding.

Q1. What is earning per share?Ans: 1,000,000 / 100,000 = $10

Common StocksThe firm will have an opportunity at year 1 to

spend $1,000,000 in a new marketing campaign. The new marketing campaign will increase earnings in every subsequent year by $210,000.

Q2. What is increase in earning per share?Ans: 210,000 / 100,000 = $2.10Q3. What is % return per year on the

project?Ans: 210,000 / 1,000,000 = 0.21 = 21%

Common Stocks The firm’s discount rate is 10%.Q4. What is the value per share before and

after deciding to accept the marketing campaign?

Ans.: EPS/r = 10/0.1 = $100The value of the marketing campaign at Year 1- C1 + C/r = -1,000,000 + 210,000/0.1

= -1,000,000 +2,100,000 = $1,100,000The value of the marketing campaign at Year 0= C/1+r = 1,100,000 / 1.1 = 1,000,000

Common StocksNPVGO per share = 1,000,000 / 100,000 = $10The value per share is =EPS/r + NPVGO = 100 + 10 = $110

Two conditions must be met in order to increase value:

1. Earnings must be retained so that projects can be funded.

2. The projects must have positive net present value.

Common Stocks

Price-Earnings RatioPrice per share = EPS/r + NPVGO

Dividing both sides of equation by EPSPrice per share / EPS = 1/r + NPVGO/EPS

Common Stocks Assignment 2

Rite Limited sells toothpicks. Gross revenues last year were $3million, and total costs were $1.5million. Rite has I million shares of common stock outstanding. Net earnings are expected to grow at 5% per year. Rite pays no income taxes. All earnings are paid out as dividends.

a). If the required discount rate is 15% and all cash flows are received at the year’s end, what is the price per share of Rite’s stock?

b). Rite has decided to produce tooth brushes. The project requires an immediate outlay of $1.5million. The year after that net cash inflows will be $600,000 and maintained in perpetuity. What effect will undertaking this project have on the price per share of the stock?