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Capital Investment Decisions EXPGP (WE)-2009-12

Sessions 3-4-5

Handout : For class room discussion only Coverage :

Capital Investment decision in practice … issues

– Cost of capital

– Cash Flows

– Risk Analysis in Capital Budgeting under uncertainty Cost of capital … intuitive meaning When investors provide a corporation with funding, they expect the company to generate an appropriate return on those funds. From the company’s perspective, the investors expected return is the cost of using their funds, and it is called….. “the cost of capital”.

Why cost of capital is important from the point of view of Capital Investment Decisions?

– Knowing the cost of capital can help the company determine their required return for capital budgeting decisions

Importance of Cost of Capital for Natural Monopolies The cost of capital is also a very important factor in the regulation of ‘utility’ companies like electric, gas and telephone companies which are ‘natural monopolies’.

Natural monopolies are firms in markets where it is economical for only one firm to provide the service ( may be in sectors requiring huge fixed cost say, so that if the market is shared then it becomes uneconomical even for two companies to operate).

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Because it has a monopoly, these utility companies if they are not regulated, could exploit customers. Therefore regulators – Determine the cost of capital investors have provided the utility – Then set the rates designed to permit the company, to earn marginally

higher than its cost of capital only , not more than that. – In a sense the regulators force the utility companies to earn only a

marginal NPV. ……… may lead to “ Gold Plated Water Filter Effect” . Required return, cost of capital and discount rate Cost of capital, required return, and appropriate discount rate are different phrases that all refer to the opportunity cost of using capital in one way as opposed to alternative financial market investments of the same systematic risk.

– required return is from an investor (providers of capital)point of view

– cost of capital is the same return from the firm’s point of view ( this is also the minimum return that the firm would require to service the providers of capital) .

– appropriate discount rate is the same return as used in a PV calculation

Weighted Average Cost of capital (WACC) It is possible to finance a firm entirely by equity. Most firms however employ several types of long term capital :

– Debt

– Preferred stock

– Common Equity All the capital components have one feature in common :

– The investors who provided the funds expect to receive a return on their investment.

If the firm’s only investors were common stock holders ,then cost of capital would have been = the required rate of return on equity

Because of different types of capital employed, and due to difference in their servicing obligation/risk, these different securities have different required rates of return.

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The required rate of return on each component is the ‘component cost’ and the weighted average of such component costs is called the WACC . WACC = wd. Kd + we.Ke + wpe.Kpe

– Where wd, we and wpe are the respective weights or proportions of debt, equity and preferred equity in the total capital employed while Kd, Ke and Kpe are the required rates of return by the debt, equity and preferred equity holders.

Components of WACC : Cost of Debt ( Kd) The rate of return required by the debt holders… Cost of debt should be ‘relevant’ or ‘marginal’ and not the same as the ‘average’ cost of all previously issued debt which are also called ‘historical or embedded rate’.

This is because when the actual money will be raised from the market historical cost will be of little significance. The current or marginal cost will be what will matter.

Historical or embedded cost is important for some decisions. For example when regulators set the rate of return a public utility will be allowed to earn, then to calculate the cost of their capital they use the average historical or embedded cost of debt.

Estimates for debt Cost if the company is estimated to be issuing “new” bond at par then its coupon rate will be an estimate of the cost of debt.

If the company has already issued bonds in the past, then the yield to maturity on these debt issues, is the estimate of market required rate of return on the firm’s debt. In this case, the coupon rate will be irrelevant because the coupon rate was approximately the rate of return that was asked by the market when the bond was issued.

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If the firm has never issued debt in the past, then one could also look at YTMs of bond issues of similar firms, for a reasonable estimate of debt cost.

Impact of tax on Debt cost Because interest paid on debt is tax deductible, the effective cost of debt to the company is actually less than the actual rate… the Govt. in effect bears a part of the cost by fore going a certain amount of tax.

The actual cost is the ‘after tax cost of debt’ = (1-T)Kd where T is the tax rate applicable for the firm.

Example : Suppose a firm borrows $1 million at 9% interest. The corporate tax rate is 34%. What is the after tax interest rate for this loan ? The total interest bill is $90,000 per year. This amount s tax deductible. So this interest paid reduces the tax bill by 0.34*$90,000 = $30,600. The after tax interest bill is therefore $90,000 - $30,600 = $59,400. The after tax interest rate is therefore $59,400/ 1 million = 5.94% Cost of Preferred Stock Preferred dividends are not tax deductible. Hence no adjustment for taxes need to be made for preferred stocks. The cost of preferred stock is given by,

– Where Dps is the preferred stock dividend and pn is the net issue price ,

which is the net price that the issuing firm receives after floatation costs. ( as floatation costs of preferred stocks are higher hence they need to be considered)

Cost of Equity (Ke) It is the rate of return expected by the equity investors in the company. More difficult to estimate the cost of equity compared to cost of debt or preferred stock. Following approaches are used in practice to obtain reasonably good estimates of ke

– CAPM approach – Discounted cash flow( DCF) approach – Bond yield plus risk premium approach

n

pspe P

DK =

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The methods are not mutually exclusive. In fact mostly all three are applied and then one is chosen from them depending on the confidence the analyst has in the data used for each . Finding Cost of equity …the CAPM Approach Use the following information to compute our cost of equity

– Risk-free rate, Rf

– Market risk premium, E(RM) – Rf

– Systematic risk of asset, β

Estimating the risk free rate No such thing as a truly risk less security. Treasury securities are free from default risk, but they suffer capital losses if interest rates rise. Many analysts are known to use the rate on long term treasury bonds. The reasons could be as follows : – Common stocks are long term securities and most stock holders do invest

on a long term basis. Therefore it is reasonable to think that stock returns embody long term inflation expectations like bonds rather than short term expectations like bills.

– In theory the CAPM is used to measure the expected return over a particular holding period. So when it is used to estimate the cost of equity on a project, the theoretically correct holding period is the life of the project. Since many projects have long lives, the holding period for the CAPM should also be long. Therefore the rate for long term T bond is a logical choice for the risk free rate.

Estimating the market risk premium The market risk premium is the expected market return minus the risk free rate.

Other names are equity risk premium or simply equity premium.

This is caused by risk aversion by the investors. Since most investors are averse to risk, they require a higher expected return( a risk premium) to induce them to invest in the risky equities versus relatively low risk debt.

))(( fMEfE RRERR −+= β

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Under the conservative assumption that, market return or risk free rate both may vary over time, but the difference of the two i.e the risk premium, which is a function of the degree of risk aversion by the investors, is relatively stable over time, the general practice is to use the historical average risk premium as an estimate of true risk premium Estimating Beta Beta is usually estimated as the slope coefficient in a regression, with the stock returns as the dependant variable (y –axis) and the market returns as the independent variable (x-axis).

The resulting beta is called a historical beta, as it is based on historical data.

There are a few problems with this approach : Estimating beta… issues

• Beta estimates are also sensitive to the number of observations used for the regression. With too few observations ,the regression loses statistical power.

• The beta estimates are also dependent on the proxy for the market that is used. Although most general market indexes like SENSEX or NIFTY or BSE 100 etc. will be highly correlated with each other, still there will be slight differences in estimates with different market proxies.

• Like any estimates, beta estimates are also statistically imprecise. That is to say, a beta estimate may come out be 1.0 but the 95% confidence interval may be 0.85 to 1.14. So what figure to use? --- judgmental call

• Further complications arise when we deal with multinational companies, especially those that raise equity capital in different parts of the world. We might be relatively confident in the beta estimates made for the parent company in its home country but less confident of the betas for subsidiaries located in other countries. An American company’s SPV raising equity money in India for its Indian subsidiary's project and trying to estimate the cost of equity is not going to get much help from the US beta estimate of the parent company.

Cost of equity.. DCF approach Have to identify a company whose equity will be roughly as risky as the project undertaken. If dividends are expected to grow at a constant rate ‘g’, then price of a stock is given by :

gr

DPs

10 −

=

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Where P0 is the current price of the stock, D1 is the dividend expected at the end of one period from now and ‘rs’ is the required rate of return from the stock by the market or investors. Re arranging we can write , the required return on equity rs as : Estimating the inputs for DCF approach Three inputs are required to use the DCF approach :

– the current stock price

– the current dividend and

– the expected growth rate of dividends Of these, the growth rate is by far the most difficult to estimate. Commonly used approaches for estimating ‘g’ are as follows :

– Historical growth rates

– Retention growth model

DCF approach…. estimating ‘g’

• Historical approach : If earnings and dividend growth rates have been relatively stable in the past, and if investors expect these rates to continue, then the past realized growth rate may be used as an estimate of the expected future growth rate. In practice however, such historical stability is rare… so a judgement call is needed to use this approach.

• Retention growth model : Most firms pay out some of their net income and retain or reinvest the rest. Payout ratio (b) is the percentage of income that is distributed as dividend, while (1-b) is known as the retention ratio. If ROE is the return on equity, then it is easy to believe that the growth rate of a firm (and its dividends therefore) should depend on the amount of retention and the return the firm earns on such retentions. Thus

– g = ROE x (1-b) However if we want to use the model to obtain a constant growth rate, we have make the following assumptions :

– The payout rate and hence the retention rate to remain constant

gPDr

0

1s +=

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– The Return on equity (on new investment) also to remain constant

Bond Yield + Risk Premium approach Some analysts use a subjective, ad hoc procedure to estimate a firm’s cost of common equity by adding a ‘judgmental’ risk premium over the same firm’s yield on issued bonds. Their logic is that the firms with risky, low rated and consequently high interest rate debt will also have risky, high cost equity. By this approach,

– rs = Bond Yield + Risk premium Empirically it has been seen that, risk premium over a firm’s own bond yield has generally ranged from 3 to 5%. With such a large range, this method gets a little subjective in estimating cost of equity. Finding the WACC Target Capital Structure : It can be shown that a ‘value maximizing’ firm will have an optimal capital structure or an optimal mix of debt, preferred equity and common equity i.e they will issue new capital in order to keep the actual capital structure near about the target all the time.

If that is the case, and if wd, wps, and we are the respective weights of debt, preferred shares and common equity in that optimum structure, then post tax or adjusted WACC will be given by :

– WACC = wd. Kd(1-T) + we .Ke + wps.Kps

WACC .. Few important issues 1)WACC is the ‘current’ weighted average cost the company would face for a new ‘marginal’ rupee or capital , it is not the average cost of rupee raised in the past.

2)The percentages of weights of each capital component should be an estimate of the firm’s optimal or target capital structure weights, and

3)These weights should be based on the market value of each component rather than the book values. Factors affecting WACC

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Factors that the firm cannot control : – level of interest rates : Higher interest rates would imply higher cost of

debt and equity. – Market risk premium : The perceived risk inherent in each stock and

investor’s risk aversion determines the risk premium. Firms cannot control that. But fluctuation in risk premium will affect cost of equity and hence WACC

– Tax rates : determined by Govt. depending on Fiscal conditions. Beyond the control of the firms.

Factors that the firm can control : – Capital structure policy : Change in the D/E ratio will affect both the

cost of equity and the cost of debt ( beta can be shown to be dependant on leverage, rating of bonds etc will change with degree of leverage ) plus the weights also change . So overall WACC is grossly affected by capital structure policy.

Effect of capital structure on WACC

• Debt increases cost of stock (rs): Increased proportion of debt concentrates the business risk on the existing equity holders and makes it risky. So cost of equity should increase, which in turn affect WACC.

• Risk of bankruptcy increases the cost of debt: As debt increases, the probability of financial distress, or even bankruptcy increases. With higher bankruptcy risk, the debt holders will insist on a higher promised return which increases pre tax cost of debt.

• Net effect on WACC by changing capital structure WACC =wd. Kd(1-T) + we.Ke + wpe.Kpe By increasing the proportion of debt (wd) the weight of low cost debt increases and the weight of high cost equity decreases. Therefore all else equal, the WACC should decrease. But all else does not remain equal.In fact both Kd and Ke may increase to some extent. Thus changing the capital structure would affect all the variables, but it is difficult to say, whether those changes will increase the WACC or decrease it. By estimating the WACC for various D/E ratios it can be seen that there is an optimal DE ratio for which the WACC will be minimum. Most firms target to maintain that .

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Other Factors affecting WACC • Dividend policy : Will affect the cost of equity if we are using the DCF

approach. Also if the payout ratio is high then the firm will need to issue new capital to fund its capital budget and will incur a lot of floatation costs. That might affect its effective cost of capital.

• Investment policy : When we estimate the cost of capital the starting

point is the required rate of return on the firm’s outstanding stocks and bonds. Those rates reflect the risk of the firm’s existing assets. Therefore we are implicitly assuming that the new capital will be invested in assets with the same degree of risk, which generally companies do. However if there is a drastic change in nature of the new investment from the companies existing line of business, due to a new investment policy, then the cost of capital should reflect the risk of the new venture rather than the existing ones.( same as saying that WACC should always be calculated on a marginal basis rather than historical one)

Adjusting cost of capital for different departments Cost of capital reflects the average risk and overall capital structure of the entire firm. But what if a firm has divisions in several business lines that differ in risk?

Does not make sense for the company to use its overall cost of capital to discount divisional or project specific cash flows that don’t have the same risk as the company’s average cash flows.

That may lead to problems as follows : Example : A company has two divisions…. Say A and B. Operation of A is relatively safe and should have a 10% cost of capital, while B is riskier and should have a cost of capital =14%. Each division is roughly the same size, so the company’s overall cost of capital comes out to be 12%.Now a manager from A has a project with 11% expected return while that of B has a project with 13% expected return. Should these projects be accepted or rejected?

If treated individually, then A’s project should be accepted (11% > 10%) and B’s project should be rejected (13 %< 14%). But if the company applies the overall cost of capital to both, just the reverse happens. A’s project is rejected, while that of B is accepted.

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Adjusting cost of capital for different departments

• Pure play Method : In this, the company tries to find several single product companies in the same line of business as the division being evaluated, and it then averages those companies’ betas to determine the cost of capital for its own divisions. But it may be difficult to find many such companies like that.

• Subjective Approach : categorizing various divisions into risk classes

and selecting different cost of capital for each. But even then the risk of not accepting good projects and accepting risky projects remain, although to a reduced level. ( Why ? )

Project A would be accepted if WACC is used but once it is classified as high risk it will be rejected. Some errors are possible like B . It will be accepted even with the classification while actually its return is less as per SML. Incorporation of Floatation costs Floatation costs are costs associated with issue of a security. For example during issue of an IPO, the costs like advertisement in print and electronic media etc. are examples of floatation cost.

If debt is privately placed or if equity is raised internally as retained earnings then there are negligible or no floatation costs.

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However if the companies issue debt or new stock to public then floatation costs can become important. NPV and Flotation Costs - Example Your company is considering a project that will cost $1 million. The project will generate after-tax cash flows of $250,000 per year for 7 years. The WACC is 15% and the firm’s target D/E ratio is .6 The flotation cost for equity is 5% and the flotation cost for debt is 3%. What is the NPV for the project after adjusting for flotation costs?

D/E = .6; Let E = 1; then D = .6 V = .6 + 1 = 1.6 D/V = .6 / 1.6 = .375; E/V = 1/1.6 = .625 PV =250,000 x PVIFA(15%,7) = 250,000 x 4.16= 1040,000 NPV = 1040,000-1000,000 = 40,000

fA = (.375)(3%) + (.625)(5%) = 4.25% PV of future cash flows = 1,040,000 NPV = 1,040,000 - 1,000,000/(1-.0425) = -4,386 ( for every 1 Re to be invested in the project, the firm has to raise 1/( 1-0.0425) Rs (> 1 Re) The project would have a positive NPV of 40,105 without considering flotation costs Once we consider the cost of issuing new securities, the NPV becomes negative Practice Problem 1 A corporation has 10,000 bonds outstanding with a 6% annual coupon rate, 8 years to maturity, a $1,000 face value, and a $1,100 market price. The company’s 100,000 shares of preferred stock pays a $3 annual dividend, and sell for $30 per share. The company’s 500,000 shares of common stock sell for $25 per share, have a beta of 1.5, the risk free rate is 4%, and the market return is 12%. Assuming a 40% tax rate, what is the company’s WACC? Solution to Practice Problem 1 MV of debt = 10,000 x $1,100 = $11,000,000 Cost of debt = YTM: T= 8 yrs ,coupon = 60,Face value =1000,Price =1100. Putting in the expression for price of bond and using trial and error, YTM =4.48% MV of preferred Stock = 100,000 x $30 = $3,000,000 Cost of preferred = 3/30 = 10%

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MV of common stock = 500,000 x $25 = $12,500,000 Cost of common stock = .04 + 1.5 x (.12 - .04) = 16%

Total MV of all securities = $11M + $3M + $12.5M = 26.5M

Weight of debt = 11M/26.5M = .4151 Weight of preferred = 3M/26.5M = .1132 Weight of common = 12.5M/26.5M = .4717

WACC = .4151 x .0448 x (1 - .4) + .1132 x .10 + .4717 x .16 = .0979 = 9.8%

Practice Problem 2 Floyd Industries stock has a beta of 1.15.The company just paid a dividend of $0.60 and the dividends are expected to grow at 5%. The expected return of the market is 11.5%, and Treasury Bills are yielding 5.5 %. The most recent stock price for Floyd is $54. A) Calculate the cost of capital using the DCF method B) Calculate the cost of capital using CAPM approach Solution to Practice Problem 2

a. Using the dividend discount model, the cost of equity is: RE = [(0.60)(1.05)/$54] + .05 RE = .0617 or 6.17%

b. Using the CAPM, the cost of equity is: RE = .055 + 1.15(.1150 – .0550) RE = .1240 or 12.40% Cost of Capital.. Practice Problem 3 A company has a debt equity ratio of 0.75. The company is considering a new plant that will cost $125 million to build. When the company issues new equity, it incurs a floatation cost of 8%.The floatation cost on new debt is 3.5%.What will be the actual cost of the plant if the company raises all equity externally? What if it typically uses 60% retained earnings? What if all equity investment is financed through retained earnings ?

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Cash flows What to discount ? Now that we are convinced that wise investment decisions should be based on the NPV rule, important question is ‘what to discount?’ while using the NPV rule. When you are faced with this problem , the following general rules should be adhered to :

i. Only cash flow is relevant, not profit ii. Estimate cash flows on an after tax basis

iii. Always estimate cash flows on an incremental basis iv. Consider incidental or side effects v. Consider working capital requirements

vi. Include opportunity costs vii. Do not include sunk costs

viii. Do not include Financing costs in cash flows ix. Adjust for inflation

Only Cash Flow is relevant

NPV depends on future cash flows where cash flow in its most naïve form is defined as ‘Cash received – cash paid out). But sometimes they are confused with accounting profits, which should not be the case because of the following reasons : First, Accountants consider profit ‘as it is earned’ rather than when the company actually receives the money from the customers. Similarly when an expense is incurred it is considered immediately as an expense although actual cash outflow towards that may happen later. Second, they sort cash outflows into two categories : current expenses and capital expenses. They deduct current expenses when calculating profits but do not deduct capital expenses. Instead they depreciate capital expenses over a number of years and deduct the annual depreciation charge from profits. As a result the upfront expenditure is not included as an expense at one go, while the later profits are reduced by the depreciation charge which is not a cash outflow at all--- this can have serious time value implications. Bottom line is cash flows are to be arrived at from accounting statement of profits. Consider incremental or relevant cash flows Cash Flows that need to be considered for taking a capital budgeting decision must be ‘relevant’ and on an ‘incremental’ cash flows

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Relevant Cash Flows : cash flows that occur because a project is undertaken. Cash flows that will occur whether or not we accept a project aren’t relevant. Defined in terms of the changes in or increments to the firm’s existing cash flows.

Consider after tax cash flows Cash flows should always be considered on an after tax basis and should be discounted at post tax cost of capital.

Also make sure that taxes should be discounted from their actual payment date ,not from the time when the tax liability is recorded in the firm’s books.( since cash flows should be recorded only when they occur ) Side effects/Erosion/Cannibalization With multi-line firms, projects often affect one another or existing products – sometimes helping, sometimes hurting. The point is to be aware of such effects in calculating incremental cash flows.

– Erosion – new project revenues gained at the expense of existing products/services.

Example : i) Suppose Kellogg’s brings out a new oat cereal, which will probably reduce existing product sales.

ii) Maruti brings out a new small car which will affect the sales of Maruti 800 or Alto.

In this case the cash flows from the new product should be adjusted downward to reflect lost profits on other lines.

Consider changes in Net working capital

Most projects need investments in net working capital in addition to long term assets. For example , a project will generally need some amount of cash on hand to pay any expenses that arise. In addition the project will need to invest in short term assets like accounts receivables, inventories , etc. This is partly financed by accounts payables but the balance needs to be supplied which represents the investment in net working capital. This has to be considered in the cash flow forecasts. When the project comes to an end, this net working capital gets recovered gradually. Inventories are sold, receivables are collected ,bills are paid and cash balances can be drawn down. These activities free up the net working capital originally invested.

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Thus the firm’s investment in net working capital is like a loan that the firm gives initially to the project and then recovers later as the project comes to an end. Changes in net working capital are to be adjusted from revenues and profit figures to arrive at cash flow figures for the project.

Opportunity costs should be considered Money that could be generated from an asset from the next best alternative use that is given up by taking up the project and using the asset in the project. Example: An old warehouse is to be converted into a selling outlet--- the next best alternative was to sell the warehouse @$10,000. which is given up if the project is taken. $10,000 is considered to be the opportunity cost.

Sunk Costs should not be considered Sunk cost – a cash flow already paid or accrued.

Like ‘spilled milk’. … already incurred and irreversible outflows. Because sunk costs are bygones, they cannot affect the decision to accept or reject a project and should not therefore be considered to be part of the project’s relevant cash flows. ( relevant cash flows are cash flows that happen only if the project is undertaken otherwise not) .

For example, an initial viability study by a consultant requires the fees of the consultant to be paid irrespective of whether the project is taken up or not. So that should not be considered as a relevant cost flow for the project.

Financing Costs should not be considered Firms typically calculate a project’s cash flows under the assumption that the project is financed only with equity.

However many projects are at least partially financed with debt and interest paid on funds borrowed despite being a cash outflow should not be a part of the relevant cash flows . Similarly dividends paid to equity holders (in the project) should also be not considered as relevant cash flows.

The argument is that from the cash flow identity we have Cash flow from assets (project)= cash flow to debtholders(in project) + cash flow to equity holders(in project). So cannot consider both sides of the identity . Consider either left hand side or right hand side , while the effect of leverage is reflected in the cost of capital as discussed above.

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The adjustments for debt financing are made in the discount rate rather than the cash flows. This is done by discounting the project’s cash flows by a weighted average(WACC) of the costs of debt, preferred stock and common equity adjusted for each component’s risk. The WACC is the rate of return necessary to satisfy all of the firm’s investors both stock holders and debt holders.

Therefore the projects cash flows discounted at WACC if it generates 0 NPV it just about satisfies everybody’s RRR. But if it earns a positive NPV the debtholders do not benefit , they still earn their RRR, but the equity holders gain more than their RRR, which again justifies that positive NPV projects create value for their equity holders.

As cost of debt is already embedded in the WACC, so subtracting interest payments from the project’s cash flows would amount to double counting interest costs.

This is different from accounting income . Accountants measure the profit available for stockholders, so interest expense is subtracted . But project cash flow is a cash flow available to investors , bondholders as well as stockholders, so interest expense is not subtracted.

Capital budgeting under inflation Let us consider a project with the following information about its cash flows ( Initial outlay =$100,000 and life =5yrs) RRR=9% and cash flow expression is CF=EAT+Deprcn Tax shield

Year 1 Year 2 Year 3 Year 4 Year 5

Expected cash inflows

$53000 $53000 $53000 $53000 $53000

Expected cash outflows

20000 20000 20000 20000 20000

EBT $33000 $33000 $33000 $33000 $33000

Multiplied by Tax rate=50%

16500 16500 16500 16500 16500

EAT $16500 $16500 $16500 $16500 $16500

Deprcn tax shelter $10000 $10000 $10000 $10000 $10000

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Expected net cash flows

$26500 $26500 $26500 $26500 $26500

Therefore NPV= Now let us consider the effect of inflation on this analysis. If expected inflation rate is 6% during the life of the project for all items considered in analysis, then both numerator and denominator will be influenced by it. Then NPV= Thus if numerator and denominator be influenced by the same rate of inflation then NPV remains same in both nominal and real terms. What happens if the inflation rate is different for inflow items and outflow items . The following table shows :

Year 1 Year 2 Year 3 Year 4 Year 5

Expected cash inflows(

$56180 $59551 $63124 $66912 $70927

Expected cash outflows

21400 22898 24501 26216 28051

EBT $34780 $36653 $38623 $40696 $42876

Multiplied by Tax rate=50%

17390 18327 19312 20348 21438

EAT $17390 $18327 $19312 $20348 $21438

Deprcn tax shelter $10000 $10000 $10000 $10000 $10000

Expected net cash flows

$27390 $28327 $29312 $30348 $31438

3074$100000$)09.1(

26500$5

1

=−∑=t

t

∑=

=−5

13074$100000$

)06.1()09.1()06.1(*26500$

ttt

t

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Now the NPV @(1.09*1.06 -1)=15.54% becomes :

Year Cash Flow Discount factor

@15.54% PV

1 $27390 0.8655 $23706

2 28327 0.7491 21220

3 29312 0.6483 19004

4 30348 0.5611 17029

5 31438 0.4857 15268

NPV= $96227-$100000 =-$3773

Thus the project that was acceptable without considering inflation now becomes un acceptable.

Cash Flow estimate for capital Budgeting A typical investment project will have three components of cash flows :

Initial investment Annual net cash flows Terminal cash flows

1)Initial Investment :

This should comprise the cost of the asset as well the transportation and installation costs. In our numerical examples this is our I.

Cash Flow estimate for capital Budgeting.. Contd.. 2)Net periodic cash flows : We denote this by NCF and we start with an assumption that all revenues(sales) are received in cash and all expenses are paid in cash

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a) Starting point : cash flows differ from profits in that profits consider interest expenses and that profits charge the initial capital expenditure on a periodic basis as depreciation which is not actually an outflow. It should therefore be added back to profit to arrive at the actual cash flow. cash flows should be considered on an after tax basis So a starting point for deriving an expression for after tax net cash flows ( without interest expense)is

NCF= Profit before interest – taxes +Deprn………………………….(1) Or, NCF = EBIT- EBIT*t + D = EBIT(1-t) + D ………(2)

b) Taking care of net working capital : If we now relax our initial assumption that all revenues are received in cash and all expenses are paid in cash and consider the realistic possibility that credit sales and credit purchases are possible , then we need to adjust expression (2) for that.

As receivables increase(decrease) cash flow should reduce(increase). So increase in receivables should be subtracted from( added to) revenues for computing actual cash receipts. Similarly as inventory increases(decreases) similar adjustments are made. As accounts payable decreases cash flow decreases( because some payment has been made to others), so decrease in accounts payables should be subtracted from( added to) profits to arrive at correct cash flow. Cash Flow estimate for capital Budgeting.. Contd.. Net periodic cash flows… contd.. Instead of adjusting the individual items we can simply adjust the change in net working capital from profit, which is given by ∆CA - ∆CL Increase in net working capital implies NCF should be reduced , so that should be subtracted from after tax profit, and decrease in net working capital added to after tax profit Therefore eqn (2) above can be extended to

NCF = EBIT(1-t)+ D- ∆NWC……………………….(3)

c) Arriving at Free cash flow expression by taking care of change in CAPEX:

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In addition to initial cash outlay, an investment project may also require some reinvestment of cash flow( for example in replacements of M/Cs etc) for maintaining the revenue generating ability of the project during its life. As a consequence net cash flow will be reduced by the cash outflow for additional capital expenditures(CAPEX). Therefore the net cash flow expression becomes finally:

NCF = EBIT(1-t) +D - ∆NWC- ∆CAPEX…………………………(4)

This is also sometimes called the Free Cash Flow and it is the cash flow that is available to service both bondholders and equity holders who have supplied respectively debt and equity.

3)Terminal cash Flows : Salvage value(SV) : market price that is available from an investment at the end of its life when it is sold. The cash proceeds net of taxes will be a terminal cash flow in the analysis. The tax treatment is as follows : – a. If SV <BV ( book value) : loss , can claim a tax credit on loss, Net

proceeds = SV-T(SV-BV) – b. if SV>BV but SV <OV( original value) then ordinary profit , taxed at

normal tax rate . Net proceeds = SV-T(SV-BV) – C. SV>OV, ordinary profit and capital gains . Net proceeds = SV-tax on

ordinary profit-tax on capital gains =SV-T(OV-BV)-tc(SV-OV) [tc is the capital gains tax rate while T is the normal corporate tax rate]

Example .. A capital budgeting problem Bharat Foods limited is a consumer goods manufacturing company. It is considering a proposal of marketing a new food product. The project will require an initial investment of Rs. 1 million in plant and machinery. It is estimated that the machinery can be sold for Rs 100,000 at the end of its economic life of 6 years. Assume that the loss of profit on the sale of the machine is subject to corporate tax rate. The company can charge an annual written down depreciation at 25% for the purpose of tax calculation. Assume that the company’s tax rate is 35% and the cost of capital is 18%. Table1 provides the investment data and the summarized profit and loss statement for the new product project. Estimate the project's cash flows and determine its NPV and IRR to conclude whether to go ahead or not.

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Table 1 : showing investment and profit and loss data for the new product project

year 0 1 2 3 4 5 6

1 Initial investment 1000

2 Depreciation 250 188 141 105 79 59

3 Accumulated Depreciation 250 438 578 684 763 822

4 Book value ( 1-4) 750 563 422 316 237 178

5 Net working capital 20 30 50 70 70 30 0

6 Salvage Value 100

7 Revenues 550 890 1840 2020 1680 1300

8 Expenses 300 472 958 1075 890 680

Table 2 : Cash Flow estimate and NPV and IRR calculation

year 0 1 2 3 4 5 6 1 Initial investment -1000 2 Revenues 550 890 1840 2020 1680 1300 3 Expenses 300 472 958 1075 890 680 4 Depreciation 250 188 141 105 79 59 5 EBIT=1-2-3 0 231 741 840 711 561 6 EBIT*(1-t)=(4)*0.65 0 150 482 546 462 364 7 EBIT*(1-t)+Depcn=5+3 250 337 623 651 541 424 8 Change in Net WC 20 10 21 20 0 -40 -30

9 NCF ( ignoring change in CAPEX)=6-7 -20 240 316 603 651 581 454

10 Afetr tax salvage value =[100-0.35(100-178) 127

11 Net cash flows=9+10 -20 240 316 603 651 581 581

12 Net cash flow considering initial investment -1020 240 316 603 651 581 581

NPV 582 IRR 34.91%

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Equivalent Annual Cost : Evaluating equipment options with different lives: Suppose we have a M/C A that costs $100 to buy and $10 per year to operate. It wears out and must be replaced every two years . M/C B costs $140 to buy and $8 per year to operate. It lasts three years and must then be replaced. Given that the suitable discount rate is 10%,how do we compare the M/Cs? PV of cost for the M/C A = -100 +(-10)/1.1+(-10)/1.12 = -117.36 PV of cost for the M/C B = -140 +(-8)/1.1+(-8)/1.12+(-8)/1.13= -159.89 Shall we say M/C A is cheaper than M/C B . Hence go for it ?

Not exactly , because B has a larger life than A.

Concept of Equivalent Annual Cost comes here.

EAC is the annuity amount which hypothetically if incurred every year would have the same present value of cost So for A, EACA x 2 yr annuity factor @10% = 117.36 Or EACA x (1-1/1.102)/0.10 = 117.36 Therefore EACA = 67.62. Similarly EACB = 64.29 Now B option seems to be more attractive

Capital Budgeting Under Uncertainty and risk analysis

Forecasting risk and approaches to tackle it

There are two main reasons for positive NPVs: (1) we have actually found a good project or (2) we have done a bad job of estimating NPV.

Similarly, a negative computed NPV might be reflective of a bad project or of a bad job of estimating NPV.

Computing an NPV is putting a market value on uncertain future cash flows. Projecting the future involves the potential for error and estimation of future cash flows is contingent on many factors as follows :

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Forecasted cash flows will depend on expected revenue and costs. Expected revenue will depend on sales volume and price. Sales volume will depend on market share and size. Again costs include variable costs, which depend on sales volume, and unit variable costs and fixed costs. Forecasting risk (or estimation of risk) is the possibility that errors in projected cash flows will lead to incorrect decisions

To tackle the situation we take help of approaches like the

– Sensitivity analysis

– Scenario analysis

– Simulation

– Breakeven Analysis

– Certainty Equivalent approach.

Sensitivity Analysis 1) Sensitivity Analysis :

A way to analyse how much the project’s NPV or IRR gets affected by a change in one of the affecting variables ( on revenue side or cost side) for at least three of four scenarios : pessimistic, expected and optimistic .

The process is then repeated for all the variables one by one and find out the most critical variable .

The greater the volatility in NPV in relation to a specific variable, the larger the forecasting risk associated with that variable, the more attention we want to pay to its estimation.

Sensitivity Analysis.. Example Consider the following project : The initial cost is $200,000 and the project has a 5-year life. There is no salvage. Depreciation is straight-line, the required return is 12%, and the tax rate is 34% Use the relation : Cash flow from assets=OCF(operating cash flow)+ NCS( change in CAPEX)+ change in NWC OCF= EBIT+Dep-Taxes = NI+Dep NCS = only initial investment during year 0

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ignore NWC Do a sensitivity analysis of the project’s NPV with the number of units sold as the decision variable.

Base Case Analysis Pro Forma Statement 1)Sales 6000*80=480000 2)VC 6000*60=360000 3)FC 30000 4)Depreciation 200000/5=40000 5)EBIT=1-2-3-4 50000 6)Taxes=0.34*5 17000 7)NI=EBIT(1-t)=5-6 33000

Cash Flows Year OCF=7 +4 NCS = CAPEX NCF 0 -200000 -200000 1 73000 73000 2 73000 73000 3 73000 73000 4 73000 73000 5 73000 73000

NPV $63,148.66 Sensitivity Analysis For Unit Sales Pro Forma Statement Base Lower Upper

Sales 480000 440000 (80 x 5500)

520000 (80 x 6500)

VC 360000 330000 (60 x 5500)

390000 (60 x 5500)

FC 30000 30000 30000 Depreciation 40000 40000 40000 EBIT 50000 40000 60000 Taxes 17000 13600 20400 NI 33000 26400 39600 Cash Flows Year 0 -200,000 -200,000 -200,000

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1 73000 66400 79600 2 73000 66400 79600 3 73000 66400 79600 4 73000 66400 79600 5 73000 66400 79600 NPV $63,148.66 $39,357.14 $86,940.19

Scenario Analysis Sensitivity Analysis assumes that the variables affecting the NPV are independent of each other. So it analyses the effect one by one. However there can be inter relationship between variables. For example sales volume and operating cost may both be related to price. A price cut may lead to high sales and thus low operating costs. Scenario analysis examines what happens to the NPV under different cash flow scenarios (caused by different combination of inputs)? At the very least look at: – Best case – high revenues, low costs – Worst case – low revenues, high costs – Normal case – somewhere in between

Scenario Analyses: Example Consider the same project : The initial cost is $200,000 and the project has a 5-year life. There is no salvage. Depreciation is straight-line, the required return is 12%, and the tax rate is 34% Use the relation : Cash flow from assets=OCF- NCS- change in NWC OCF= (EBIT+Dep-Taxes )= NI+Dep NCS = only initial investment during year 0 ignore NWC Calculate the project’s NPVs under the following scenarios:

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Base Lower Upper

Unit Sales 6000 5500 6500 Depreciation

Price per unit 80 75 85 40000 VC per unit 60 58 62 No NWC FC 30000 30000 30000 Base Case Analysis Pro Forma Statement Calculation Sales 480000 =6000 x 80 VC 360000 =6000 x 60 FC 30000 Depreciation 40000 =200,000/5

EBIT 50000 =(480-360-30-40) x1000

Taxes 17000 = 34% x 50000 NI 33000 =50000 - 17000

Year

Operating CF( = NI + Dep)

NCS( net Capital Spending )

NCF( cash flow from assets)(=OCF-NCS-Change in NWC)

0 200000 -200000

1

73000= 33000 + 40000 73000

2 73000 73000 3 73000 73000 4 73000 73000 5 73000 73000

NPV $63,148.66 Pro Forma Statement Base Worst Best Sales 480000 412500 552500 VC 360000 341000 377000 FC 30000 30000 30000 Depreciation 40000 40000 40000 EBIT 50000 1500 105500 Taxes 17000 510 35870 NI 33000 990 69630

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Cash Flows Year 0 -200,000 -200,000 -200,000 1 73000 40990 109630 2 73000 40990 109630 3 73000 40990 109630 4 73000 40990 109630 5 73000 40990 109630 NPV @12% $63,148.66 -$52,240.22 $195,191.62

Simulation Analysis..Monte Carlo Simulation

In Scenario Analysis, we let all the different variables change, but we consider only a few combinations.

In Sensitivity Analysis we let only one variable change, but we consider many values of that variable. We saw that sensitivity assumed independence among variables which was not true . Scenario analysis considered in a way considered inter relationship among variables because it varied all the variables together, but both approaches suffered from the fact that they do not consider the probability distribution of the affecting variables. A lot of subjective decision making is therefore involved in arriving at the values of the decision variables chosen.

Simulation is really just an expanded sensitivity and scenario analysis, which considers – Inter relationship among decision variables – Probability distribution of the decision variables

Monte Carlo simulation does not consider the project’s NPV as a single number but it gives the probability distribution of the NPV. This involves the following steps : Step 1: First identify the decision variables that influence the cash flows and hence the NPV. These could be market size, market share, price, variable costs, fixed costs, product life cycle, and initial investment and terminal value . Step 2 : Specify the relationship between the decision variables ( should be mathematical relationship identifiable by the simulation program). For example ,

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revenue depends on sales volume and price, sales volume is given by market size, market share, and market growth. Similarly operating expenses depend on the production, sales, fixed and variable costs. Step 3 : Indicate the probability distribution of each variable . Some variables will have more uncertainty than others. For example it is more difficult to predict price or market growth.

Step 4 : Now run the computer program ( Simtool of Excel which can be called as an add in excel compatible simulation softwares like Risk and Crystal ball) . The program should be able to select at random one value of each decision variable from its distribution and uses these values to calculate the project’s NPV. It does so for a large number of times ….. May be a 1000 times and stores each NPV value in its memory . From these stored values the program gives the distribution of NPV along with its expected value and standard deviation. The management may now take a decision based on these values . Limitations of Monte Carlo Simulation The approach helps in generating the probability distribution of the NPV of the project but it does not help in making the decision whether to accept or reject the project.

Like sensitivity and scenario analyses this approach also considers the risks of the projects in isolation but not in combination with other projects. A risky project may have a negative correlation with the other projects of the company and therefore accepting this project may reduce the overall risk of the firm.

Breakeven Analysis When we do a sensitivity analysis or a scenario analysis of a project which is risky, we are asking how serious it would be if sales and costs turned out to be worse than we forecasted. Managers sometimes change this question slightly and ask--- “HOW BAD SALES CAN GET BEFORE THE PROJECT BEGINS TO LOSE MONEY”. .. This exercise is known as breakeven analysis. Accounting Breakeven Accounting breakeven is the sales volume at which net income [i.e EBIT*(1-t)]= 0 Net Income =(Sales –VC-FC-D)(1-T) If net income =0, S-VC= FC +D

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Or Q(P-v)=FC+D ( sales = P*Q and VC=v*Q , v being the variable cost per unit of the qty sold) Or, Q = (FC+D)/(P-v) Implication of Accounting Breakeven: A project that just breaks even on an accounting basis has a payback period equal to its life and hence a negative NPV.( Why?) NCF=EBIT(1-t)+D-∆CAPEX-∆NWC If EBIT(1-t)=0, and we ignore ∆CAPEX and ∆NWC then , NCF= D Therefore,

Hence the project just pays back over its life.

Knowing the accounting breakeven we have the idea about the sales volume that is required to just recover the costs. If we already have firm commitments from buyers for a sales amount = the breakeven amount then we are confident that we can perhaps sell more. In that case forecasting risk will be smaller. If we are not confident about the volume, then we know that the estimates made are questionable. Accounting break-even can therefore be used as an early stage screening number

Cash Breakeven The sales volume that results in 0 operating cash flow (OCF) – Now NCF= 0 i.e EBIT(1-t) +D - ∆CAPEX-∆NWC

we ignore ∆CAPEX and ∆NWC then EBIT(1-t) +D =0 – (Q.P – Q.v – FC – D)*(1-T) + D =0 – i.e Q(P-v) = FC – DT/(1-T) – Q = [FC – DT/(1-T)]/(P-v) – If we ignore taxes, i.e T=0 this reduces to – Q = FC/(P-v)

Implication of Cash Breakeven : the project just recovers its own fixed cost and nothing else. The project never pays back , which implies that :

IDNCFN

ii

N

ii ==∑∑

== 11

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NPV is negative (= - I ) and IRR = -100%. (Why ?)

NPV = -I +0+0 +0 +….. = -I For IRR we take the reinvestment rate assumption i.e I*(1+IRR)^N= FV of all the cash flows at the end of the life of the project = C1*(1+IRR)^(N-1) + etc. = 0 since C1=C2=..CN= 0 i.e I*(1+IRR)^N= 0 Therefore IRR = -100%

Example Consider the following project. A new product requires an initial investment of $5 million and will be depreciated to an expected salvage of zero over 5 years. The price of the new product is expected to be $25,000 and the variable cost per unit is $15,000.The fixed cost is $1 million. a) What is the accounting break-even point each year? b) What is the operating cash flow at the accounting break-even point (ignore tax, ∆CAPEX and ∆NWC)? c) What is the cash break-even quantity? (Ignore tax, ∆CAPEX and ∆NWC) Solution : a)Depreciation = 5,000,000 / 5 = 1,000,000. Q = (1,000,000 + 1,000,000)/(25,000 – 15,000) = 200 units b) OCF = (S – VC – FC - D) + D – OCF = (200*25,000 – 200*15,000 – 1,000,000 -1,000,000) + 1,000,000 =

1,000,000 c) Q = ( FC) / (P – v) – Q = (1,000,000) / (25,000 – 15,000) = 100 units

Financial Breakeven Financial breakeven point is the sales volume for which the NPV of the project is zero. If we say that particular OCF for which this happens is = OCF* then, OCF * = EBIT (1-t)+ Depreciation = [Q(P-v)-FC –D](1-t) + D ( ignoring ∆CAPEX and ∆NWC )……………………(1)

The corresponding Q can be found from the above relation. If we ignore taxes, then more simplistically we can say that, Q = (FC + OCF*)/(P-v) …………..(2)is the financial breakeven sales volume.

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But how do we find OCF* ? OCF* is found out by using the following relation. Assuming OCF* to happen every year over the life of the project( say ‘t’ years) OCF*x PVIFA(r,t) = Initial investment=I Knowing OCF* then, we plug in its value in either the expression (1) or (2) above , to find the value of Q. Practice Problem 1 The Wettway sail boat corporation is considering whether to launch its new luxury sailboat. The selling price will be Rs.40,000 per boat. The variable costs are Rs.20,000 per boat. The fixed costs of the operation will be, Rs.500,000 per year. The initial investment will be Rs.3500,000. Wettway appointed a consultant who has projected a sales volume equal to 85 sail boats an year. Do a breakeven analysis using accounting, cash and financial breakeven and comment on the viability of the project to Wettway top management. Assume that Wettway uses straight-line depreciation over a life of 5 years. Ignore taxes. Assume a discount rate of 20% for finding the financial break even point.

Operating Leverage and degree of Operating leverage Fixed costs act like a ‘lever’ in the sense that a small percentage change in operating revenue can be magnified into a large percentage change in operating cash flow and NPV if the fixed cost is too high. Operating leverage measures the degree to which a project/firm is committed to fixed production costs and the degree to which the operating cash flow is affected by a change in operating revenue. A firm with low operating leverage will have low fixed costs compared to a firm with high operating leverage. It is measured by “degree of Operating leverage” ( DOL) given by :

DOL = % change in OCF / % change in Sales qty

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Based on the relation between OCF and Q, it can be shown that :

DOL = 1 + [FC*(1 – tc) – tCD]/OCF0

The DOL is expressed as: DOL = %∆OCF / %∆Q DOL = {[(OCF1 – OCF0)/OCF0] / [(Q1 – Q0)/Q0]} The OCF for the initial period and the first period is: OCF1 = [(P – v)Q1 – FC](1 – tC) + tCD OCF0 = [(P – v)Q0 – FC](1 – tC) + tCD

The difference between these two cash flows is: OCF1 – OCF0 = (P – v)(1 – tC)(Q1 – Q0) Dividing both sides by the initial OCF we get: (OCF1 – OCF0)/OCF0 = (P – v)( 1– tC)(Q1 – Q0) / OCF0 Rearranging we get: [(OCF1 – OCF0)/OCF0]/[(Q1 – Q0)/Q0] = [(P – v)(1 – tC)Q0]/OCF0 = [OCF0 – tCD + FC(1 – t)]/OCF0 Therefore , DOL = 1 + [FC*(1 – tc) – tCD]/OCF0

Ignoring taxes the relation gets simplified to

DOL =1+(FC/OCF) Practice problem 2 Consider the following project

– A new product requires an initial investment of Rs.5 million and will be depreciated to an expected salvage of zero over 5 years

– The price of the new product is expected to be Rs.25,000 and the variable cost per unit is Rs.15,000

– The fixed cost is Rs.1 million Suppose sales are 300 units. a) What is the DOL at this level? b) What will happen to OCF if unit sales increases by 20%? ( Ignore taxes)

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Solution : a)

– OCF = [Q(P-v)-FC-D]+D( Ignoring taxes)=(25,000 – 15,000)*300 – 1,000,000 = 2,000,000

– DOL = 1+FC/OCF( Ignoring taxes)=

– =1 + 1,000,000 / 2,000,000 = 1.5 b)

– Percentage change in OCF = DOL*Percentage change in Q

– Percentage change in OCF = 1.5(.2) = .3 or 30%

– OCF would increase to 2,000,000(1.3) = 2,600,000

Certainty Equivalents .. another way to adjust for risk We have seen so far that as the cash flows expected from a project are risky, a risk adjusted discount rate is used to discount the cash flows form the project to arrive at the PV and then NPV.

We generally make the important assumption that the risk of the cash flows remain constant throughout the life of the project and hence a constant rate is used. This may be an over simplistic assumption.

There is another way adjust for riskiness in the cash flows which is by converting the expected cash flows into Certainty equivalents and then discounting them by the risk free rate.

Example : Let us say there is a project involving the construction of an office building that you plan to sell next year for Rs. 420,000. Since the cash flow is uncertain, you discount at the risk adjusted discount rate of 12%. The risk free rate is 5%. The PV of the cash flow is 420,000/(1.12)= Rs.375,000 Now suppose a real estate company approaches you and enters into a contract to buy that building from you at the end of the year. This guarantee removes all uncertainty about the payoff. So you should be willing to accept a lower figure than the uncertain amount of Rs. 420,000.

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But by how much? If the PV of the cash flow from the building is 375,000 then this PV should be equal to the PV of the certain amount discounted at risk free rate ( Why discounted ? To take care of time value of money only). Therefore, PV=(Certain cash flow)/1.05=375,000 therefore Certain cash flow =Rs. 393,750

This cash flow of Rs.393,750 has exactly the same PV discounted at risk free rate as the risky cash flow of 420,000 discounted at risk adjusted rate.