Sessions 11 and 12: Capital Budgeting and Risk

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1 6049 Lecture Slides, Academic Year 2010/2011 Sessions 11 and 12: Capital Budgeting and Risk Hannes Wagner

2 Topics Covered Cost of capital for projects and firms Measuring the cost of equity Setting discount rates when you do not know Beta Certainty equivalents Discount rates for international projects Expectations This material is closely tied to chapters 8 and 9 but less technical. Literature BMA Chapter

3 Company Cost of Capital A firm s value can be stated as the sum of the value of its various assets You already knew this - recall value additivity of present values! Firm value PV(AB) PV(A) PV(B)

4 Company Cost of Capital A company s cost of capital can be compared to the CAPM required return. Take Microsoft as an example: Required return SML Company Cost of Capital (Microsoft) Project Beta

5 Examples of Company Cost of Capital Category Speculative ventures 30% New products 20% Expansion of existing business Cost improvement, known technology 10% Discount Rate 15% (Company COC)

6 Debt and COC r equity r ( r r ) f equity COC r portfolio r assets m f E, D, and V are all market values of Equity, Debt and Total Firm Value Then, the return on the company s assets is simply the weighted average of the expected returns on the firm s securities: WACC r assets WACC after tax (1 T c ) r r debt debt D r V D V r equity equity E V E V

7 Expected return (%) Capital Structure & COC Expected Returns and Betas prior to refinancing 20 R equity =15 R assets =12.2 R rdebt = debt assets equity

8 Measuring Betas The SML shows the relationship between return and risk CAPM uses Beta as a proxy for risk Other methods can be employed to determine the slope of the SML and thus Beta Regression analysis can be used to find Beta E.g. monthly returns (60 months) for the firm and the market

9 Measuring Betas Intel Computer Price data: July 1996 June R 2 =.29 = 1.54 Slope determined from plotting the line of best fit. R 2 : percentage of variation of dependent variable explained by independent variable(s) Intel return, % Market return, %

10 Measuring Betas Intel Computer Price data: July 2001 June 2006 R 2 =.30 = Inte el return, % Slope determined from plotting the line of best fit How to run this regression yourself? One way is to use Excel instructions are here: Market return, %

12 Eti Estimated tdbt Betas Burlington Northern Beta equity Standard Error Santa Fe Canadian Pacific CSX Kansas City Southern Norfolk Southern Union Pacific Industry portfolio Standard error: the estimated standard deviation of the error made in estimation, estimates the standard deviation of the difference between the measured/estimated and the true parameter values

13 BMA Question 13 The following table shows estimates of the risk of two well-known Canadian stocks A) What proportion of each stock s risk was market risk and what proportion was unique risk?

14 BMA Question 13 CONT B) What is the variance of Alcan, what is the unique variance? C) What is the confidence level on Canadian Pacific s beta? D) If the CAPM is correct, what is the expected return on Alcan? Assume a risk-free rate of 5% and an expected market return of 12%. E) Suppose next year the market provides a zero return. Knowing this, what return would you expect from Alcan?

15 Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER 10 (High betas) (Low betas) Source: Sharpe and Cooper (1972)

16 Company Cost of Capital A simple approach: The company cost of capital is based on the average beta of the assets The average Beta of the assets is based on the % of funds in each asset Example 1/3 New Ventures beta=2.0 1/3 Expand existing business beta=1.3 1/3 Plant efficiency beta=0.6 AVG beta of assets =

17 Capital Structure Capital Structure - the mix of debt & equity within a company Expand CAPM to include CS becomes R = r f + ( r m -r f ) R equity = r f + (r m - r f ) (We could also have used APT)

18 When do you do not have beta estimates Avoid fudge factors Do not add unknown risk factors to the discount factor. Adjust cash flows instead (if you have to). Think about the determinants of asset betas. Cyclicality Operating leverage Don t be fooled by diversifiable risk Correlations with the market or macro factors?

19 Avoid fudge factors - Example Project Z generates one cash-flow, is regarded as average risk and discounting is at 10% C ,000,000 PV 909,100 1 r 1.1 You discover that engineers are running behind schedule. There is now a small chance that the project may not work. How to update r? Don t! Unbiased forecasts of cash flows:

20 Avoid fudge factors - Example

21 Asset Betas revenue fixed cost PV(fixed cost) PV(revenue) variable cost PV(variable cost) PV(revenue) asset PV(asset) PV(revenue)

22 Cyclicality of asset betas Unique versus systematic risk! Cyclical firms firms whose revenues and earnings are strongly dependent on the stage of the business cycle tend to be high beta firms. These firms demand a higher rate of return from investments. But: Gold prospector firms do not!

23 Asset Betas and Operating Leverage erage PV ( fixedcost ) PV (var iablecost ) revenue fixedcost var PV ( revenue) iablecost PV ( revenue) asset assets revenue PV ( asset) PV ( revenue ) PV(revenue)-PV(variable cost) PV(asset) revenue 1 PV(fixed cost) PV(asset)

24 Risk,DCF and CEQ We introduce certainty equivalent cash flows: PV C CEQ t t ( 1 r) t (1 r ) f t

25 Two ways to calculate PV

26 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? Project r r B( r r ) Year Cash Flow 12% f m 6.75(8) 12% f Total A PV

27 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? Project A Year Cash Flow 12% Total PV r rf B ( rm r 6.75(8) 12% f ) Now assume that the cash flows change, but are RISK FREE. What is the new PV?

28 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? Project A Project B Year Cash Flow 12% Year Cash Flow 6% Ttl Total PV Total PV Since the 94.6 is risk free, we call it a Certainty Equivalent of the

29 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project? DEDUCTION FOR RISK Year 1 Cash Flow 100 CEQ 94.6 Deduction for risk

30 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? The difference between the 100 and the certainty equivalent (94.6) is 5.4% this % can be considered the annual premium on a risky cash flow Risky cash flow certainty equivalent cash flow

31 Risk,DCF and CEQ Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of.75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV? Year Year Year

32 BMA Question 21 A project has the following forecasted cash flows The estimated project beta is 1.5. The market return is 16% and the risk free rate is 7%. A) Estimate the opportunity cost of capital and project NPV (using the same rate to discount each cash flow)

33 CONT B) What are the certainty-equivalent cash flows in each year? C) What is the ratio of the certainty-equivalent cash flow to the expected cash flow in each year? D) Explain why this ratio declines

34 When you cannot use a single discount rate EXAMPLE A firm is considering going ahead with a pilot product. The preliminary phase will take one year and cost $125,000. There is a 50% chance the product is successful. If yes, a $1 million plant will generate in perpetuity annual cash flows of $250,000 after tax. If no, the project will have to be dropped. Expected cash flows are C0 125 C 1/ 2( 1, 000) 1/ 2(0) C 1/ 2(250) 1/ 2(0) 125 2,3,...,

35 When you cannot use a single discount rate The project is considered very risky and discounted at 25% rather than the company standard 10%: NPV t Is this correct? If the test phase fails, there is no risk (and no project). If it succeeds, the project risk may be similar to the firm s previous risky projects. Thus, we could view the project as offering an expected payoff of ½(1,500)+1/2(0)=750 at t=1 for an initial investment of 125. The certainty equivalent will be less than 750 but it is unlikely to be very small. Assume it is half of the CF, then with r f =7%: CEQ1 1/ 2(750) NPV C r 1.07 f t2

36 International Risk Ratio of Standard Deviations Correlation Coefficient Beta Argentina Brazil China Egypt India Indonesia Mexico Sri Lanka Turkey Ratio - Ratio of standard deviations, country index vs. S&P composite index

37 Do Costs of Capital Differ Between een Countries? We already know that interest rates differ between countries. Does this generate arbitrage opportunities? Don t forget interest rates are quoted in national currencies, units therefore cannot be compared. But what if you measure interest in real terms? Carry trades Borrowing in one currency, investing in another currency Attached FT article Yen Low Sparks Carry Trade Alert

38 Review material Chapter 10 BMA quiz questions (answers are in Appendix B) Chapter 10 online quiz questions ( answers are provided online) Selected BMA exercises As needed: additional Ch. 10 practice questions

Title: Risk, Return, and Capital Budgeting Speaker: Rebecca Stull Created by: Gene Lai. online.wsu.edu

Title: Risk, Return, and Capital Budgeting Speaker: Rebecca Stull Created by: Gene Lai online.wsu.edu MODULE 9 RISK, RETURN, AND CAPITAL BUDGETING Revised by Gene Lai 12-2 Risk, Return and the Capital