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An in-depth analysis of how changes in capital structure and acceptance of projects affect the expected returns, required returns, and betas of a firm's securities. It covers topics such as estimating stock betas, using the wacc and asset betas of comparable companies to determine the discount rate, and the implications of incorrectly using the wacc instead of the sml to evaluate projects.
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Chapter 9 - Capital Budgeting and Risk In this chapter we will further develop our understanding of how to determine the discount rate for a project’s cash flows. In particular we will:
Chapter 9 - Capital Budgeting and Risk Summary so far : Chapter 1 – Why most large businesses operate as a corporation Chapter 2 – Overview of investment decisions (cash flows, risk, opportunity cost of capital) as they relate to the objective of the firm Chapter 3 – Time value of money Chapter 5 – NPV should be used to make investment decisions Chapter 6 – How to calculate project cash flows Chapter 7 & 8 – Risk and return and the CAPM Chapter 9 is a continuation of Chapters 7 and 8. The ultimate goal is to answer the question: What discount rate should the corporation use to evaluate a project? Note: In this chapter, we will assume financial markets are perfect, efficient, and in equilibrium. What do we want? Project cash flows should be discounted at the project’s opportunity cost of capital Definition : The opportunity cost of capital for the cash flows of a project is the expected rate of return for investments in the financial markets that have the exact same amount of risk as the project’s cash flows. Risk-free cash flows. Use the risk-free interest rate. The current one-month Treasury Bill rate is a good estimate of the risk free rate. (We have been using 5% as the risk free rate.) What about risky cash flows? From Chapters 7 and 8:
The WACC is the required return (and expected return) for a portfolio of all of the firm's securities. The WACC tells us what it will cost the firm (on average) to raise new capital to fund a project. In this chapter, we ignore income taxes. Assuming no income taxes: rassets = WACC = (debt %) (rD) + (equity %) (rE) Important! The effect of income taxes on the WACC is discussed in Chapter 19. The with tax formula is: rassets = WACC = (debt %) (1 – T) (rD) + (equity %) (rE) I use the terms WACC and company cost of capital interchangeably. The book appears to only use WACC as the with-tax formula above. Example of the calculation of the WACC : ABC Inc.’s market value balance sheet. Asset (1) has a market value of $300 and a beta of 0. Asset (2) has a market value of $600 and a beta of 0. Debt has a market value of $540. The debt is risk free. Beta = _______ Equity has a market value of $360. The beta of the equity is 1. Current firm market value = $900. The risk-free interest rate is 5%. The expected (required) return for the market is 13.4%. (The market risk premium is 8.4%.) Questions :
Region 1: Region 2: Region 3: Region 4: How do the mistakes affect the company? Risk Expected return Value (at time 0) When (if ever) is it proper to use the WACC as the discount rate for a project’s cash flows? The average beta risk for the firm's assets The average beta for a firm’s assets equals the weighted-average beta for each of the firm's individual assets assets = (asset(1) %) (asset (1)) + (asset(2) %) (asset (2)) +... + (asset(N) %) (asset (N)) It is also equal to the weighted-average of the betas of the firm's securities. assets = (debt %) (D) + (equity %) (E) What is the average beta for the assets of ABC Inc.? assets = Use the CAPM to calculate the required return for the firm’s assets. Using CAPM: rassets = Therefore , the WACC for ABC Inc. can be used to discount a project with a beta equal to _______. Describe what this type of project looks like. How often would you expect to find such a project? Expanded Market Value Balance Sheet Market Value Beta Req. Return Market Value Beta Req. Return Asset 1 D Asset 2 E Total Total Some intuition concerning why Project A is a bad project and Project B is a good project Why is Project A unacceptable even though it has a 20% expected return? With Project B, the firm invests $100 and receives, on average, $93.20 in one year. The IRR for Project B is negative 6.8%. Why should the firm accept Project B even if it is expected to lose money? Can you think of another good “investment” that companies (or individuals) make that has a negative expected return? How does a change in capital structure affect the WACC of a corporation?
Example : Assume that ABC Inc. issues $180 of additional debt. Because ABC is more highly levered, the newly issued debt has a beta of 0.4. (The existing debt remains risk-free.) Assume the $180 is used to repurchase $ of ABC's stock. There is no change in ABC's assets.
Conclusion - Since the expected return on the debt is equal to its required return (5%), the NPV of the financing is zero. Therefore, the financing choice can be disregarded in the capital budgeting decision. 0 1 NPV Project A (base case) cash flows Financing cash flows Project “after financing” cash flows Does the same hold true if we had financed with equity in the above example? Yes Is the financing NPV always $0? No. Will we talk about this more in Chapter 9? No. Some “real world” information on the determination of the risk-adjusted discount rate using the CAPM. First – an example to work with. Our goal is to calculate the NPV of the following projects. Project A: $1000 initial investment, $1250 expected cash flow in one year Project B: $1000 initial investment, $250 per year for years 1 – 4, $1250 expected cash flow at year 5 Project C: $1000 initial investment, $250 per year for years 1 – 19, $1250 expected cash flow at year 20 Assume each cash flow for each of the three projects has the following risk: m,proj = 2/3, proj = 0.60, m = 0. How do we determine the discount rate for these projects? According to the CAPM equation, the discount rate is: r = rf + (MRP)
high returns in periods when the market has high returns and vice versa.) What about projects with counter-cyclical cash flows? ii) Projects with a high percentage of fixed costs with cyclical cash flows tend to have high positive betas. (Similar to stock betas increasing when leverage is high.) iii) High project standard deviation does not necessarily mean high positive beta. Remember the formula for the project's beta is proj = proj,m [proj/ m]. Need to estimate m,proj! Skip discussion on Certainty Equivalents (only skim section 9.4) Final thoughts Income taxes. Remember that we have been ignoring income taxes in this chapter’s discussion of the determination of the discount rate. A detailed discussion is included in Chapter 19. Foreign projects can have a very high variance of returns, but a low beta. Why? How do you compute beta for a foreign project?
Observation : Compare the relative impact of using the wrong discount rates.
Selected quiz questions from the textbook for Chapter 9 : 9-1, 9-3, 9-5, 9-6, 9-7. Chapter 9 Review Questions
Chapter 9 Practice Problems Problems 1 – 5 use a common set of assumptions:
1. Assume that the risk-free rate is 5% and the market risk premium is 8.4%. If XYZ Inc. has $700 of debt (beta = 0.2) and $300 of equity (beta = 1.5), what is the WACC for this firm? 9.956% 2. What is the average beta for XYZ's securities? 0.5900 (Cross-check your answer with the CAPM.) 3. Assume that XYZ has three assets: a risk-free Treasury Bill (market value = $100), a risky corporate bond of another company (beta = 0.4, market value = $200), and an existing project (beta = ____, market value = $700). A) What is the beta of the existing project? 0. B) What is the required return for the existing project? 11.12% C) What is the average required return for the firm's assets? 9.956% 4. Assume that XYZ Inc. issues $100 of debt and uses the proceeds of the debt issue to retire $100 of its stock. This new debt has a beta of 0.4. The beta of the existing debt stays at 0.2. Assume that the composition and riskiness of the firm's assets remains the same. Compute the following: A) Required rate of return for the firm's new debt. 8.36% B) Average beta for the firm's assets. 0. C) WACC for the firm. 9.956% D) Required rate of return for the firm's equity. 22.22% E) Beta for the firm's equity. 2. 5. Assume that XYZ Inc. has $700 of debt and $300 of equity (as described in the original problem). XYZ Inc. issues $100 of new stock and uses the proceeds of the stock issue to invest in Project B. (Project B is described in the Chapter 7 notes, has a beta of -1.63175, a PV of future cash flows of $102.0885, and a NPV of $2.0885.) Assume that the beta of the $700 of debt remains at 0.2. Compute the following: A) Market value of the firm and equity. $1102.0885 and $402.0885 respectively B) Average asset beta. 0.38420 (Notice the risk reducing benefits of Project B!) C) WACC. 8.2272% D) Required rate of return for the firm's equity. 10.9209% E) Beta for the firm's equity. 0.70486. 6. Using of the following information, what is the average beta for Green Inc.’s assets? 1. Green Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $500 1.2 15.080% Debt #1 $500 0 5.000% Asset #2 $300 0.5 9.200% Debt #2 $100 0.3 7.520% Asset #3 $200 2 21.800% Equity $400 2.8 28.520% Total $1,000 Answer $1, 7. Using of the following information, what is the beta for Blue Inc.’s equity? 1. Blue Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $400 0.7 10.880% Debt #1 $200 0 5.000% Asset #2 $300 1.5 17.600% Debt #2 $100 0.1 5.840% Asset #3 $300 1.9 20.960% Equity $700 Answer
Total $1,000 1.3 15.920% $1,000 1.3 15.920%
8. Using of the following information, what is the average beta for the AAA Inc.’s assets? 0. AAA Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $500 Debt #1 $250 0.000 5.000% Asset #2 $200 Debt #2 $350 0.400 8.360% Asset #3 $300 Equity $400 2.000 21.800% Total $1,000 Answer $1, 9. Using of the following information, what is the beta for the BBB Inc.’s equity? 2. BBB Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $200 0.5 9.200% Debt #1 $400 0.000 5.000% Asset #2 $300 1 13.400% Debt #2 $180 0.200 6.680% Asset #3 $500 1.5 17.600% Equity $420 Answer Total $1,000 $1,000 1.150 14.660% 10. Using of the following information, what is the WACC for Alpha Inc.? (Assume that the risk free rate = 5%, the market risk premium = 8.4%, and the CAPM is used to determine required returns.) 12.392% Alpha Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $500 1.00 Debt #1 $500.00 0. Asset #2 $400 0.50 Debt #2 $200.00 0. Asset #3 $100 1.80 Equity $300.00 2. Total $1,000 0.88 $1,000.00 Answer 11. Using of the following information, what is the required return for the Zeta Inc.’s equity? (Assume that the risk free rate = 5%, the market risk premium = 8.4%, and the CAPM is used to determine required returns.) 20.96% Zeta Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $300 1.20 15.08% Debt #1 $300.00 0.00 5.00% Asset #2 $500 0.70 10.88% Debt #2 $200.00 0.20 6.68% Asset #3 $200 1.40 16.76% Equity $500.00 Answer Total $1,000 0.99 13.316% $1,000.00 0.99 13.316% 12. Using the following information, what is the beta of the firm’s equity? 2. Market Value Beta Required Return Market Value Beta Required Return Asset #1 $400 1.400 16.76% Debt $580 0.000 5.00% Asset #2 $600 0.800 11.72% Equity $
13. Using of the following information, what is the beta for Brown Inc.’s equity? 1. Brown Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $500 0.20 6.680% Debt #1 $400 0.00 5.000% Asset #2 $300 1.40 16.760% Debt #2 $100 0.30 7.520% Asset #3 $200 2.00 21.800% Equity $500 Answer Total $1,000 0.92 12.728% $1,000 0.92 12.728% 14. Using of the following information, what is the required return for Brown Inc.’s equity? (Assume that the risk free rate = 5%, the market risk premium = 8.4%, and the CAPM is used to determine required returns.) 20.204% Brown Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $400 0.20 6.680% Debt #1 $400 0.10 5.840% Asset #2 $250 2.00 21.800% Debt #2 $100 0.20 6.680% Asset #3 $350 1.10 14.240% Equity $500 Answer Total $1,000 0.965 13.106% $1,000 0.965 13.106% 15. Using of the following information, what is the beta for XYZ Inc.’s equity? 1. XYZ Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $300 0.4 8.360% Debt #1 $400 0.1 5.840% Asset #2 $500 0.8 11.720% Debt #2 $200 0.4 8.360% Asset #3 $200 1.5 17.600% Equity $400 Answer Total $1,000 0.820 11.888% $1,000 0.820 11.888% 16. Using of the following information, what is the required rate of return for XYZ Inc.’s equity? (Assume that the risk free rate = 5%, the market risk premium = 8.4%, and the CAPM is used to determine required returns.) 22.64% XYZ Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $400 0.2 6.68% Debt #1 $300 0.1 5.84% Asset #2 $100 0.8 11.72% Debt #2 $200 0.4 8.36% Asset #3 $500 2.0 21.80% Equity $500 Answer Total $1,000 1.160 14.744% Total $1,000 1.160 14.744% 17. Refer back to the facts of the previous problem. Assume that the beta risk of debt #1 was 0 (instead of 0.1), and the required rate of return was 5.0% (instead of 5.84%). All the other numbers presented in the previous problem stay the same. How do these changes in assumption affect your answer to the previous problem? A. The required rate of return for equity is higher than the correct answer to the previous problem. (Correct) B. The required rate of return for equity is the same as the correct answer to the previous problem. C. The required rate of return for equity is lower than the correct answer to the previous problem.
18. Using of the following information, what is the beta for XYZ Inc.’s equity? 2. XYZ Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $900 0.200 6.680% Debt #1 $1,100 0.100 5.840% Asset #2 $600 1.300 15.920% Debt #2 $400 0.400 8.360% Asset #3 $500 1.500 17.600% Equity $500 Answer Total $2,000 0.855 12.182% Total $2,000 0.855 12.182% 19. Refer back to the facts of the previous problem. Assume that the market value of debt #1 was $1,200 (instead of $1,100) and the market value of the equity was $400 (instead of $500). All the other numbers presented in problem #1 stay the same. How do these changes in assumption affect your answer to problem #1? A. The beta for equity is the same as the correct answer to problem #1. B. The beta for equity is higher than the correct answer to problem #1. (Correct) C. The beta for equity is lower than the correct answer to problem #1. 20. Assume that the risk free rate = 5%, the market risk premium = 8.4%, and the CAPM is used to determine required returns and discount rates. What is the WACC for AAA Inc.? 12.644% AAA Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $900 0.800 11.720% Debt #1 $1,200 0. Asset #2 $700 0.600 10.040% Debt #2 $300 0. Asset #3 $400 1.700 19.280% Equity $500 3. Total $2,000 Total $2,000 Answer 21. What is the equity beta for BBB Inc.? 1. BBB Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $1,200 0.600 10.040% Debt #1 $600 0.000 5.000% Asset #2 $500 0.800 11.720% Debt #2 $400 0.200 6.680% Asset #3 $300 1.000 13.400% Equity $1,000 Answer Total $2,000 0.710 10.964% Total $2, 22. What is the equity beta for AAA Inc.? 1. AAA Inc. Assets Market Value Beta Req. Return Liabilities / Equity Market Value Beta Req. Return Asset #1 $800 0.7 10.88% Debt #1 $700 0.1 5.84% Asset #2 $1,200 0.8 11.72% Debt #2 $800 0.2 6.68% Asset #3 $500 1.3 15.92% Equity $1,000 Answer Total $2,500 0.868 12.2912% Total $2,
Similar to the discussion in class, where does Project X plot on the graph described in class? Above the WACC, above the SML
28. Project X requires an initial investment of $100 and has a time one expected cash flow of $112. Therefore, its expected return (based on the $100 initial investment) is 12%. The company’s WACC is 10%. The company correctly uses the CAPM to determine a discount rate. Using this discount rate, the project NPV is -$1.00. Similar to the discussion in class, where does Project X plot on the graph described in class? Above the WACC, below the SML 29. Assume a firm decides whether to accept or reject a project based on its NPV. That is, it accepts projects with positive NPVs and rejects projects with negative NPVs. To calculate the NPV, this firm uses its WACC (equal to 10%) as the discount rate for all projects. (Assume, however, that the correct discount rate should be based on the CAPM security market line.) This firm is faced with the following two projects. Determine in each case whether the firm (using the WACC as the discount rate) will make a mistake in its project selection / rejection decision. (The risk free rate is 5% and the market risk premium is 8.4%.) Project A (beta = 0.2) Time 0 1 Expected Cash Flows -$100 $ A. The firm will make a mistake by accepting this project when it really has a negative NPV. B. The firm will make a mistake by rejecting this project when it really has a positive NPV. (Correct) C. The firm will not make a mistake with this project, i.e., it will make the correct decision. Project B (beta = 1.5) Time 0 1 Expected Cash Flows -$100 $ A. The firm will make a mistake by accepting this project when it really has a negative NPV. B. The firm will make a mistake by rejecting this project when it really has a positive NPV. C. The firm will not make a mistake with this project, i.e., it will make the correct decision. (Correct) 30. The following are base-case, financing, and after-financing cash flows for a project. Discount rates are given in the last column. Based on this information, and using the procedure discussed in Chapter 9, what is the “after-financing” NPV for the project? $24. 0 1 Discount Rate Project “base-case” cash flows -$3500 $4240 18.0% Financing cash flows $3500 -$3790 6.2% Project “after financing” cash flows $0 $ 31. Assume that the annual yield for a one-month T-Bill is 5%. The five-year Treasury Note has a yield of 6.8%. Using a five-year maturity premium of 1% and a market risk premium of 8.4%, what discount rate should the firm use for a five-year project (with a beta of one)? 14.2% 32. Using the following information, what is the discount rate for a five-year project? 15.80% The yield-to-maturity for one-month Treasury Bills is currently (as of today’s Wall Street Journal) = 2.20% The yield-to-maturity for a 5-year Treasury bond is currently (as of today’s Wall Street Journal) = 4.80% The medium-term maturity risk premium (i.e., the average difference in yields between 5-year Treasury Bonds and one-month Treasury Bills as calculated by Ibbotson Associates) = 1.6%. The beta for the year 5 cash flow = 1. The market risk premium = 8.4%
33. Consider the following information: Project beta = 1. Market risk premium = 8.4% From the latest issue of the Wall Street Journal One-month Treasury Bill yield-to-maturity = 1.75% Five-year Treasury Bond yield-to-maturity = 5.10% From the latest issue of the brown book by Ibbotson Associates Average annual return since 1926 from investment in one-month Treasury Bills = 3.8% Average annual return since 1926 from investment in five-year Treasury Bonds = 5.4% Medium-term (5-year) maturity risk premium = 5.4% - 3.8% = 1.6% Using the CAPM and the type of analysis we discussed in Chapter 9, what discount rate should be used for a 5-year project? 16.1% 34. Consider the following information: Project beta = 1. Market risk premium = 8.4% From the latest issue of the Wall Street Journal One-month Treasury Bill yield-to-maturity = 1.05% Five-year Treasury Bond yield-to-maturity = 3.98% From the latest issue of the brown book by Ibbotson Associates Average annual return since 1926 from investment in one-month Treasury Bills = 3.8% Average annual return since 1926 from investment in five-year Treasury Bonds = 5.4% Medium-term (5-year) maturity risk premium = 5.4% - 3.8% = 1.6% Using the CAPM and the type of analysis we discussed in Chapter 9, what discount rate should be used for a 5-year project? 12.46% 35. Consider the following information: Project beta = 1. Market risk premium = 8.4% From the latest issue of the Wall Street Journal One-month Treasury Bill yield-to-maturity = 0.95% Five-year Treasury Bond yield-to-maturity = 2.73% Historical information from Ibbotson Associates Average annual return since 1926 from investment in one-month Treasury Bills = 3.8% Average annual return since 1926 from investment in five-year Treasury Bonds = 5.4% Medium-term (5-year) maturity risk premium = 5.4% - 3.8% = 1.6% Using the CAPM and the type of analysis we discussed in Chapter 9, what discount rate should be used for a 5-year project? 12.05%