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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:
- Learn why discounting at the WACC (or the project's financing cost) is only appropriate in limited circumstances.
- Learn how to calculate the WACC and asset betas.
- Understand how changes in capital structure affect the expected returns, required returns, and betas of the firm's securities.
- Understand how acceptance of a project affects the expected returns, required returns, and betas of the firm's securities.
- Learn how to estimate stock betas and how to use these estimates to calculate asset betas.
- Learn how to use the WACC and asset betas of comparable companies to determine the discount rate.
- Learn how to estimate beta in tough situations.
- Understand why projects with different degrees of risk over time cause special problems.
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:
- We calculated risk of the project’s cash flows (we used beta as a measure of risk)
- We used the CAPM to calculate the required (expected) return for financial assets with the same beta risk as the project’s cash flows. (Remember, with perfect, efficient, and in equilibrium markets, a financial asset’s expected rate of return equals its required rate of return.)
- We used the CAPM required (expected) return as the discount rate for the project’s cash flows The WACC (weighted-average cost of capital, or “company cost of capital”) can also be used in certain circumstances as the discount rate for a project’s cash flows.
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 :
- What are the debt and equity percentages?
- What is rD and rE? (Use CAPM)
- What is the WACC for ABC Inc.? When can the WACC be used as the discount rate for project cash flows? Assume the firm has two potential projects (projects A and B from the Chapter 7 and 8 notes). State 1 2 3 Economy Boom Normal Recession Probability 20% 60% 20% Risk-Free $105 $105 $ Market $143 $116 $ Project A $155 $135 $ Project B $15 $105 $ Project A has an expected (t = 1) cash flow of $120. proj A = 1.80887, discount rate = 20.1945% Project B has an expected (t = 1) cash flow of $93.2. proj B = -1.63175, discount rate = -8.7067% From the previous chapter, we determined that Project B had a positive NPV and Project A had a negative NPV
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.
- What are the new debt and equity percentages?
- What is the new rD(1)? What is rD(2)? (Use CAPM)
- What is the new beta for ABC's assets? (Hint: remember that there is no change in the composition or riskiness of ABC's assets.) What is the new WACC for ABC Inc.?
- What is the new rE? What is the new E? Is the new beta for ABC's equity consistent with the new rE and CAPM? Summary - Expanded Market Value Balance Sheet Market Value Beta Req. Return Market Value Beta Req. Return Asset 1 $300 0.90 12.56% D(1) $540 0 5% Asset 2 $600 0.27 7.268% D(2) $180 0. E $ Total $900 Total $ Should the cost of funds used to finance the project be considered in the analysis? No! The opportunity cost of capital for a project reflects where the funds are used, not where the funds come from. Example : Assume that Project A will be accepted and financed with a risk-free debt issue (and B rejected). Assume that the interest rate on the risk-free debt issue is 5%. Aside. Is it reasonable to assume that ABC Inc. can issue risk-free debt to finance a risky project? What are the expected after financing cash flows for Project A? 0 1 Project A (base case) cash flows Financing cash flows Project “after financing” cash flows What is the NPV of the project “after financing” cash flows? What about the IRR? However , the NPV of Project A is -$0.1618. Shouldn’t acceptance of the project be bad for the firm's stockholders? Perhaps the low interest rate on the financing changed the project NPV from negative to positive. Information on risk and required returns Average beta of existing assets: 0. Required return for the existing assets: 9.032% Beta of Project A: 1. Required return for Project A: 20.1945% Project A cash flows (boom = $155, normal = $135, recession = $40, expected t = 1 cash flow = $ Present value of Project A’s expected time 1 cash flow = $120 / 1.201945 = $99.
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)
- Beta : proj = m,proj [proj/ m] = ___________ We will discuss methods for estimating this from sample data later in the notes
- Market Risk Premium (rm - rf). What do you want? The expected return for the “market” portfolio minus the risk-free interest rate (i.e., the premium investors require to own the market portfolio). U.S. corporations should use the U.S. market risk premium As discussed, Brealey, Myers, and Allen suggest a U.S. market risk premium in the 5% - 8% range. We will use 8.4% in this class.
- Risk-Free Rate (rf). What do you want? The rate of return on a security with no risk. Here are some possibilities: Interest rate (yield to maturity) on corporate bonds. Interest rate (yield to maturity) on long-term (20-year) U.S. Treasury Bonds. Interest rate (yield to maturity) on medium-term (5-year) U.S. Treasury Bonds. Interest rate (yield to maturity) on short-term (30-day) U.S. Treasury Bills. Which one should we select? What’s wrong with the other three?
- Maturity risk premium. If evaluating a medium- or long-term project , we need to make an adjustment to the risk free rate used in the CAPM equation. (See footnote 8 in the textbook.) First some numbers (from Ibbotson Associates SBBI 1998 yearbook – data from 1926-1997): Long-term maturity risk premium: Avg. difference in returns for 20-year T-Bond and one-month T-Bill) = Medium-term maturity risk premium: Avg. difference in returns for 5-year T-Bond and one-month T- Bill) = Risk free rate for the long-term (20-year) project = Risk free rate for the medium-term (5-year) project =
- CAPM. Plug this information into the CAPM to determine a discount rate for the project. Make the maturity adjustment as needed Discount rate for Project A cash flows = ___________, Project NPV = ___________. Discount rate for Project B cash flows = ___________, Project NPV = ___________. Discount rate for Project C cash flows = ___________, Project NPV = ___________.
- Is the CAPM the best / most sophisticated method for determining a discount rate? No. The APT is an alternative method for determining the discount rate. More details on estimating the beta and discount rate for a project’s cash flows. For illustration purposes, we calculated the exact beta for a project’s cash flows (in Chapter 7 notes) based on project cash flows in different states of the economy. Since this information is rarely available, we need to estimate beta. What you need? The beta for the project (i.e., how risky is the project under consideration). General procedure - calculate the beta of the assets of a company whose assets are just as risky as the project cash flows. Use the CAPM to get the discount rate. What do you need? For a simple comparable company: (% debt) (debt beta) + (% equity) (equity beta) = asset beta So, we need four pieces of information: MV of debt, beta of debt, MV of equity, and beta of equity What’s available? Let’s start with the equity MV of Equity = _______________ Beta of equity = typically estimated using historical stock returns and market returns The historical stock beta is estimated by regressing the historical stock returns against the historical market returns. For example : regress monthly stock returns against monthly market returns using data from the last five years. Beta for the stock is equal to the slope of the regression line. Alpha for the stock is equal to the intercept of the regression line. (Average return for the stock when market return equals 0.) Graphical examples are on page 220 of the text.
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?
- U.S. corporation with a U.S. project – compute project beta with respect to U.S. market returns: us proj = us proj,m(us) [us proj/ m(us)]
- German corporation with a German project – compute project beta with respect to German market returns german proj = german proj,m(germany) [german proj/ m(germany)]
- How about a U.S. corporation with a German project? german proj = german proj,m(us) [german proj/ m(us)] Once the beta is calculated, use the home country’s risk free rate and market risk premium to determine the discount rate. Some questions: How does #2 compare to #3? Why do we compute betas in this way? When would we want to use a “world” market risk premium and a beta calculated with respect to a “world” market portfolio? Long-Term Risky Projects : Cash flows from long-term risky projects may be unduly penalized if their risk decreases over time. This is likely if uncertainty is resolved as the project progresses – see pages 230-231. Note - Properly understanding this example involves an understanding of certainty equivalents The effects of using the wrong discount rate : Assume that a project has two expected positive cash flows, one in one year ($50) and another in ten years ($180). The first cash flow is risky (beta = 1) and the second cash flow is risk free. Initial investment = $100. Using 8.4% as the market risk premium, 5% as a risk-free rate, and the CAPM, what is the NPV of the project? Correct Calculations: NPV = Consider the following incorrect calculations:
NPV = -$100 + $50/1.05^1 + $180/1.05^10 = $58.
NPV = -$100 + $50/1.134^1 + $180/1.134^10 = -$4.
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
- What is the WACC? How do you calculate the WACC?
- Be able to calculate the required return for the firm's equity, debt, and assets.
- Using the graph drawn in class, how can you determine if a project has a positive, negative, or zero NPV?
- Using the graph drawn in class, when will the use of the WACC as the discount rate give the same acceptance/rejection recommendation as using the SML to determine the discount rate? In what areas will the firm accept a bad project (or reject a good project) using the WACC as a discount rate? What implications does this have for the composition of a firm's assets?
- Know how to calculate the average beta for a firm's securities and assets.
- How does a change in capital structure affect the firm?
- Understand the intuition of why is it inappropriate to use the cost of financing as the discount rate for a project.
- How does acceptance of a project affect a firm?
- What "risk-free" rate should be used in the CAPM? What "market-risk premium" should be used in the CAPM? Where would you look to get current figures? What adjustment should be used to evaluate projects with long-term cash flows? What is the purpose of this adjustment?
- When should the U.S. market risk premium be used (as opposed to the German, or some other country’s market risk premium)? When should beta be calculated with respect to the US market (as opposed to the German market, or some other country’s market.)?
- How do you estimate the beta for a stock? Why is it better to use an industry beta than an individual stock beta? How do you convert stock betas to asset betas? How do you use this estimate to determine the beta (and discount rate) for a project’s cash flows?
- Understand the discussion in the section titled "Computational hints when it is difficult to determine project beta." A) What does it mean to "avoid fudge factors"? B) Why do cyclical cash flows tend to have positive betas? Why do counter-cyclical cash flows tend to have negative betas? What if project cash flows are uncorrelated with market factors? C) Remember that high variance does not necessarily mean a high positive beta. D) What is the relationship between fixed costs and betas?
- Understand why high (variance) risky foreign projects can have a low beta risk.
- Understand the discussion on "long-term risky projects." Be able to calculate the net present value of a long-
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%
