fin 310 exam 2

Q8.P15. (20 points) Consider the following two mutually exclusive projects: Look at the Chapter 8 Example Exam Question sheet for the chart Whichever project you choose, if any, you require a 13 percent return on your investment.

(a) If you apply the payback criterion, which investment will you choose? Briefly why? (b) If you apply the NPV criterion, which investment will you choose? Briefly why? (c) If you apply the profitability index criterion, which investment will you choose? Briefly why? (d) Based on these answers, which project will you finally choose? Briefly why? (e) Is the IRR on project A larger or smaller than the required return? Briefly describe how you can tell.

11.21. Which of the following statements is FALSE?

A. Asset-specific risks can be easily diversified with highly correlated assets in a portfolio B. Asset-specific risks can be easily diversified with numerous assets in a portfolio C. Bearing risk is rewarded with higher expected returns D. Only market-wide risks, not asset-specific risks, should earn rewards A.

11.24. Fill in the blanks: Standard deviation measures ______ risk, while beta measures ______ risk.

A. Asset-specific; market-wide B. Market-wide; total C. Total; market-wide D. Total; asset-specific C.

12.MC32. A firm uses its weighted average cost of capital to evaluate the proposed projects

A. Automatically gives preferential treatment in the allocation of funds to its riskiest division B. Encourages the division managers to only recommend their most conservative projects C. Maintains the current risk level and capital structure of the firm D. Automatically maximizes the total value created for its shareholders A.

8.24. Which one of the following methods of analysis is most similar to computing the return on assets (ROA)?

A. Average accounting return B. Payback C. Internal rate of return D. Profitability index A.

11.C5. Which of the following statements is TRUE?

A. By investing in varied and numerous assets, an investor is able to virtually eliminate all asset-specific risks in her portfolio, both easily and cheaply. B. It is possible, but not very easy, for an investor to control market-wide risks in his portfolio, and increases in these market-wide risks are costly because they reduce expected returns. C. The most important characteristic in determining the expected return of a well-diversified portfolio is the total variance risks of the individual assets in the portfolio. D. When a portfolio has a positive investment in every one of its assets, its standard deviation cannot be less than that on every asset in the portfolio. A.

Ch8.P15c. (16 points) Consider the following mutually exclusive projects: Look at the Chapter 8 Example Exam Question sheet for the chart You require 10% return on your investment in either of these projects. a) Calculate each project's NPV. Show your work. Based solely on the NPV criterion, which investment should be chosen? Briefly why? b) The IRR on project A is 15.5%. Is the IRR on project B larger or smaller than 15.5%? Show or describe how you can tell. And based solely on the IRR criterion, which investment should be chosen? c) [Dropped from question] Based on your NPV and IRR analysis, which project(s) will you finally choose? Briefly explain? d) If you are capital constrained and unable to accept all of the positive NPV projects available to you, which project should you rank higher?

A. Discounting the cash flows at 10%, the NPVs are NPVA = + $62.6 NPVB = + $19.6 Both projects' NPVs are positive, but they are mutually exclusive. So take project A since its NPV is higher. B. Using a 15.5% discount rate on Project B's cash flows, its NPV would be +6.7. Since that is positive, the IRR on project B must be larger than 15.5%, and in fact it is 18.8%. Both IRRs exceed the 10% required return, and since project B has a higher IRR, the IRR criterion would lead to the choice of project B. (Note: this exemplifies the size problem for IRRs: the higher 18.8% IRR is the expected return on project B's investment of only $100, compared to project A's 15.5% expected return on its larger investment of $860. Project A creates more value.) C. These are mutually exclusive projects, so only one or neither, but not both, could be accepted. You should take project A and reject project B because, while both would create value, project A creates more value than project B does. D. The profitability index on project B is higher, primarily since it requires a smaller initial cash outflow. PIA = (62.6 + 860) / 860 = 1.073 PIB = (19.6 + 100) / 100 = 1.196 Rank project B higher, when facing a capital constraint.

10.2. Which of the following statements is TRUE?

A. Efficient markets will protect investors from wrong choices if they do not diversify. B. Consistent with efficient markets, stock prices reach equilibrium several times per week. C. Efficient markets react to new information by instantly adjusting the price of a stock to its new fair market value without any delay or overreaction. D. Weak form efficiency implies that all information is reflected in stock prices. C.

11.1. Which of the following statements is TRUE?

A. If a portfolio has a positive investment in every asset, the standard deviation on the portfolio can be less than that on every asset in the portfolio. B. Labor strikes and part shortages are examples of market-wide systematic risks. C. Market-wide systematic risks can be significantly reduced by diversification. D. Asset-specific unsystematic risks can be substantially reduced with less numerous and less correlated assets in a portfolio. A.

8.ROA. The average accounting return method of analyzing projects:

A. Incorporates cash flows. B. Is similar to calculating the Return on Assets. C. Is difficult to estimate using information from accounting statements. D. Should accept all projects with positive AAR. B.

10.21. Which of the following statements is TRUE?

A. It is better to use Geometric Return than Average Return to forecast what the stock market over the next 50 years B. The return earned in an average year over a multiyear period is known as the geometric return C. The compound return earned per year over a multiyear period is known as the arithmetic average return D. The average return is always smaller than the geometric return A.

8.Quiz2. If any, which of the following statements is FALSE?

A. NPV measures the value created by taking on an investment B. NPV indicates how much a project will improve owner wealth C. NPV is the discounted present value of a project's expected future accounting net income at the required return, subtracting the initial investment D. None of the above statements is false C.

8.2. Which of the following statements is FALSE?

A. One reason why the Average Accounting Return is a flawed measure in making business decisions is that it is based on cash flows. B. IRR measures the dollar-weighted return on an investment. C. In order to use the Payback Rule as a tool to determine if an investment is acceptable, a manager needs to provide a pre-specified limit of time for recouping investment costs. D. The Profitability Index measures the value created per dollar invested, based on the time value of money. A.

9.1. Which of the following statements is TRUE?

A. Opportunity costs are those values that have already been incurred, cannot be recouped, and should not be considered in an investment decision. B. Under hard capital rationing, a business enforces limits on investment budgets because it prefers not to raise financing from the capital markets. C. Managerial real options can be very valuable but difficult to measure, and ignoring them will underestimate a project's true Net Present Value. D. Forecasting risk is more troublesome when NPV estimates are particularly large. C.

10.E1. Which of the following statements is FALSE?

A. Over the long run, investments in small-company stocks have had the largest return but also the most risk, when compared with large-company stocks, bonds, and T-Bills. B. The average return is always greater than the geometric return. C. Investors who hold bonds instead of stocks over long horizons can be rational and relatively averse to risk. D. Like the dividend yield, the capital gains yield can never be negative. D.

10.1. Which of the following statements is FALSE?

A. Over the long run, investments in small-company stocks have had the largest return but also the most risk, when compared with large-company stocks, bonds, and T-Bills. B. The average return is always less than the geometric return. C. Investors who hold bonds instead of stocks over long horizons can be rational and relatively averse to risk. D. Unlike the capital gains yield, the dividend yield can never be negative. B.

Ch8.P15b. (15 points) Consider the following independent projects (these are not mutually exclusive): Look at the Chapter 8 Example Exam Question sheet for the chart Whichever project you choose, if any, you require a 10% return on your investment. a) Calculate each project's payback, and show your work. If you require projects to pay back within 2 years, which investment(s) will you choose? Briefly why? b) Calculate each project's NPV given that you require 10% return on your investment, and show your work. Which investment(s) will you choose? Briefly why? c) Based on these answers, which project(s) will you finally choose? Briefly why? d) Is the IRR on project A larger or smaller than zero? Is it larger or smaller than the required return? Briefly describe how you can tell?

A. Project A pays back within 2 years: PaybackA = 1 + (160-110)/60 = 1.83 years Project B pays back beyond 2 years: PaybackB = 2 + (100-20-50)/80 = 2.38 years Using payback, accept project A and reject project B. B. NPVA = - $2.9 NPVB = + $19.6 Reject project A since its NPV is negative, but take project B since its NPV is positive. C. These are independent projects, so both, one, or neither could be accepted. You should reject project A and only take project B because project A destroys value and project B creates value. D. The IRR on project A is greater than zero since it does pay back over time, yet it is below the required return since its NPV is negative. (When a project's initial investment is followed by only positive cash flows, the IRR criterion is consistent with NPV.)

MC8. Newly issued securities are sold to investors in which one of the following markets?

A. Proxy B. Inside C. Secondary D. Primary D.

11.Hwk10. Which one of the following represents the amount of compensation an investor should expect to receive for accepting the unsystematic firm-specific risk associated with an individual security?

A. Security beta multiplied by the market rate of return B. Market risk premium C. Risk-free rate of return D. Zero D.

9.41&42&LectE. Which of the following statements is FALSE?

A. Sensitivity analysis helps determine the reasonable range of expectations for a project's outcome. B. The impacts of estimation errors and forecasting risks are small when NPVs are large and negative. C. Under intense competition, positive NPV projects are rare. D. The error of commission, or Type 1 error NPV estimation, is the risk that a project will be accepted when its true NPV is negative. A.

9.71. Which of the following statements is FALSE?

A. Since errors of commission are often readily apparent, managers have a tendency to be cautious when evaluating new projects B. Errors of omission can result in lost potential value as much as errors of commission can destroy value. C. Type 1 errors occur when managers reject projects whose true NPVs are positive D. Errors in projected cash flows create large forecasting risks when their net present values are particularly small in magnitude. C.

Hwk9. An agent who buys and sells securities from inventory is called a:

A. Specialist B. Dealer C. Broker D. Floor Trader B.

Q8.24F. (10 points) Consider the following cash flows (in $ millions) for a project: Look at the Chapter 8 Example Exam Question sheet for the chart For this project, you require an 8 percent return on your investment. (a) Calculate the payback. If a company requires all projects to pay back within 4 years, will it invest in this project? Briefly explain. (b) Calculate the NPV. Interpret it. (c) Calculate the profitability index. If you apply the profitability index criterion, will you make this investment if funds are available? Briefly discuss.

A. Technically yes, since it pays back between years 1 and 2 and exactly in 1 + (500-240)/300 = 1.87 years. Yet given the negative cash flow at the end, all of its pay back is erased—the sum of the future cash flows equals the initial investment in this case. B. Discounting the cash flows at 8%, the NPV is -40.6. Do not take this investment because it would destroy $40.6 million in value. C. PI = -40.6 / 500 + 1 = .919 The profitability index is less than one. Do not take this project even if funds are available.

7.1 Which of the following statements is FALSE?

A. The Gordon Growth Model assumes constant dividend growth and implies that stock prices grow at the same rate. B. A stock's price is the present value of the expected dividends and capital gains. C. Dealers buy and sell securities from their own inventory, while brokers bring buyers and sellers together to complete transactions. D. Holders of preferred stock have greater voting rights in corporate decisions than holders of common stock. D.

7.16. Which of the following statements is TRUE?

A. The Gordon Growth Model assumes constant dividend growth but implies that stock prices grow at a different rate. B. A stock's price is the present value of its future cash flows, namely, its expected capital gains and dividends. C. Brokers buy and sell securities from their own inventory, while dealers bring buyers and sellers together to complete transactions. D. Holders of common stock have greater voting rights in corporate decisions than holders of preferred stock, but they have less voting rights than creditors of the corporation. B.

9.24. If any, which of the following does NOT have the potential to increase the net present value of a proposed investment?

A. The ability to immediately shut down a project should the project become unprofitable B. The ability to wait until the economy improves before making the investment C. The option to increase production beyond that initially projected D. All of the above have the potential to increase the NPV of a proposed investment D.

7.21. Which of the following statements is FALSE?

A. The bid price is the price that a dealer is willing to pay for a security and is lower than the ask price. B. Bonds trade less frequently than stocks. C. In the stock market, the secondary market is the market where new securities are originally sold to investors by the issuing company. D. Dividends received by corporations have a 70% to 100% exclusion from taxable income. C.

12.1. Which of the following statements is FALSE?

A. The cost of capital is the minimum required return to compensate financial investors. B. The cost of capital for a project depends primarily on the source of funds. C. The cost of equity is the return required by equity investors given the risk of the cash flows from the firm. D. A firm's WACC reflects the average risk of the existing projects undertaken by the firm. B.

12.L5B. Which of the following statements is FALSE?

A. The cost of debt for bonds is the same as the yield implied by their market quoted prices, except when that promised yield is too high due, for example, to the high default probabilities for junk bonds. B. The cost of preferred stock equals its dividend yield as a percent of the current price, rather than the preferred dividend as a percent of its stated liquidating value, which is usually $100. C. Judgment is typically required when estimating the cost of equity, particularly when a company pays no dividends and when its beta estimate is imprecise. D. Due to its lower priority and greater risk, a firm's cost of equity can sometimes be, and often is, less that its after-tax cost of debt. D.

12.21. Which of the following statements is FALSE?

A. The cost to a firm for capital funding equals the expected return to the providers of those funds B. A firm's cost of capital depends primarily on the source of the funds, not the use C. WACC is affected by market conditions including interest rates, tax rates, and the market risk premium D. A firm's WACC reflects the average risk of the existing projects undertaken by the firm B.

9.28a. Which of the following should not be included in the analysis of a proposed investment?

A. The current market value of an existing building to be used in the project. B. The amount paid 4 years ago for an existing building to be used in the project. C. The expected after-tax salvage value at the end of a project of an existing building to be used in the project. D. The net working capital balance remaining at the end of the project. B.

9.41&42&Lect. Which of the following statements is FALSE??

A. The impacts of estimation errors and forecasting risks are small when NPVs are large and positive. B. Under intense competition, positive NPV projects are as common as negative NPV projects. C. Scenario analysis helps determine the reasonable range of expectations for a project's outcome. D. Sensitivity analysis helps identify the variable within a project that presents the greatest forecasting risk. B.

8.HwkMC. Which of the following statements is FALSE?

A. The internal rate of return is defined as the discount rate which results in a zero net present value for the project. B. The primary advantage to payback analysis is that it biases companies to invest in long-term projects that require large current expenditures on research and development. C. The average accounting return ignores cash flows is most similar to computing the return on assets (ROA). D. The profitability index reflects the value created per dollar invested. B.

10HWK. Under Munich, a footwear manufacturer, recently announced that they have just designed a new footwear product which includes the latest technology. This news is totally unexpected and viewed as a major advancement in the footwear industry. Which one of the following reactions to this announcement indicates the market for New Labs stock is efficient?

A. The price of Under Munich doesn't change, but then it increases one week after the announcement. B. The price of all stocks quickly increase in value and then all but Under Munich stock fall back to their original values. C. The price of Under Munich's stock suddenly increases, and then remains at that price. D. The price of Under Munich's stock increases rapidly, and then settles back to its pre-announcement level. C.

10.Hwk10. Which one of the following statements is TRUE?

A. The risk-free rate of return has a risk premium of 1.0. B. The reward for bearing risk is called the standard deviation. C. Risks and expected return are inversely related. D. The higher the expected rate of return, the wider the distribution of returns. D.

11.MC22. Portfolio diversification eliminates which of the following?

A. Total investment risk B. Reward for bearing risk C. Market-wide risk D. Unsystematic risk D.

7.10. A broker is an agent who:

A. Trades on the floor of an exchange for himself or herself. B. Buys and sells from inventory. C. Offers new securities for sale to dealers only. D. Brings buyers and sellers together. D.

7.Lectp1. Which of the following statements is FALSE?

A. Unlike equity holders, debt holders are not owners B. Lenders can exert control over a company's managers by voting for its board of directors. C. A corporation cannot deduct its payments to preferred shareholders before it pays taxes D. Holders of convertible bonds can force bankruptcy if their coupons are not paid B.

7.Quiz1. Fill in the blanks: Stock prices fall if investors either expect _________ growth rates or require _________ returns.

A. higher, higher B. higher, lower C. lower, higher D. lower, lower C.

9.Hwk10. Sensitivity analysis:

A. looks at the most reasonably optimistic and pessimistic results for a project. B. helps identify the variable within a project that presents the greatest forecasting risk. C. is generally conducted prior to scenario analysis just to determine if the range of potential outcomes is acceptable. D. illustrates how an increase in operating cash flow caused by changing both the revenue and the costs simultaneously will change the net present value for a project. B.

10.24. If the financial markets are semi-strong form efficient, then:

A. only the most talented analysts can determine the true value of a security. B. only individuals with private information have a marketplace advantage. C. technical analysis provides the best tool to use to gain a marketplace advantage. D. no one individual has an advantage in the marketplace. B.

Ch10.P18B. (6 points) Over the long term, small cap stocks have averaged 16.4% return with 33.0% volatility per year. Using history as a guide, what range of returns would you expect to see 95 percent of the time for small cap stocks?

Assuming that returns are normally distributed, the range of returns you would expect to see 95 percent of the time is within two standard deviations of the mean. μ - 2σ ≤ r ≤ μ + 2σ 16.4% - 2(33.0%) ≤ r ≤ 16.4% + 2(33.0%) -49.6% to 82.4% That's an extremely wide range for anticipated returns in any given year, and 5% of the time (or 1 in 20 years), small cap returns are anticipated to be outside of that range!

Ch11.P19B. (8 points) Stock J has a volatility of 50%, a beta of 0.90, and an expected return of 8%. If the risk-free rate is 2% and the market risk premium is 6%, is this stock undervalued, correctly priced, or overvalued? Briefly explain why.

CAPM indicates that, given Stock J's level of market risk (volatility is irrelevant since much of it can be diversified away), its expected return should be E[rJ] = rF + βJ * MRP = 2% + 0.90*6% = 7.4% Comparing that to the actual 8% expected return on Stock J, the actual expected return is too high given its risk. Stock J plots above the SML and is undervalued. In other words, its price must increase now so that its future expected return will drop to 7.4%. Alternatively, compare Stock J's reward-to-risk ratio to the SML slope. The reward-to-risk ratio for any asset is its risk premium divided by its beta: (E[ri] - rF) / βi For Stock J, the reward-to-risk ratio for J = (.08 - .02) / 0.90 = .0667 We know the market has βM =1, so the reward-to-risk ratio for the market is (.06) / 1 = .06 Since all assets must have the same reward-to-risk ratio, the reward-to-risk ratio for Stock J is too high, which means the stock plots above the SML and is undervalued. Its current price must increase until its reward-to-risk ratio is equal to the market reward-to-risk ratio.

Ch11.P19A. (8 points) Stock Y has a beta of 1.30 and an expected return of 13%. If the risk-free rate is 4.5% and the market risk premium is 7%, is this stock undervalued, correctly priced, or overvalued? Briefly explain or show why.

CAPM indicates that, given Stock Y's level of risk, its expected return should be E[rY] = rF + βY * MRP = .045 + 1.30*(.07) = .1360 or 13.60% Comparing that to actual 13% expected return on Stock Y, the actual expected return is too low given its risk. Stock Y plots below the SML and is overvalued. In other words, its price must decrease now so that its future expected return will increase to 13.60%. Alternatively, compare Stock Y's reward-to-risk ratio to the SML slope. The reward-to-risk ratio for any asset is its risk premium divided by its beta: (E[ri] - rF) / βi For Stock Y, the reward-to-risk ratio for Y = (.13 - .045) / 1.30 = .0654 We know the market has βM =1, so the reward-to-risk ratio for the market is (.07) / 1 = .07 Since all assets must have the same reward-to-risk ratio, the reward-to-risk ratio for Stock Y is too low, which means the stock plots below the SML is overvalued. Its current price must decrease until its reward-to-risk ratio is equal to the market reward-to-risk ratio.

Ch9.P11B. (9 points) Constock is considering a new three-year expansion project that requires an initial fixed asset investment of $24m. The fixed asset will be depreciated straight-line to zero over its three-year tax life. The project is estimated to generate $20m in annual sales, with annual cash costs of $14m (excluding depreciation expense). The marginal tax rate is 35%. In addition, the project requires an initial investment in new working capital of $1m, which will be recovered at the end of the project, and the fixed asset will have a market value of $2m at the end of the project. What is the project's net cash flow in Year 3 at the end of the project?

Operating Cash Flow = (Sales-Costs)(1-T) + Depr*T = (20 - 14)(1-.35) + (24/3)*.35 = $6.7m NWC Recovery = 1m After-tax Salvage = SalePrice - T*(SalePrice - Book) = 2 - .35(2 - 0) = 1.3m Total Year 3 net cash flow = 6.7 + 1 + 1.3 = $9.0m

Ch9.Hwk9-2. (9 points) Currently Perla sells 200,000 Contractor grade windows per year at $200 each, and 100,000 Architect grade windows per year at $600 each. The company plans to introduce a Builder grade window and expects to sell 120,000 of these windows per year at $500 each. Because these Builder grade windows will be more easily matched with the Contractor grade windows, Perla expects to be able to sell an additional 30,000 Contractor grade windows. However, Perla also expects that the Builder grade windows will compete with and reduce its sales of Architect grade windows by 40,000 units. What is the relevant amount to use as the annual sales figure when evaluating this project? Briefly explain why.

Sales due solely to the new Builder grade product are 120,000 windows * $500 per window = $60 million Due to synergies with the new Builder grade windows, the Contractor grade window sales will increase by 30,000 windows * $200 per window = $6 million gained sales Due to erosion caused by the Builder grade windows, the Architect grade window sales will decrease by 40,000 windows * $600 per window = $24 million lost sales The relevant net sales due to the introduction of the Builder grade windows is therefore: $60 million + $6 million - $24 million = $42 million.

Q9.P1B. (5 points) Kenny, Inc. is looking at setting up a new manufacturing plant in South Park. The company bought some land seven years ago for $9.8 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent facilities elsewhere. The land would net $7.2 million if it were sold today. The company now wants to build its new manufacturing plant on this land; the plant will cost $22.1 million to build, and the site requires $1.1 million worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project?

The $9.8 million acquisition cost of the land seven years ago is a sunk cost. The $7.2 million current aftertax value of the land is an opportunity cost if the land is used rather than sold off. The $22.1 million cash outlay and $1.1 million grading expenses are the initial fixed asset investments needed to get the project going. Therefore, the proper year zero cash flow to use in evaluating this project is Cash flow = 7.2m + 22.1m + 1.1m = $30.4m

Ch12.LectEx.1. (20 points) Estimate the existing weighted average cost of capital using this information for a company with a 35% marginal tax rate: Existing bonds with $300m face outstanding mature in 13 years, with an 8% coupon rate paid semiannually, rated A1 by Moody's, with a current quoted yield of 5% per year, and trading for 128.426% of face value. 3m preferred shares each pay a $6 annual dividend and have a current market price of $96. 10m common shares with a current market price of $60. Each paid $3 dividend last year, which is expected to grow at a stable rate of 4% forever. Also, this company's beta is 0.9. The current risk-free rate is 2%, the equity market's risk premium is expected to be 6%. (For this problem, round aggregate capital values to millions of dollars.)

The quoted bond yield of 5% could be used to confirm that the bond price is: =128.426 as a percent of par Or n = 2*13 = 26, i = 5/2 = 2.5, PMT = 8/2 = 4, FV = 100 PV = -128.426 Since the bonds are high investment grade with low default risk, their required return is the yield. The total market value of debt is $300m (128.426%) = $385m Investors' required return on the preferred stock is rPfd = $6 / $96 = 6.25% The current market value of preferred is 3m * $96 = $288m Using the divided discount model, investors' required return on the common shares is rE = D0 (1+g) / P0 + g = 3 (1+.04) / $60 + .04 = 9.2% Using the CAPM, investors' required return on the common shares is rE = rF + βE * MRP = 2% + 0.9 * 6% = 7.4% Use the average of these to estimate the cost of equity at 8.3% The market value of the common shares is 10m * $60 = $600m The total market value of the firm's financial claims is V = D + Pfd + E = $385m + $288m + $600m = $1,273m Using all these components, estimate the WACC: WACC = 385/1273*(1-.35)*5% + 288/1273*6.25% + 600/1273 * 8.3% = 6.31%

Ch12.P15E. (12 points) A large industrial company with a 28% marginal tax rate, is financed with: Debt: 30 million bonds outstanding with $1,000 par value each, 7.8% coupons paid semiannually, 12 years to maturity, high investment grade rating, a quoted yield of 5.5%, and selling for 120% of par. Common stock: 2,000 million shares of common stock selling for $27 per share with a 1.2 beta and 80% volatility. Market: The current risk-free rate is 2% and investors expect a 5% market risk premium. Estimate this company's WACC.

The quoted bond yield of 5.5% could be used to confirm that the bond price is: = 120.01 as a percent of par Or n = 2*12 = 24, i = 5.5/2 = 2.75, PMT = 7.8/2 = 3.9, FV = 100 PV = -120.01 The market values of the company's debt, equity, and total firm value are: D = 30m($1,000)(1.20) = $36b E = 2,000m($27) = $54b V = $36b + $54b = $90b Due to its high investment grade rating, the cost of debt is the 5.5% YTM of the bonds, and the after-tax cost of debt is: rD= (1 - .28)5.5% = 3.96% Using CAPM, the cost of equity is: rE = rF + βE * RPM = 2% + 1.2 * 5% = 8.0% A stock's volatility can be diversified in a portfolio and is not relevant to the return required on equity by diversified investors in the market.

Ch11.P2&12. (12 points) Assume these are your forecasts for the returns on 2 stocks: Expected Return Volatility Market Beta Stock A 8.0% 40% 1.2 Stock B 6.0% 50% 0.8 Your portfolio is (unwisely) invested entirely in these stocks, with $3m in stock A and $2m in stock B. a) What is the expected return on your portfolio? b) Is the volatility of your portfolio higher than, lower than, or equal to 44%? c) Is the beta of your portfolio higher than, lower than, or equal to the average market risk?

a. Your total portfolio is worth 3 + 2 = $5m, and the weights on these stocks in your portfolio are: wA = $3m / $5m = .6 and wB = $2m / $5m = .4 Your portfolio's expected return is the weighted average: E[rP] = wA E[rA] + wB E[rB] = .6 (8.0%) + .4 (6.0%) = 7.2% b. When the weights are all positive and the stocks not perfectly correlated, then volatility risk is diversified and the portfolio's volatility is strictly less than the weighted average of the component volatilities: σP < wA σA + wB σB = .6 (40%) + .4 (50%) = 44% To calculate the portfolio's volatility, the correlation between stocks A and B would be required. c. A portfolio's beta equals the weighted average of the component betas: βP = wA βA + wB βB = .6 (1.2) + .4 (0.8) = 1.04 The portfolio is weighted more toward the stock with more than average market risk, sufficiently so that the portfolio's beta is more than 1. Hence, the portfolio has more than average market risk.

Ch8.Hwk9AAR. (13 points) To expand your company's production, you are considering installing a new plant at a cost of $1,200 million, which will be depreciated straight line to zero over its four-year life. The following are projections of its net income and free cash flows over these years. Only the numbers in the boxes were provided on the exam. Memorize the chart a) What is the project's average accounting return (AAR)? If the company uses AAR to make decisions and its preset target rate is 12%, will it take this project? Briefly explain. b) What is the project's Net Present Value if the appropriate cost of capital for this project 12%? Should the company take this project? Briefly explain. c) Without calculating this project's Internal Rate of Return, what can you tell about this project's IRR? Is it higher or lower than the project's cost capital? Briefly explain why.

a. AAR = Average Net Income / Average Book Value = [(104 + 234 + 26 - 26) / 4] / (1200 + 900 + 600 + 300 + 0) / 5] = 84.5 / 600 = 14.1% Since that exceeds the 12% target, the company will take this project if it makes decisions based on AAR alone. (This would be a mistake in this case given the negative NPV shown below.) b. Calculate the NPV by discounting the FCFs at a rate of 12% to show that its NPV = -$7.41m No, if the company accepted this project, it would destroy $7.41m in value of its investors' capital. c. Since this project has the typical pattern of one cash outflow followed by only inflows of cash, and since its NPV is negative, the IRR must be less than the cost of capital. The discount rate would have to be reduced to increase its negative NPV up to zero. [Note also, this project's free cash flows add up to +$338m. Hence, using a 0% discount rate, the NPV of the FCFs would be positive. So, this project's IRR is larger than 0%.]

Q8.P15G. (16 points) Consider the following two mutually exclusive projects: (Italicized data were not provided on the exam.... means you have to know how to do the NPV and IRR) Whichever project you choose, if any, you require 11% return on your investment. a) If you apply the payback criterion, which investment will you choose, if any? Show and briefly explain. b) If you apply the NPV criterion, which investment will you choose? Show and briefly explain c) The IRR for Project A is 26%. Is the IRR on Project B higher or lower than 26%? If you apply the IRR criterion, which investment will you choose? Briefly show and describe how you can tell. d) Based on these answers, which project will you finally choose? Explain why.

a. Considering only the payback criterion, an investor would choose Project B since it pays back in exactly 2 years, while Project A takes longer and exactly 3 years to pay back its initial investment. b. Calculate the NPVs to show that Project A has a positive and higher NPV and therefore creates positive value and moreso than Project B. Choose project A. c. At a 26.0% required return, the NPV on Project B is still positive at $5.7m. (Also it only has one IRR since its cash flows change signs only once.) So the discount rate that makes Project B's NPV equal to zero is higher. In fact its IRR is 36.1%. According to the IRR criterion, choose Project B since its IRR is higher. d. While Project B pays back faster and has a higher dollar-weighted return (IRR), Project A has a larger NPV and creates more value. Therefore invest in Project A.

Ch12.P9. (12 points) Mulligan Corporation has a target capital structure of 30% debt, 10% preferred stock, and 60% common stock. Its cost of debt is 6.80%, its cost of preferred stock is 6.00%, and its cost of equity is 10.40%. Its marginal tax rate is 35%. a) After taxes, is debt financing cheaper or more expensive for Mulligan than financing with either preferred stock or common stock? b) What is Mulligan's weighted average cost of capital? c) What discount rate should Mulligan use when evaluating expansion projects? Briefly explain.

a. Interest is tax deductible (unlike dividends), so the company's after tax cost of debt is (1 - TC) rD = (1 - .35) 6.80% = 4.42% After taxes, debt is cheaper than financing with either preferred or common stock. b. WACC = .30 (1 - .35) (6.80%) + .10 (6.00%) + .60 * (10.40%) = 8.17% c. Mulligan should use the 8.17% WACC because it represents the cost of capital for existing operations from all financing sources, and expansion projects have similar risks to existing operations.

Ch10.P20B. (12 points) A stock has had returns of -18%, 25%, and 11% over the past three years. (a) What was its historical arithmetic average return? And what was its geometric return? (b) What was the historical volatility for this stock? Show your calculation. The deviations of each of these returns from the 6% mean arithmetic average return are:

a. The arithmetic average return is the sum of the returns divided by the number of returns Arithmetic average return = (-.18 + .25 + .11) / 3 = .06 = 6% The geometric return is the annualized compounded growth of a dollar invested: Geometric average return = [(1 - .18)(1 + .25)(1 + .11)](1/3) - 1 = .044 = 4.4% Remember that the geometric average return is less than the arithmetic average return if the returns have any variation. b. -24%, 19%, and 5% To calculate variance, square each deviation, sum them, and divide by one less than the sample number [(-24)2 + (19)2 + (5)2 ] / (3 - 1) = 481 To calculate standard deviation, take the square root. Volatility = σ = √529

Ch10.P20c. (12 points) A stock has had returns of 30%, -36%, and 15% over the past three years. a) What was its historical arithmetic average return? How much would $1 invested in this stock three years ago be worth today (that is, calculate the total return index over these three years)? b) What was the historical volatility for this stock? Show your calculation.

a. The arithmetic average return is the sum of the returns divided by the number of returns Arithmetic average return = (.30 - .36 + .15) / 3 = .03 = 3% The geometric return is the annualized compounded growth of a dollar invested: Geometric average return = [(1 + .30)(1 - .36)(1 + .15)](1/3) - 1 = -.0146 = -1.46% Remember that the geometric average return is less than the arithmetic average return if the returns have any variation. The total return index after 3 years is (1 - .0146)3 = [(1 + .30)(1 - .36)(1 + .15)] = $0.9568. Even though the arithmetic average return was positive, this stock lost value, and a dollar invested in it is worth less than a dollar today. b. The deviations of each of these returns from the 3% mean arithmetic average return are: 27%, -39%, and 12% To calculate variance, square each deviation, sum them, and divide by one less than the sample number [(27)2 + (-39)2 + (12)2 ] / (3 - 1) = 1,197 To calculate standard deviation, take the square root. Volatility = σ = √1,197 = 34.6% which is a percentage because volatility has the same units as the returns

Ch10.P20e1. (14 points) A stock has had returns of 70%, -50%, 14%, and 22% over the past four years. a) What was its historical arithmetic average return? Show your calculation. b) What was the historical volatility for this stock? Show your calculation. The deviations of each of these returns from the 14% mean arithmetic average return are: c) Calculate either the exact or the approximate geometric compound return. Discuss how it compares to the arithmetic average return.

a. The arithmetic average return is the sum of the returns divided by the number of returns Arithmetic average return = (.70 - .50 + .14 + .22) / 4 = .14 = 14% b. The deviations of each of these returns from the 14% mean arithmetic average return are: 56%, -64%, 0%, and 8% To calculate variance, square each deviation, sum them, and divide by one less than the sample number [(.56)2 + (-.64)2 + (0)2 + (.08)2 ] / (4 - 1) = .2432 To calculate standard deviation, take the square root. Volatility = σ = √.2432 = .493 = 49.3% which is a percentage because volatility has the same units as the returns. [That is about the same volatility as a typical single stock, and it is considerably larger than the volatility of a diversified portfolio of stocks.] c. The total return index of $1 invested in this stock four years ago would today be worth $1 * [(1 + .70)(1 - .50)(1 + .14) (1 + .22)] = $1.1822 The exact geometric average return is the annualized compounded growth of that dollar invested, or Exact geometric average return = [$1.1822](1/4) - 1 = .0427 = 4.27% The approximate average return can be estimated from the arithmetic average and the volatility Geometric average ≈ arithmetic average - ½ volatility2 = .14 - ½ (.493)2 = .0184 = 1.84% [This approximation would match the exact geometric (or compound) average return if the returns followed a normal distribution, unlike this sample of only 4 observations.] The geometric average return is considerably less than the arithmetic average return. The arithmetic average return represents the return expected in an average year. The geometric average return represents the annualized compound return over a period of many years.

Ch10.P18E. (10 points) Historically, long-term Treasury bonds have averaged about 6% return with 10% volatility per year. Currently, long-term Treasury bond yields are about 2%. a) What return should investors expect to earn if they hold long-term Treasury bonds until maturity? Briefly explain. b) Using the historical data as a guide, what range of returns would you expect to see 99 percent of the time for long-term Treasury bonds?

a. Yields on safe bonds represent the return that investors should expect to earn on bonds in the future. While investors have historically earned 6% on bonds, they should only expect to earn the current 2% yield on these in the future. b. Assuming that returns are normally distributed, the range of returns you would expect to see 99 percent of the time is within three standard deviations of the mean. μ - 3σ ≤ r ≤ μ + 3σ 6% - 3*(10%) ≤ r ≤ 6% + 3*(10%) -24% to 36% [Given that yields, and thus future expected returns, are currently only 2%, not 6%, the mean is lower by 4% and the forecasted range should actually be -28% to 32%.] That's a rather wide range for anticipated returns in any given year, particularly given that bonds are considered to be relatively safe investments. Also, 1% of the time (or 1 in 100 years), long-term bond returns are anticipated to be outside of that range! While long-term Treasury bond yields represent safe returns if they are held to maturity, their prices change over time and, hence, their returns fluctuate during the time they are held, which is a risk if they are sold before maturity and/or their coupons are reinvested at then-prevailing market rates.

Ch10.Q72. (16 points) Suppose these are statistics from total annual returns over many years in the past. Today the Wall Street Journal reports that the yield on 1-year Treasury Bills is currently 0.4% and the yield on 20-year Treasury Bonds is currently 3%. Otherwise, assume that future returns will be similar to past returns and follow a Normal distribution. a) If you invest $1,000 in 20-year Treasury Bonds today, about how much will your investment be worth in 20 years? Show and discuss. b) If you invest in small-company stocks, what percent return would you expect in 1 year? c) If you invest in small-company stocks, what range of returns would you expect to observe in any given year about 68% of the time? d) If you invest in large-company stocks, what annualized percent return would you expect to earn compounded over a long time period like 40 years?

a.The history is not particularly relevant for known safe future returns, like current Treasury yields. Using today's 3% yield on 20-year T-Bonds, $1,000 invested today will be worth in 20 years: FV = $1,000 * (1+.03)20 = $1,806 (The only risk, assuming that government bonds are truly safe and will not default, is whether the interim coupons received will be reinvested at a lower subsequent return than today's 3% T-Bond yield.) b. The historical average (arithmetic mean) return was 16%, and that is the best estimate for short horizons. c. For returns which follow a Normal distribution, the range will be within one standard deviation of the mean with 68% probability, or for the small-company stock data, between 16% - 1*(30%) = -14% and 16% + 1*(30%) = +46% That's a large range of returns for any given year In addition, for ½(1 - 68%) = 16% of the time or about one in six years, returns would be lower than -14% On the up side, for the other 16% of the time or about one in six years, returns would be higher than 46% d. The geometric average return is the best estimate for annual returns earned over long-term horizons. Geometric average ≈ arithmetic average - ½ volatility2 (which is exact for Normally distributed returns) = 12% - ½ * (.20)2 = 10% annualized return After 40 years, $1,000 invested in large-company stocks would be worth about $1,000 * (1+10%)40 = $45,259 [Do NOT compound the arithmetic average when returns are risky: that would suggest over twice the value at $1,000 * (1+12%)40 = $93,051]