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Question 1 True, false or “It depends”? Explain briefly in each case. a. If the nominal interest rate is 8% and expected inflation is 2%, then the real interest rate is 8 – 2 = 6% b. A one-year forward price, say for Brent crude oil, reveals investors’ consensus expectation of the Brent spot price that will prevail one year hence. c. The PV of a cash-flow stream that grows only with inflation (constant in real terms) can be calculated by dividing the next cash flow by the difference between the nominal opportunity cost of capital and the future inflation rate. d. If the term structure of spot interest rates is upward-sloping, then a Treasury bond paying a 6% coupon will trade at lower yield to maturity than a Treasury bond with the same maturity but a 2% coupon. e. Put-call parity assures that the price of a put and a call are exactly equal, provided of course that the underlying asset and maturity are the same. f. If two investments are perfectly negatively correlated ( ρ = − 1), then the two investments can be combined in a portfolio with zero risk. g. It makes sense to invest in stocks that have delivered positive alphas, and to avoid stocks that have generated zero or negative alphas. Question 2 According to modern portfolio theory, the best portfolio of risky securities is the portfolio with the highest Sharpe ratio. Explain why this is so. Hint: You will probably want to draw a plot of portfolio risk and return. Question 3 Kansas City Southern railroad (KSU) pays a dividend of DIV = $1.12 per share. Security analysts forecast 2015 earnings per share at EPS = $5.50. The stock closed at $114.25 on December 8, 2014. a. Is the earnings-price ratio EPS/ PKSU = 5.50/114.25 = .048 a plausible estimate of the true “cost of equity” (rE!) for KSU? Why or why not? b. Sometimes the following “dividend growth” formula is used to estimate rE!: rE! = DIV P + g Security analysts forecast KSU’s EPS growth at 9.95 % per year over the next five years. Solve for rE using the EPS growth forecast for g. In what circumstances would your answer be a plausible estimate of the true cost of equity? Explain. Question 4 The current market values of Bariloche Corp’s defined- benefit pension assets (PA) and liabilities (PL) are: PA = $1.115 billion PL = $1.465 billion Thus the plan is underfunded by $350 million. The pension assets are invested in a “balanced” portfolio of about 80% equities and 20% fixed income, with expected return of 8.0% and annual standard deviation of 14%. The duration of the fixed-income assets is 10 years, and the duration of PL is 20 years. The term structure is flat at 6%. a. Bariloche’s CFO is worried about another recession like 2008-2009. She asks you what would happen if the stock market drops by 20% and the Fed pushes interest rates down to 4%. (Assume the term structure remains flat.) Explain how to calculate the approximate changes in PA, PL and the amount of underfunding. (You can do the calculations if you wish, but a detailed and specific outline is OK.) Why are these changes approximations? b. A large insurance company offers to take over all the PLs for a one-time payment of $1.565 billion. The takeover would release the PAs, so the net cost to Bariloche would be $1.565 − 1.115 = $.450 billion or $450 million. Several board members argue strongly for this action in order to reduce the risks that Bariloche’s pension strategy imposes on the company and its stockholders. Do you agree? Explain. Question 5 a. Calculate the after-tax WACC for Federated Junkyards, using the following information. • Debt: $750 million book value outstanding. The debt is trading at 95% of book value. Yield to maturity is 9%. • Equity: 25 million shares trading at $43 per share. Book value per share is $30. The expected rate of return on Federated’s stock is 15%. • Tax rate = .38. b. A year later, Federated has moved to a more conservative debt policy. Debt is paid down to $500 million. The yield to maturity has fallen to 8.6% and the debt is now trading at par value. Shares are now trading at $48 (book value = $32). Recalculate WACC, assuming that Federated’s business risk, opportunity cost of capital and tax rate have not changed. Question 6 Reliable Electric is considering a proposal to manufacture a new type of industrial electric motor that would replace most of its existing product line. A research breakthrough has given Reliable a two-year lead on its competitors. The project proposal is summarized in Table 6.7 below. 2013 2014 2015 2016–2023 1. Capital expenditure -10,400 2. Research and development -2,000 3.Working capital -4,000 4.Revenue 8,000 16,000 40,000 5. Operating costs -4,000 -8,000 -20,000 6. Overhead -800 -1,600 -4,000 7. Depreciation -1,040 -1,040 -1,040 8. Interest -2,160 -2,160 -2,160 9. Income -2,000 0 3,200 12,800 10. Tax 0 0 420 4,480 11. Net cash flow -16,400 0 2,780 8,320 12. Net present value = +13,932 Table 6.7 Cash flows and present value of Reliable Electric’s proposed investment ($ thousands). Notes: 1. Capital expenditure: $8 million for new machinery and $2.4 million for a warehouse extension has been charged to this project, although only about half of the warehouse space is currently needed. Since the new machinery will be housed in an existing factory building, no charge has been made for land and building. 2. Research and development: $1.82 million spent in 2012. This figure was corrected for 10% inflation from the time of expenditure to date. Thus 1.82×1.1 = $2 million. 3. Working capital: Initial investment in inventories. 4. Revenue: These figures assume sales of 2,000 motors in 2014, 4000 in 2015, and 10,000 per year from 2016 through 2023. The initial unit price of $4,000 is forecasted to remain constant in real terms. 5. Operating costs: These include all direct and indirect costs. Indirect costs (heat, light, power, fringe benefits, etc.) are assumed to be 200% of direct labor costs. Operating costs per unit are forecasted to remain constant in real terms at $2,000. 6. Overhead: Marketing and administrative costs, assumed equal to 10% of revenue. 7. Depreciation: Straight-line for 10 years. 8. Interest: Charged on capital expenditure and working capital at Reliable’s current borrowing rate of 15%. 9. Income: Revenue less the sum of research and development, operating costs, overhead, depreciation, and interest. 10. Tax: 35% of income. However, income is negative in 2013. This loss is carried forward and deducted from taxable income in 2015. 11. Net cash flow for 2014-2023: Assumed equal to income less tax. 12. Net present value: NPV of net cash flow at a 15% discount rate. Read the notes to the table carefully. Which entries make sense? Which do not? Why or why not? What additional information would you need to construct a version of Table 6.7 that makes sense? Question 7 Mom and Pop Groceries has a two-year contract to supply groceries to the government of the Central Antarctic Republic. The contract calls for two payments of $500,000 after each of two annual shipments arrives by snow train. The first payment should be received 12 months from now and the second 24 months from now. Unfortunately there is a 20% per year chance of a coup d’état, in which case the new government will not pay. Thus the probability of receiving the first payment is only 80%. If the existing government survives and makes the first payment, Mom and Pop will face the same 20% risk of non-payment in year two. Mom and Pop’s controller therefore decides to discount the payment at 32%, rather than at the company’s 12% cost of capital. (12% + 20% = 32%) a. What’s wrong with using a 32% discount rate to offset this political risk? b. How much are the $500,000 payments really worth if the odds of a coup d’état are 20% in year 1 and again 20% in year 2 if the government survives in year 1?

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Answer 1:
a. False. This is because the nominal interest rate is found using the formula (1 + 8%)/(1 + 2%) – 1. The method showed is an approximation method.
b. True. This is because the investors take long and short positions according to their expectations and that influences the forward rate.
c. False. This is because the next cash flow would be in nominal terms and it cannot be discounted using real discount rate. The real cash flows should be discounted using ...
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