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Chapters 3 and 4 Questions Chapter 3 17. Price and Yields -A sixyear government bond makes annual coupon payment of 5% and offers a yield of 3% annually compounded. Suppose that one year later the bond still yields 3%. What return has the bondholder earned over the 12month period? Now suppose that the bond yields 2% at the end of the year. What return did the bondholder earn in this case? 23. Duration - The formula for the duration of a perpetual bond that makes an equal payment each year in perpetuity is (1 + yield)/yield. If each bond yields 5%, which has the longest duration - perpetual bond or a 15 year zerocoupon bond? What if the yield is 10% 28. Nominal and Real Returns - Suppose that you buy a twoyear 8% bond at its face value. A. What will be your total nominal return over the two years if inflation is 3% in the first year and 5% in the second? What will be your real return? B. Now suppose that the bond is a TIPS. What will be your total 2year real and nominal returns? 29. Bond Ratings - A bond's credit rating provides a guide to it's price. As we write this in early 2015. Aaa bonds yield 3.4% and Baa bonds yield 4.4% If some bad news causes a 10%fiveyear bond unexpectedly downrated from Aaa to Baa. What would be the effect on the bond price? (Assume annual coupons.) 32. Price and spot interest rates - Find the arbitrage opportunity (opportunities?). Assume for simplicity that coupons are paid annually. In each case the face value of the bond is $1,000. Bond Maturity(Years) Coupon($) Price($) A 3 0 751.30 B 4 50 842.30 C 4 120 1,065.28 D 4 100 980.57 E 3 140 1,120.12 F 3 70 1,001.62 G 2 0 834.00 Chapter 4; 25. DCF and free cash flow - Permian Partners(PP) produces from aging oil fields in west Texas. Production is 1.8 million barrels per year in 2016, but production is declining at 7% per year for the foreseeable future. Cost of production, transportation, and administration add up to $25 per barrel. The average oil price was $65 per barrel in 2016. PP has 7 million shares outstanding. The cost of capital is 9%. All of PP's net income is distributed as dividends. For simplicity, assume that the company will stay in business forever and that costs per barrel are constant at $25. Also ignore taxes. A. What is the ending 2016 value of PP share? Assume that oil prices are expected to fall to $60 per barrel in 2017, $55 per barrel in 2018, and %50 per barrel in 2019. After 2019 assume a longterm trend of oil price increases at 5% per year. B. What is PP's ESP/P ratio and why is it not equal to the 9$ cost of capital 27. Value free cash flow Mexican Motors' market cap is 200 billion pesos. Next years free cash flow is 8.5 billion pesos. Security analysts are forecasting that free cash flow will grow by 7.5% per year for the next five years. A. Assume that the 7.5% growth rate is expected to continue forever. What rate of return are investors expecting? B. Mexican Motors has generally earned about 12% on book equity (ROE=12%) and reinvested 50% of earnings. The remaining 50% of earnings has gone to free cash flow. Suppose the company maintains the same ROE and investment rate for the long run. What is the implication for the growth rate of earnings and free cash flow? For the cost of equity? Should you revise your answer to part (a) of this question? 29. Constant -Growth DCF formula The constantgrowth DCF formula DIV 1 P0 = rg is sometimes written as ROE(1b)BVPS P0= rbROE where BVPS is book equity value per share, b is the plowback ratio, and ROE is the ratio of earnings per share to BVPS. Use this equation to show how the pricetobook ratio varies as ROE changes. What is pricetobook when ROE =R 30. DCF Valuation - Portfolio managers are frequently paid a proportion of the funds under management. Suppose you manage a $100 million equity portfolio offering a dividend yield of (DIV1/P0)5%. Dividends and portfolio value are expected to grow at a constant rate. Your annual fee for managing this portfolio is . 5% of portfolio value and is calculated at the end of each year. Assuming that you will continue to manage the portfolio from now to eternity, what is the present value of the management contract? How would the contract value change if you invested in stocks with a 4% yield