# sample_midterm2_answers_4000_fall2008 - Sample Midterm Exam...

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Sample Midterm Exam #2—Suggested Solutions Fi 4000—Spring 2008 Problem 1 (25 points) Suppose that, at the end of 2007, Value Line projects the following for XYZ stock: Year EPS Dividend (= 50% of earnings 2008 \$0.90 \$0.45 2009 \$1.10 \$0.55 2010 \$1.58 \$0.79 Value Line forecasts that the dividend growth rate will level off and stay constant after 2010. In addition, Value Line believes that the dividend payout ratio will remain at 0.5 and the ROE will remain at 15%. a. Compute a reasonable estimate of the steady-state (post-2010) growth rate in dividends. [5 points] . 075 . 0 5 . 0 15 . 0 = × = × = b ROE g b. Suppose that the beta for XYZ is 1.6, the risk-free rate is 5%, and the market risk premium is 7.6%, and these are expected to remain constant for the foreseeable future. What is the market rate of capitalization for XYZ stock? [6 points] We can use the CAPM to derive the market capitalization rate: 1716 . 0 ) 076 . 0 ( 6 . 1 05 . 0 ) ) ( ( = + = - + = f m f r r E r k β 1

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c. Using the dividend discount model, compute the intrinsic value of XYZ stock as of the end of 2007. [8 points] From the dividend discount model, g k g D k k D k D k D P - + × + + + + + + + = ) 1 ( ) 1 ( 1 ) 1 ( ) 1 ( 1 2010 3 3 2010 2 2009 2008 0 Plugging in for k, g, and the dividends, we have that 7198 . 6 \$ 444 . 5 4912 . 0 4007 . 0 3841 . 0 075 . 0 1716 . 0 ) 075 . 0 1 ( 79 . 0 ) 1716 . 1 ( 1 ) 1716 . 1 ( 79 . 0 ) 1716 . 1 ( 55 . 0 1716 . 1 45 . 0 3 3 2 0 = + + + = - + × + + + = P d. Based on your valuation of XYZ stock, what is the present value of XYZ’s growth opportunities? [6 points] 475 . 1 \$ 1716 . 0 90 . 0 72 . 6 \$ Therefore, 2008 0 = - = - = PVGO k E P PVGO 2
Problem 2 (20 points) Suppose the current yield curve for default-free zero coupon bonds is as follows: Maturity (years) Yield to Maturity 1 7% 2 8% 3 9% a. What are the implied one-year forward rates for years 2 and 3? [6 points] To calculate the forward rates, we use the formula 1 1 ) 1 ( ) 1 ( ) 1 ( - - + + = + n n n n n y y f or, 1 ) 1 ( ) 1 ( 1 1 - + + = - - n n n n n y y f % 03 . 11 1103 . 0 1 08 . 1 09 . 1 % 01 . 9 0901 . 0 1 07 . 1 08 . 1 2 3 3 2 2 = = - = = = - = f f So b. Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will the yields to maturity be next year for the one and two year zero coupon bonds? [7 points] If the expectations hypothesis is correct, we know from part a. that in a year the short-term interest rate in year 2 will be 9.01% and the short-term interest rate in year 3 will be 11.03%. Thus, a year from now the price of a one-year bond will be 35 . 917 0901 . 1

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## sample_midterm2_answers_4000_fall2008 - Sample Midterm Exam...

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