Name:... ECO 4368 Summer 2016 Midterm 2. There are 4 problems and 8 True-False questions. TOTAL POINTS: 100

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1 Name:... ECO 4368 Summer 2016 Midterm 2 There are 4 problems and 8 True-False questions. TOTAL POINTS: 100 Question 1 (20 points): A company with a stock price P 0 = $108 had a constant dividend growth rate last estimated to be g = 8%. Suppose now that the market updates its beliefs on the constant dividend growth rate, and it is now estimated to be g new = 4%. After this new estimate, the stock price went down to P0 new = $52. The required rate of return on the market portfolio is r m = 6% and the risk-free rate is 2% and did not change. The company s beta also remained the same. a) (15 points) What is the last dividend D 0 of the company? Answer: Since r m, r RF and β s did not change, we have rs before = rs after D 0 (1 + g) + g = D 0(1 + g new ) P 0 P0 new D 0 ( ) = D 0( ) (0.01)D = (0.02)D (0.01)D 0 = 0.04 D 0 = 0.04 (0.01) = $4 1

2 b) (10 points) What is the beta of the company? Hence we have rs before = D 0( ) 108 r before s = 4( ) = 12% rs before = 12% = r RF + β s (r M r RF ) 12% = 2% + β s (6% 2%) β s = 2.5 2

3 Question 2 (15 points): A company recently paid a dividend of $1.00 per share (D 0 = $1). The company has a constant dividend growth rate of g = 8% and a beta equal to 2. The required rate of return on the market is r M = 8% and the risk-free rate is r RF = 2%. a) (5 points) What should be the company s stock price according to the constant dividend growth rate model? Answer: P 0 = D 0(1 + g) r s g r s = 2% + 2(8% 2%) = 14% P 0 = 1( ) = $18 3

4 b) (10 points) The company is considering a change of policy which will reduce its g to 5%. If market conditions remain unchanged, what new beta will cause the stock price of the company to remain unchanged? Answer: Let s first find the required return on the stock when we have g new = 5% Hence we can write r new s = 1( ) = 10.83% rs new = r RF + β new s (r M r RF ) 10.83% = 2% + β new s (8% 2%) β new s = 8.83% 6% =

5 Question 3 (16 points): A company recently paid a dividend of $2 per share (D 0 = $2). The company had a constant dividend growth rate last estimated to be g = 3%. Suppose now that the market updates its beliefs on the constant dividend growth rate, and it is now estimated to be g new = 4%. After this new estimate, the stock price be P0 new = $52. The required rate of return on the market portfolio is r m = 6% and the risk-free rate is 2% and did not change. The company s beta also remained the same. What was the price P 0 before the change in g? Answer: Since r m, r RF and β s did not change, we have rs before = rs after D 0 (1 + g) + g = D 0(1 + g new ) P 0 P new 2( ) = P P 0 = P 0 = ( ) 52 P 0 = = $

6 Question 4 (25 points): Suppose a company conducts a study to evaluate the benefits and costs of selling off their secondary business In particular, if they keep their secondary business, they will have β current 1.6 and g = 8%. If they sell it off, they will have a new beta given by β new s = 2 and a new dividend growth rate g new which is unknown. The last dividend of the company is D 0 = $1. Assume that r M = 8% and risk free rate is r RF = 4% a) (15 points) If the company is trying to maximize its current stock price, what is the lowest value of g new such that the company is better off selling the secondary business? Answer: If the company keep the business, we have P 0 = D 0(1 + g) where r s g r s = 4% + 1.6(8% 4%) = 10.4% P 0 = 1( ) = = $45 If the company sells the business, we have r new s = 4% + 2(8% 4%) = 12% The company is better off selling the business if which implies P new 0 = D 0(1 + g new ) $45 rs new gnew 1(1 + g new ) gnew 1(1 + g new ) 45 (0.12 g new ) 1 + g new g new s = 46g new 4.4 g new = 9.56% Hence the minimum g new that makes selling the business the better option is g new = 9.56%. 6

7 b) (10 points) What would be the stock s dividend return and the capital gains return at the dividend growth rate g new that you found in part (a)? At g new = 9.56%, the capital gains return would be 9.56%. At g new = 9.56%, the dividend return would be r new s g new = 12% 9.56% = 2.44% 7

8 True False Questions (3 points each, 24 points total) Suppose the stock s beta increases. The risk free rate (r RF ) and return on market portfolio (r M ) both remain the same, and the dividend growth rate g goes UP. Then dividend return on the stock must go down....false... Suppose, the company beta increases, the risk free rate and return on market portfolio remain the same. For the stock price to remain constant, the dividend growth rate estimate g must go down....false... Suppose the required return r M on the market portfolio increases, the dividend growth rate estimate g goes up, and company beta remains constant. This implies that the dividend return on the stock must DECREASE....FALSE... If the market lowers its estimate of a company s beta, increases its dividend growth estimate g and all else constant, this means dividend return must increase....false... If the capital gains return on a stock goes up and all else is the same and then this means the stock price also goes up....true... Suppose the company beta, risk free rate and return on market portfolio remain the same, and the dividend growth rate g goes down. This implies that the dividend return on the stock must increase....true... 8

9 Suppose the company beta increases, the risk free rate and return on market portfolio remain the same. For the stock price to remain constant, the capital gains return must increase....true... Suppose the required return r M on the market portfolio increases, the dividend growth rate estimate g goes down, and company beta remains constant. This implies that the dividend return on the stock must increase....true... 9

10 SOME FORMULAS: CAPM Equation: r s = r RF + β s (r M r RF ) Constant Dividend Growth Stock Valuation P 0 = D 0(1 + g) r s g or P 0 = D 1 r s g r s = D 1 P 0 + g The required return on equity (stock) can be computed in two ways. r s = D 1 P 0 + g or r s = r RF + β s (r M r RF ) 10

FIN FINANCIAL INSTRUMENTS SPRING 2008

FIN FINANCIAL INSTRUMENTS SPRING 2008 FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 OPTION RISK Introduction In these notes we consider the risk of an option and relate it to the standard capital asset pricing model. If we are simply interested