Question

You have assigned the following values to these three firms: Price Upcoming Dividend Growth Beta US Bancorp $ 29.80 $ 3.20 8.80 % 1.59 Praxair 59.15 1.51 13.00 2.20 Eastman Kodak 36.50 1.00 11.50 0.98 Assume that the market portfolio will earn 15.50 percent and the risk-free rate is 5.70 percent. Compute the required return for each company using both CAPM and the constant-growth model. (Do not round intermediate calculations and round your final answers to 2 decimal places.)

Answer 1

Solution:

The required return as per CAPM is kp = rf + beta (rm - rf)

Where:

kp is the required return , rf is the risk free rate, rm -> market return , beta -> beta value of the firm

As per Constant growth model we have:

V = D1 / (k - g)

Where, V is the value of the stock, g -> annual growth rate of the dividends , k -> required rate of return, D1 ->next year's dividend.

Given rf = 5.70% , rm = 15.50%

Company	Price	Upcoming Div	Growth	Beta	CAPM	Constant Growth
US Bancorp	29.80	3.20	8.80%	1.59	kp = 5.70% + 1.59(15.50% - 5.70%) = 5.70% + 1.59(9.8%) = 5.70% + 15.582% kp =21.282%	v = D1 / k -g 29.80 = 3.20/ k - 8.80% k - .088 = 3.20/29.80 k - 0.088 = .10738255 k = .19538255 = 19.53%
Praxair	59.15	1.51	13%	2.20	kp = 5.70% + 2.20(15.50% - 5.70%) = 5.70% + 2.20(9.8%) = 5.70% + 21.56% kp =27.26%	59.15 = 1.51/ k - 13% k - 13% = 1.51/59.15 k - 0.13 = .025528318 k = .155528318 = 15.55%
Eastman Kodak	36.50	1	11.50%	.98	kp = 5.70% + .98(15.50% - 5.70%) = 5.70% + .98(9.8%) = 5.70% + 9.604% kp =15.304%	36.50 = 1/ k - 11.50% k - 11.50% = 1/36.50 k - 0.115 = .02739726 k = .14239726 = 14.23%