Investment Analysis HW Week 13 Solutions
1. What should the price of the following stocks be? In each case, the OCC is 10%
(a) Expected dividend in one year is $5 and is constant forever. The fair value of the stock is the PV of the dividends at the OCC, or 5/.1 = 50
(b) Expected dividend in one year is $5 and grows at 2% forever. This is a growing perpetuity, and its PV is C/(r -- g), where C is the first payment that comes in one period. Here, the value is 5/(.1 -- .02) = 62.5.
(c) Expected dividend in one year is $5, in two years $4, in three years $2.5, and grows at 2% forever after. We can divide up the payments into a growing perpetuity that starts after year 2, and two individual payments at year 1 and year 2. Standing at year 2 and looking forward, the payments are a growing perpetuity. and its PV at year 2 is C/(r - g), where C is the first payment that comes in one period. Here, the value is 2.5/(.1 - .02) = 31.25. This is at year 2, so its value at year 0 is 31.25/1.12 = 25.83. The first two payments are worth 5/1.1 + 4/1.12 at time 0, or 7.85 In total, the stock is worth 33.67.
(d) Dividend just paid is $5 and is expected to grow at 2% forever. We do not include the payment just made. We need the expected future payments. You are told that the dividends are expected to grow at 2%, which means that the dividend expected in one year is 5 1.02 = 5.1. Since this is a growing perpetuity with first payment in one year, the PV of it is 5.1/(.1 - .02) = 63.75.
2. A company had net income of $20,000 this year on equity of $100,000 last year. Its ROE is expected to be constant. Answer the following questions:
(a) What is its ROE? 20000/100000=20%
(b) The company retains 40% of its earnings. What are earnings next year expected to be? What are dividends next year expected to be?
1
It retained 40% of its earnings, or .4 20000 = 8000. Thus, its equity this year is 108,000. If its ROE is constant at 20%, its expected earnings next year are 108,000 x .2 = 21,600. Its dividends are (1 - .4) 21600 = 12,960.
(c) What is the growth rate of earnings? What is the growth rate of dividends? The growth rate of earnings and dividends is b x ROE = .4 x .2 = 8%. Check this: next year's earnings are 21,600, while this year's were 20,000 - they grew at 8%.
(d) The beta of the returns on the stock has been 1. The risk-free rate is 5% and the return on the market is expected to be 10%. What is the discount rate (OCC) on the company's stock? Using the SML, the CAPM says the expected ret