CHAPTER 4
The Value of Common Stocks

Answers to Problem Sets

1. a. True b. True 2. Investors who buy stocks may get their return from capital gains as well as dividends. But the future stock price always depends on subsequent dividends. There is no inconsistency.

3. P0 = (5 + 110)/1.08 = $106.48

4. r = 5/40 = .125.

5. P0 = 10/(.08 - .05) = $333.33.

6. By year 5, earnings will grow to $18.23 per share. Forecasted price per share at year 4 is 18.23/.08 = $227.91.

7. 15/.08 + PVGO = 333.33; therefore PVGO = $145.83.

8. Z’s forecasted dividends and prices grow as follows:

Calculate the expected rates of return:

From year 0 to 1:

From year 1 to 2:

From year 2 to 3:

Double expects 8% in each of the first 2 years. Triple expects 8% in each of the first 3 years.

9. a. False b. True.

10. PVGO = 0, and EPS1 equals the average future earnings the firm could generate under no-growth policy.

11. Free cash flow is the amount of cash thrown off by a business after all investments necessary for growth. In our simple examples, free cash flow equals operating cash flow minus capital expenditure. Free cash flow can be negative if investments are large.

12. The value at the end of a forecast period. Horizon value can be estimated using the constant-growth DCF formula or by using price–earnings or market– book ratios for similar companies.

13. If PVGO = 0 at the horizon date H, horizon value = earnings forecasted for H + 1 divided by r.

14. Newspaper exercise, answers will vary

15. | Expected Future Values | Present Values | Horizon Period (H) | Dividend (DIVt ) | Price (Pt ) | Cumulative Dividends | Future Price | Total | 0 | | 100.00 | | 100.00 | 100.00 | 1 | 10.00 | 105.00 | 8.70 | 91.30 | 100.00 | 2 | 10.50 | 110.25 | 16.64 | 83.36 | 100.00 | 3 | 11.03 | 115.76 | 23.88 | 76.12 | 100.00 | 4 | 11.58 | 121.55 | 30.50 | 69.50 | 100.00 | 10 | 15.51 | 162.89 | 59.74 | 40.26 | 100.00 | 20 | 25.27 | 265.33 | 83.79 | 16.21 | 100.00 | 50 | 109.21 | 1,146.74 | 98.94 | 1.06 | 100.00 | 100 | 1,252.39 | 13,150.13 | 99.99 | 0.01 | 100.00 | Assumptions 1. Dividends increase at 5% per year compounded. 2. Capitalization rate is 15%.

16.

At a capitalization rate of 10%, Stock C is the most valuable. For a capitalization rate of 7%, the calculations are similar. The results are: PA = $142.86 PB = $166.67 PC = $156.48 Therefore, Stock B is the most valuable.

17. a.

b. First, compute the real discount rate as follows: (1 + rnominal) = (1 + rreal) (1 + inflation rate) 1.095 = (1 + rreal) 1.0275 (1 + rreal) = (1.095/1.0275) – 1 = .0657 = 6.57% In real terms, g = 0. Therefore:

18. a. Plowback ratio = 1 – payout ratio = 1.0 – 0.5 = 0.5 Dividend growth rate = g= Plowback ratio × ROE = 0.5 × 0.14 = 0.07 Next, compute EPS0 as follows: ROE = EPS0 /Book equity per share 0.14 = EPS0 /$50 EPS0 = $7.00 Therefore: DIV0 = payout ratio × EPS0 = 0.5 × $7.00 = $3.50 EPS and dividends for subsequent years are: Year | EPS | DIV | 0 | $7.00 | $7.00 × 0.5 = $3.50 | 1 | $7.00 × 1.07 = $7.4900 | $7.4900 × 0.5 = $3.50 × 1.07 = $3.7450 | 2 | $7.00 × 1.072 = $8.0143 | $8.0143 × 0.5 = $3.50 × 1.072 = $4.0072 | 3 | $7.00 × 1.073 = $8.5753 | $8.5753 × 0.5 = $3.50 × 1.073 = $4.2877 | 4 | $7.00 × 1.074 = $9.1756 | $9.1756 × 0.5 = $3.50 × 1.074 =