Question

Suppose that a firm’s recent earnings per share and dividend per share are $2.10 and $1.10, respectively. Both are expected to grow at 9 percent. However, the firm’s current P/E ratio of 20 seems high for this growth rate. The P/E ratio is expected to fall to 16 within five years. Compute the dividends over the next five years. (Do not round intermediate calculations. Round your final answer to 3 decimal places.)

Dividends Years

First year $

Second year $

Third year $

Fourth year $

Fifth year $

Compute the value of this stock in five years. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Stock price

$

  

Calculate the present value of these cash flows using an 11 percent discount rate. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Present value

$

Answer 1

Answer a.

D0 = $1.10

Growth rate, g = 9%

D1 = $1.100 * 1.09 = $1.199
D2 = $1.199 * 1.09 = $1.307
D3 = $1.307 * 1.09 = $1.425
D4 = $1.425 * 1.09 = $1.553
D5 = $1.553 * 1.09 = $1.692

Answer b.

E0 = $2.10
Growth rate, g = 9%

E5 = E0 * (1 + g)^5
E5 = $2.10 * 1.09^5
E5 = $3.231

P/E Ratio at the end of Year 5 = P5 / E5
16 = P5 / $3.231
P5 = $51.696

So, stock price in five years is $51.70

Answer c.

Discount Rate = 11%

Present Value = $1.199/1.11 + $1.307/1.11^2 + $1.425/1.11^3 + $1.553/1.11^4 + $1.692/1.11^5 + $51.70/1.11^5
Present Value = $35.89