Question

Suppose that a firm’s recent earnings per share and dividend per share are $3.90 and $2.90, respectively. Both are expected to grow at 7 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 and round your final answers to 3 decimal places.) Dividends Years First year $ 3.10 Second year $ 3.32 Third year $ 3.55 Fourth year $ 3.80 Fifth year $ 4.07

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

Calculate the price of this stock today, including all six cash flows at discount rate of 9 percent. (Do not round intermediate calculations and round your final answer to 2 decimal places.) Present value $?

Answer 1

EPS in Year 0 = $3.90

g= 7%

So,

Year EPS($) A DF@9% B PV @ 9% (A*B)

1 3.9(1+0.07) = 4.173 0.9174 3.8283  

2   4.173(1.07)= 4.465 0.8416 3.7577

3   4.465(1.07)= 4.777 0.7721 3.6883

4   4.777(1.07)= 5.112 0.7084 3.6213

5   5.112(1.07)= 5.469 0.6499 3.5544

Total 18.45

Add: EPS Year 0 3.90

PV of Cash flows today 22.35

So, P/E in 5th year = 16

P/E = MPS/EPS

16 = MPS/5.47

MPS = 16 x 5.47

MPS = $87.52

The value of this stock in five years is $87.52

The price of stock today, including all six cash flows at discount rate of 9 percent (MPS ) = P/E TODAY * EPS = 20*22.35 = $447