Question

Suppose that a firm’s recent earnings per share and dividend per share are $2.50 and $1.50, respectively. Both are expected to grow at 9 percent. However, the firm’s current P/E ratio of 24 seems high for this growth rate. The P/E ratio is expected to fall to 20 within five years.

Compute the dividends over the next five years.

Compute the value of this stock in five years.

Calculate the present value of these cash flows using an 11 percent discount rate.

Answer 1

D0 1.50

D1 1.60

D2 1.78

D3 1.94

D4 2.12

D5 2.31

Price of the stock after 5-year $ 77

PV $ 81.75

Step-by-step explanation:

Earning per share 2.5

Dividend per share 1.5

grow ratio 9%

P/E ratio 24

within 5 year is expected to fall to 20

We solve for the dividend by multiplying the dividends by the grow rate of 9%

We solve for the earning after 5 years:

`Principal \: (1+ r)^(time) = Amount`

Principal 2.50

time 5.00

rate 0.09000

`2.5 \: (1+ 0.09)^(5) = Amount`

Amount 3.85

Then we multiply by 20 to get the value of the stock:

$ 3.85 x 20 = $ 77

We solve the horizon value:

`(D_1)/(r-g) = PV\\(D_0(1+g))/(r-g) = PV\\`

`(1.5(1+0.09))/(0.11 - 0.09) = PV\\`

PV $ 81.75