You expect that Bean Enterprises will have earnings per share of $2 for the coming year.Bean plans to retain all of its earnings for the next three years.For the subsequent two years,the firm plans on retaining 50% of its earnings.It will then retain only 25% of its earnings from that point forward.Retained earnings will be invested in projects with an expected return of 20% per year.If Bean's equity cost of capital is 12%,then the price of a share of Bean's stock is closest to:

Question

Quizplus · Accepted Answer

The present value of Bean's stock can be calculated using the dividend discount model, with the assumption that the dividends will grow at a varying rate for the next five years and then remain constant.

The calculation can be broken down into three parts:

1) Calculating the present value of the dividends for years 1-3, using the formula:

PV = D/(1+r)^t

where PV is the present value, D is the dividend, r is the discount rate, and t is the time period.

In this case, the dividends for years 1-3 will be $2 each year, and the discount rate is 12%.

So:

PV1 = $2/(1+0.12)^1 = $1.79 
PV2 = $2/(1+0.12)^2 = $1.59 
PV3 = $2/(1+0.12)^3 = $1.42

2) Calculating the present value of the dividends for years 4-5, using the formula:

PV = D*(1+g)/(r-g)/(1+r)^t

where g is the growth rate of the dividend.

In this case, the dividends for years 4-5 will be 50% of the previous year's dividend, so:

D4 = $2*0.5 = $1.00 
D5 = $1.50*0.5 = $0.75

The growth rate can be calculated as:

g = (D5/D4)^(1/2) - 1 = (0.75/1)^0.5 - 1 = -0.22

(Note: a negative growth rate means that the dividend is decreasing from year to year.)

So:

PV4 = $1.00*(1-0.22)/(0.12-(-0.22))/(1+0.12)^4 = $1.02 
PV5 = $0.75*(1-0.22)/(0.12-(-0.22))/(1+0.12)^5 = $0.84

3) Calculating the present value of the dividends beyond year 5, using the formula:

PV = D/(r-g)/(1+r)^t

In this case, the dividends beyond year 5 will be 25% of the previous year's dividend (i.e. the growth rate is -75%), so:

D6 = $1.50*0.25 = $0.38 
D7 = $0.38*0.25 = $0.09 
D8+ = $0.09*1.20 = $0.11

So:

PV6+ = $0.38/(0.12-(-0.75))/(1+0.12)^6 + $0.09/(0.12-(-0.75))/(1+0.12)^7 + $0.11/(0.12-(-0.75))/(1+0.12)^8 = $1.01

Finally, the present value of the stock can be calculated by adding up the present values of all the dividends:

PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6+ = $6.17

Therefore, the price of a share of Bean's stock is closest to:

Price = PV = $27.75

You Expect That Bean Enterprises Will Have Earnings Per Share