Even better products has come out with a new and improved product. as a result, the firm projects an roe of 20%, and it will maintain a plowback ratio of 0.30. its projected earnings are $2 per share. investors expect a 14% rate of return on the stock.

a.

at what price and p/e ratio would you expect the firm to sell? (do not round intermediate calculations. round your answers to 2 decimal places.)

price $

p/e ratio

b.

what is the present value of growth opportunities? (do not round intermediate calculations. round your answer to 2 decimal places.)

Explanation:

a.)

First, find the growth rate using the ROE and the retention rate;

g = ROE + retention rate

g = 0.20 * 0.30

g = 0.06 or 6%

Next, find price using Dividend discount model (DDM);

Price = Div/ (r-g)

where Div = next year's dividend

r = required return

g = growth rate ,

Div = earnings * (1- plowback rate)

Div = $2* 0.70 = $1.4

Next, plug in the numbers to the formula above;

Price = 1.4/ (0.14 - 0.06)

Price = $17.50

Price earnings ratio; PE = Price/ earnings per share

PE = 17.50/ 2 = 8.75

b.) Present value of growth opportunities (PVGO)

Use PVGO formula to find the answer. It is as follows;

PVGO = Price - (E/r)

whereby, E= earnings per share = $2

r = investors required rate of return = 14%

Price = $17.50

PVGO = 17.50 + (2/0.14)

= 17.50 + 14.2857

= 31.7857

Therefore, Present value of growth opportunities is $31.79

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