Question

Next year's earnings are estimated to be $4. The company plans to reinvest 20% of its earnings at 10%. If the cost of equity is 7%, what is the present value of growth opportunities?

$7.07

$7.86

$6.86

$5.86

Answer 1

Given,

Earnings = $4

Retention ratio = 20% or 0.20

Return on investment = 10% or 0.10

Cost of equity = 7% or 0.07

Solution :-

Growth rate (g) = retention ratio x return on investment

= 0.20 x 0.10 = 0.02

Value with growth = [earnings x (1 - retention ratio)] (cost of equity - g)

= [$4 x (1 - 0.20)] (0.07 - 0.02)

= [$4 x 0.80] 0.05

= $3.2 0.05 = $64

Value without growth = earnings cost of equity

= $4 0.07 = $57.14

Present value of growth opportunities = Value with growth - value without growth

= $64 - $57.14 = $6.86