Metatrend’s stock will generate earnings of $4 per share this year. The discount rate for the stock is 10%, and the rate of return on reinvested earnings also is 10%. a. Find both the growth rate of dividends and the price of the stock if the company reinvests the following fraction of its earnings in the firm: (i) 0%; (ii) 30%; (iii) 50%. (Do not round intermediate calculations. Enter the growth rates as a whole percent.) b. Redo part (a) now assuming that the rate of return on reinvested earnings is 15%. What is the present value of growth opportunities (PVGO) for each reinvestment rate? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

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jepessoa jepessoa · Answer 1 · 2020-10-07T17:10:49+02:00

Answer:

sustainable growth rate = retention rate x ROE

ROE = 10%

a) growth rate:

if retention rate is 0%, growth rate = 0. P₀ = $4 / 10% = $40

if retention rate is 30%, growth rate = 3%. P₀ = $4.12 / 7% = $58.86

if retention rate is 50%, growth rate = 5%. P₀ = $4.20 / 5% = $84

b) growth rate if ROE increases to 15%

if retention rate is 0%, growth rate = 0. P₀ = $4 / 10% = $40

if retention rate is 30%, growth rate = 4.5%. P₀ = $4.20 / 5.5% = $76.36

if retention rate is 50%, growth rate = 7.5%. P₀ = $4.30 / 2.5% = $172

c) What is the present value of growth opportunities (PVGO) for each reinvestment rate?

PVGO = stock price - value of no growth

value of no growth = $40

when g = 0%, then PVGO = $40 - $40 = $0

when g = 3%, then PVGO = $58.86 - $40 = $18.86

when g = 5%, then PVGO = $84 - $40 = $44

when g = 4.5%, then PVGO = $76.36 - $40 = $36.36

when g = 7.5%, then PVGO = $172 - $40 = $132