A stock sells for $50

Finance Jan 15, 2021

A stock sells for $50. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is a constant 10% and the company reinvests a constant 40% of earnings in the firm, what must be the discount rate? (Do not round your intermediate calculations. Enter your answer as a whole percent.) Discount rate %

Expert Solution

Given,

Stock price = $50

Next dividend = $4

Return on reinvested funds = 10% or 0.10

Retention rate = 40% or 0.40

Solution :-

Growth rate = Return on reinvested funds x Retention rate

= 0.10 x 0.40 = 0.04

Now,

Let discount rate be 'r'

Stock price = Next dividend/(r - growth rate)

$50 = $4/(r - 0.04)

r - 0.04 = $4/$50

r - 0.04 = 0.08

r = 0.08 + 0.04 = 0.12 or 12%

So, the discount rate must be 12%.

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