How to figure out a discount rate?

Question

A stock sells for $40. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is 15 percent and the company reinvests 40 percent of earnings in the firm, what must be the discount rate?

Answer 1

This question is asking for an annuity valuation on a dividend discount model.

Assuming no taxes.

NPV = Coupon / (r - g)
$40 = $4 / (r - g)
$40 = $4 / [r - (retained profits x 15%)]
$40 = $4 / [r - (60% x 15%)]
$10 = 1/(r-9%)
1/10 = r - 9%
0.10 + .09 = r
r = 19%