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

r = 16%

Explanation:

The Common Stock Valuation method is also simply referred to as the Value of the Stock Method and it is calculated taking different items such as growth rate of dividend, the dividend itself and number of periods into consideration

FIrst, we identify the formula of rate of return where dividend inceases constantly and at a compound rate

P0 = Div1 / r-g

Where Po is the price of the stock, Div1 is the next year's dividend, r is the rate of return and g is the growth rate of teh dividend

Secondly, we look at the growth rate with thereinvestment of 40% stock and a rate of return on reinvestmetn of 15% according to the question

Growth rate = r x e, where r is the rate of return and e is the reinvestment earning

Growth rate = 0.15 x 0.40 = 0.6

Finally, we calculate The rate of return or the discount rate using the first formula

P0 = Div1 / r-g

$40 = $4/r-0.06

r = ($4/$40) + 0.06

r = 16% or 0.16