Maris Motors Co. pays a $2.15 dividend every quarter for its perpetual

Maris Motors Co. pays a $2.15 dividend every quarter for its perpetual stock. If you expect an annual return of 8.75% on your investment, compute the stock price that you would be willing to pay, using quarterly data.

Now compute the value using annual data. Explain your two answers. What would you be willing to pay for 100 preferred shares?
What will be an ideal response?

ANSWER

Answer: When computing a perpetuity, we have to make sure that both the payment and the discount rate represent the same period. In this problem, we first use 3 months as our period. Thus, we restate the annual required rate of 8.75% as a quarterly (or three-month) rate of = 2.1875% (or 0.028175). Applying the constant dividend model with infinite horizon model, with the quarterly rate of return and a quarterly dividend of $2.15, we get: Price = = = $98.2857. We can get the same answer using annual data. For example, the annual dividend is 4 × $2.15 = $8.60. Thus, Price = = = $98.2857. The answer is the same because the equations are mathematically equivalent. For example, if we divide the numerator and denominator of by four we get . With a price of $98.2857, we get 100 × $98.2857 = $9,828.57 as the cost to purchase 100 preferred shares.