# Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly payments

Suppose that a firm always announces a yearly dividend at the end of the first quarter of the year, but then pays the dividend out as four equal quarterly payments. If the next such “annual” dividend has been announced as \$5, it is exactly one quarter until the first quarterly dividend from that \$5, the effective annual required rate of return on the company’s stock is 14 percent, and all future “annual” dividends are expected to grow at 4 percent per year indefinitely, how much will this stock be worth?

Since dividends come quarterly, we first need to convert the 14 percent EAR into an effective quarterly rate: 3.33 percent. The present value of the first year’s dividends will be the present value of a four-period annuity with payments of \$1.25. PMT = 1.25, N= 4, I = 3.33, FV = 0, PV = 4.6099 Since each year’s dividends are expected to grow at 4 percent, the present value of each year’s dividends at the beginning of that year will also grow at 4 percent, so we can value the stock’s dividends as the present value of a growing, perpetuity due: PV = \$4.6099 + {(4.6099 × 1.04)/(0.14 − 0.04)} = \$52.55

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