Question

Apple Inc. pays quarterly dividends. The next dividend will be paid 2 months from now. The last dividend was paid 1 month ago and the amount was $0.73 per share. Suppose the concensus belief is that the dividend will be growing at a rate of 1% per dividend. If we assume an annual discount rate of 6% (expressed as EAR), what is the fair value of Apple's stock?

a.156.95

b.156.99

c.158.52

d.159.29

Answer 1

Next Dividend is expected to be 1 % more than the last dividend. Further, the discount rate is 6% per annum or (1.06)^(3/12) - 1 = 0.014674 or 1.4674 % per quarter (3 months). As last dividend was paid a month ago, the running quarter has only 2 months left and the fair value needs to be determined right now.

Last Dividend = $ 0.73 and Expected Next Dividend = 1.01 x 0.73 = $ 0.7373 and Expected Dividend After the Next = D2 = 0.7373 x 1.01 = $ 0.744673

Effective Interest Rate for the Remaining Two Months = (1.06)^(1/12) -1 = 0.004868 or 0.4868 %

PV of Perpetual Growth Dividends two months from now (t=3 if 1 month ago t= 0) = D2 / (0.014674 - 0.01) = 0.744673 / (0.014674 - 0.01) = $ 159,3224

PV of Perpetual Dividends now = 159.3224 / (1.004868)^(2) = $ 157.7825

PV of D1 now = 0.7373 / (1.004868)^(2) = $ 0.7302

Fair Price of Stock = PV of D1 + PV of Perpetual Dividends Now = 157.7825 + 0.7302 = $ 158.5127 ~ $ 158.52

hence, the correct option is (c)