Aussie Applications Inc. (API) has been growing at rate of 60% per year in recen

Question

Aussie Applications Inc. (API) has been growing at rate of 60% per year in recent years. This growth rate is expected to last for another three years, followed by 6 years of 30% growth, after which growth will be at a constant rate o f 30%, and after that growth will decline to nonconstant growth rate of 5% per year. If D_0 = $2.60 and r_s = 15%, what is API's stock worth today? Now assume API's two periods of supernormal (aka conconstant) growth last one fewer years each. What is API's stock now worth today?

Explanation / Answer

(a)

In year 10, PV of future fividends ($) = (51.40 x 1.05) / (0.15 - 0.05) = 539.7

Discounted to year 0, its PV = 539.7 / (1.15)10 = 539.7 / 4.0456 = 133.41

Price of stock ($) = Sum of all discounted future dividends = 81.60 + 133.41 = 215.01

(b)

In year 8, PV of future fividends ($) = (45.55 x 1.05) / (0.15 - 0.05) = 478.28

Discounted to year 0, its PV = 478.28 / (1.15)8 = 478.28 / 3.059 = 156.35

Price of stock ($) = Sum of all discounted future dividends = 45.55 + 156.35 = 201.90

Year Dividend ($) Discount factor @15% Present value of Dividend ($) 0 2.60 1.0000 2.60 1 4.16 0.8696 3.62 2 6.66 0.7561 5.03 3 10.65 0.6575 7.00 4 13.84 0.5718 7.92 5 18.00 0.4972 8.95 6 23.40 0.4323 10.12 7 30.42 0.3759 11.43 8 39.54 0.3269 12.93 9 51.40 0.2843 14.61 Sum of PV (+$) = 81.60

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