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Marcel Co
Marcel Co. is growing quickly. Dividends are expected to grow at a rate of 0.12 for the next 4 years, with the growth rate falling off to a constant 0.04 thereafter. If the required return is 0.13 and the company just paid a $1.46 dividend, what is the current share price? Answer with 2 decimals (e.g. 45.45).
Expert Solution
Answer
21.99
Step-by-step explanation
Calculate first the annual dividend:
Year 1 = 1.46 x (1+0.12) = 1.6352
Year 2 = 1.6352 x 1.12 = 1.831424
Year 3 = 1.831424 x 1.12 = 2.05119488
Year 4 = 2.05119488 x 1.12 = 2.297338266
Year 5 = 2.297338266 x 1.04 = 2.389231796
Calculate the price at year 4.
Price year 4 = Dividend year 5 / (rate - growth rate)
Price year 4 = 2.389231796 / (0.13 - 0.04)
Price year 4 = 26.54701996
Price at year 0:
1)calculate first the present value of dividends from year 1 to 4.
PV of dividends = (1.6352 / (1+0.13)1) + (1.831424 / (1+0.13)2) + (2.05119488 / (1+0.13)3) + (2.297338266 / (1+0.13)4)
PV of dividends = 5.71193480426832
- value of the dividend from year 5 and beyond
PV = 26.54701996 / (1+0.13)4
PV = 16.2817845
Current share price = 5.71193480426832 + 16.2817845 = 21.99
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