## Answers

We calculate the present value of a growing annuity as :

PV = (P / (r - g)) * [1 - ((1 + g) / (1 + r))^{n}]

where P = first dividend payment

r = required return per year

g = constant growth rate

n = number of periods

P is the first dividend, which is $1.25 + 10% = $1.375

**a] **PV = (1.375 / (0.18 - 0.10)) * [1 - ((1 + 0.10) / (1 + 0.18))^{5}] = $5.09

**b]** PV = (1.375 / (0.18 - 0.10)) * [1 - ((1 + 0.10) / (1 + 0.18))^{20}] = $12.97

**c]** PV = (1.375 / (0.18 - 0.10)) * [1 - ((1 + 0.10) / (1 + 0.18))^{25}] = $14.22

**d]** PV = (1.375 / (0.18 - 0.10)) * [1 - ((1 + 0.10) / (1 + 0.18))^{40}] = $16.15

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