Question

Homework: Homework 7 Save HW Score: 54.55%, 30 of 55 pts 7 of 11 (6 complete) Score: 0 of 5 pts P7-7 (similar to) Question Help Miles Hardware has an annual cash dividend policy that raises the dividend each year by 10 %. Last year's dividend, Divo share. Investors want a return of 18% on this stock. What is the stock's price if was $1.25 per a. the company will be in business for 5 years and not have a liquidating dividend? b. the company will be in business for 20 years and not have a liquidating dividend? c. the company will be in business for 25 years and not have a liquidating dividend? d. the company will be in business for 40 years and not have a liquidating dividend? e. the company will be in business for 80 years and not have a liquidating dividend? f. the company will be in business forever? a. What is the price of this stock if the company will be in business for 5 years and not have a liquidating dividend? (Round to the nearest cent.)

Answer 1

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