Question

Miles Hardware has an annual cash dividend policy that raises the dividend each year by 10​%. Last​ year's dividend, Div 0​, was $ 1.50 per share. Investors want a return of 18​% on this stock. What is the​ stock's price if

a.  the company will be in business for 10 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 30 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 10 years and not have a liquidating​ dividend?

Answer 1

Given, D0 = $1.50

Growth Rate of dividend = g = 0.10

Required rate of return = r = 0.18

Let number of years for which dividends are paid be n

The Present Value of the stock is the sum of Present Value of all future dividends

=> P0 = D1/(1+r) + D2/(1+r)² + ..... Dn/(1+r)ⁿ

=> P0 = D0(1+g)/(1+r) + D0(1+g)²/(1+r)² + ..... D0(1+g)ⁿ/(1+r)ⁿ

=> P0 = D0(1+g)/(1+r) [1 - (1+g)ⁿ/(1+r)ⁿ] / [1 - (1+g)/(1+r)] = D0(1+g)/(r-g) [1 - (1+g)ⁿ/(1+r)ⁿ]

(a) When n = 10,

P0 = 1.50(1+0.10)/(0.18-0.10) [1 - (1+0.10)¹⁰/(1+0.18)¹⁰] = $10.40

(b) When n = 20,

P0 = 1.50(1+0.10)/(0.18-0.10) [1 - (1+0.10)²⁰/(1+0.18)²⁰] = $15.56

(c) When n = 30,

P0 = 1.50(1+0.10)/(0.18-0.10) [1 - (1+0.10)³⁰/(1+0.18)³⁰] = $18.11

(d) When n = 40,

P0 = 1.50(1+0.10)/(0.18-0.10) [1 - (1+0.10)⁴⁰/(1+0.18)⁴⁰] = $19.38

(e) When n = 80,

P0 = 1.50(1+0.10)/(0.18-0.10) [1 - (1+0.10)⁸⁰/(1+0.18)⁸⁰] = $20.55

(f) If the company is in business forever,

P0 = D0(1+g)/(1+r) + D0(1+g)²/(1+r)² + .....

=> P0 = D0(1+g)/(1+r) [1 - (1+g)/(1+r)] = D0(1+g)/(r-g)

=> P0 =  1.50(1+0.10)/(0.18-0.10) = $20.625