Question

FPT is a mature manufacturing firm. The company just paid a dividend of $5.40 but management expects to reduce the payout by 3.2 percent per year, indefinitely. If you require a return of 10 percent on this stock, what will you pay for a share today?

Please show steps for full credit.

Answer 1

Solution:

As per the information given in the question we have

Required rate of return K_e = 10 % = 0.10

Dividend paid by the company D₀ = $ 5.40

Reduction in payout ratio = 3.2 % = 0.032

Thus the reduced current year dividend D₁= $ 5.40 * ( 1 - Reduction in payout ratio )

= $ 5.40 * ( 1 – 0.032 )

= $ 5.40 * 0.968

= $ 5.2272

Thus D₁ = $ 5.2272

The formula for calculating the Price of a share = D₁ / ( K_e – g )

where

D₁ = Current year dividend ; K_e  = Required rate of return ; g = growth rate

As per the information available we have

Required rate of return K_e = 10 % = 0.10

Growth rate of dividend = g = Reduction in dividend payout ratio = - 3.2 % = - 0.032

Current Year Dividend = D₁ = $ 5.2272

Applying the above information in the formula we have

= $ 5.2272 / ( 0.10 - ( - 0.032 ))

= $ 5.2272 / ( 0.10 + 0.032 )

= $ 5.2272 / 0.132

= $ 39.6000

= $ 39.60 ( When rounded off to two decimal places )

Thus the price that we will pay for a share of stock today = $ 39.60