Question

Problem 8-17 Nonconstant Dividends [LO1]

Lohn Corporation is expected to pay the following dividends over the next four years: $16, $12, $11, and $6.50. Afterward, the company pledges to maintain a constant 6 percent growth rate in dividends forever. If the required return on the stock is 16 percent, what is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Current share price

$

Answer 1

Solution :

The current price of a stock / share = present value of dividends + present value of stock at year n where the firm experience non constant dividends

Thus the current price of the stock / share = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ D₄ * ( 1 / ( 1 + r)⁴ ) ] + [ P₄* ( 1 / ( 1 + r)⁴ ) ]

As per the information given in the question we have

D₁ = $ 16 ; D₂ = $ 12   ; D₃ = $ 11   ; D₄ = $ 6.50   ;   g = 6 % = 0.06   ;   K_e = 16 % = 0.16

Calculation of price of share at year 4:

Price of the share at year 4 where the firm expects a constant growth rate of 6 %

The formula for calculating the price of the share at year 4

P₄ = [ D₄ * ( 1 + g ) ] / ( K_e – g )

We know that

D₄ = $ 6.50 ; g = 6 % = 0.06   ; K_e = 16 % = 0.16 ;

P₄ = [ $ 6.50 * ( 1 + 0.06 ) ] / ( 0.16 – 0.06 )

= ( $ 6.50 * 1.06 ) / ( 0.16 – 0.06 )

= ( $ 6.50 * 1.06 ) / 0.10

= $ 6.89 / 0.10

= $ 68.90

Thus the price of the share at year 4 = $ 68.90

Calculation of price of stock today :

Thus the current price of the stock = [ D₁ * ( 1 / ( 1 + r)¹ ) ] + [ D₂ * ( 1 / ( 1 + r)² ) ] + [ D₃ * ( 1 / ( 1 + r)³) ] + [ D₄ * ( 1 / ( 1 + r)⁴ ) ] + [ P₄* ( 1 / ( 1 + r)⁴ ) ]

Applying the available information in the formula we have the price of the stock as follows :

= [ $ 16 * ( 1 / 1.16 )¹ ] + [ $ 12 * ( 1 / 1.16 )² ] + [ $ 11 * ( 1 / 1.16 )³ ] + [ $ 6.50 * ( 1 / 1.16 )⁴ ] + [ $ 68.90 * ( 1 / 1.16 )⁴ ]

= [ $ 16 * 0.862069 ] + [ $ 12 * 0.743163 ] + [ $ 11 * 0.640658 ] + [ $ 6.50 * 0.552291 ] + [ $ 68.90 * 0.552291 ]

= $ 13.793103 + $ 8.917955 + $ 7.047234 + $ 3.589892 + $ 38.052857

= $ 71.401041

= $ 71.40 ( when rounded off to two decimal places )

Thus the current share price = $ 71.40