Question

The Leprechaun Corp. last paid a $1.50 per share annual dividend. The company is planning on paying $3.00, $5.00, $7.50, and $10.00 a share over the next four years, respectively. After that the dividend will be a constant $2.50 per share per year. What is the market price of this stock if the market rate of return is 15%?

Group of answer choices

$17.04

$22.39

$26.57

$29.08

$33.71

Answer 1

Solution:

The market price of a stock = Present value of dividends earn from Year to Year “ n “ + Present value of stock at year “ n “

Thus the Market 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 ) ]

As per the information given in the question we have

Thus we have D₁ = $ 3 ; D₂ = $ 5   ; D₃ = $ 7.5   ; D₄ = $ 10   ;

Calculation of price of share at year 4:

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

P₄ = [ D₄ * ( 1 + g ) ] / ( K_e – g )

We know that

D₄ = $ 2.50 ; g = 0 % = 0.00   ; K_e = 15 % = 0.15 ;

P₄ = [ $ 2.50 * ( 1 + 0.00 ) ] / ( 0.15 – 0.00 )

= ( $ 2.50 * 1. ) / ( 0.15 – 0.00 )

= $ 2.50 / 0.15

= $ 16.666667

Thus the price of the share at year 4 = $ 16.666667

Calculation of market price of stock :

Thus the market 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 Market price of the stock as follows :

= [ $ 3 * ( 1 / 1.15 )¹ ] + [ $ 5 * ( 1 / 1.15 )² ] + [ $ 7.50 * ( 1 / 1.15 )³ ] + [ $ 10 * ( 1 / 1.15 )⁴ ] + [ $ 16.666667 * ( 1 / 1.15 )⁴ ]

= [ $ 3 * 0.869565 ] + [ $ 5 * 0.756144 ] + [ $ 7.50 * 0.657516 ] + [ $ 10 * 0.571753 ] + [ $ 16.666667 * 0.571753 ]

= $ 2.608695 + $ 3.780720 + $ 4.931370 + $ 5.717530 + $ 9.529217

= $ 26.567532

= $ 26.57 ( when rounded off to two decimal places )

Thus the market price of the stock = $ 26.57

The solution is option 3 = $ 26.57