Question

royal mediterranean cruise lines common stock is selling for 45.69 per share. the last dividend was 1.46, and dividends are expected to grow at a 7% annual rate. flotation costs on the new stock sales are 12% of the selling price. what is the cost of royals new common stock

Answer 1

Solution:

The following formula is used to calculate cost of new common stock :

r_e = [ D₁ / (P *( 1 – F )) ] + g           

r_e = [ ( D₀ * ( 1 + g ) ) / (P *( 1 – F )) ] + g

Where,

r_e = Cost of external equity
D₁ = Expected dividend = [ D₀ * ( 1 + g ) ]

D₀ = Recent dividend
P = Issue price of common stock
F = Flotation cost as a percentage of the issue’s gross proceeds
g = Growth rate of dividend

As per the information given in the question we have

D₀ = $ 1.46

P = Issue price of common stock = $ 45.69
F = Flotation cost as a percentage of the issue’s gross proceeds = 12 % = 0.12
g = Growth rate of dividend = 7 % = 0.07

Applying the above values in the formula we have

= [ ( 1.46 * ( 1 + 0.07 ) ) / ( 45.69 * ( 1 – 0.12 ) ) ] + 0.07

= [ ( 1.46 * ( 1.07 ) ) / ( 45.69 * ( 0.88 ) ) ] + 0.07

= [ ( 1.46 * 1.07 ) / ( 45.69 * 0.88 ) ] + 0.07

= [ 1.5622 / 40.2072 ] + 0.07

= 0.038854 + 0.07 = 0.108854

=10.8854 %

= 10.89 % ( when rounded off to two decimal places )

Thus the cost of royals new common stock = 10.89 %