Question

5. A local Bahamian firm has the following preferred stocks outstanding:

PFD A: $40 annual dividend; $1,000 par value; no maturity

PFD B: $95 annual dividend; $1,000 par value; maturity after twenty-five years If comparable yields are 9 percent, what should be the price of each preferred stock? Explain your answer. (10 points)

Answer 1

Price of PFD A: Since dividend will be received in perpetuity, formula of present value of perpetuity should be used

Price of PFD A = Annual dividend/ Required rate of interest

Annual dividend = $40

Required rate of return = 9%

Price of PFD A = 40/9%

=444.44$

i.e 444 $

Price of PFD B : here Dividend will be received for 25 years and at end of 25th year face value of the preference share will be received, hence one need to find present value of all dividends and face value

Thus Price of PFD B = [Annual dividend x PVIFA(r%,n)] + [Face value x PVIF(r%,n)]

r = required rate of return = 9%

n =no of year till maturity= 25

PVIFA(r%,n) = [1-(1/(1+r)^n / r ]
PVIFA(9%,25) = [1-(1/(1+9%)^25 / 9%]
=[1-(1/(1+0.09)^25 / 0.09]
=[1-(1/(1.09)^25 / 0.09]
=[1-0.1159 / 0.09]
=0.8840/0.09
=9.8226
PVIF(9%,25) = 1/(1+9%)^25
=1/(1.09)^25
= 0.115968

Thus Price of PFD B = [ 95 x 9.8226] + [1000x 0.115968]

=933.1451 + 115.9678

=1049.11 $

i.e 1049 $