Question help: Valuing share price based on future dividend payments

Question

Bill Bailey and Sons pays no dividend at the present time. The company plans to start paying an annual dividend in the amount of $.30 a share for two years commencing two years from today. After that time, the company plans on paying a constant $1 a share dividend indefinitely. How much are you willing to pay to buy a share of this stock if your required return is 14 percent?

A: $4.82

B: $5.25

C: $5.39

D: $5.46

E: $5.58

The right answer is B. I have understood the question but not able to get the right answer.

Neil Harkness · Accepted Answer

To calculate this, sum up the present value (PV) of three components:

$0.30 payment 2 years from now
 	$0.30 payment 3 years from now
 	$1 annual payment to perpetuity 4 years from now

Present value of a payment to perpetuity is

PV = C / R

Where:

PV = Present value
C = Amount of continuous cash payment ($1 in your example)
r = Interest rate or yield (14% in your example)

Calculations:

$0.30 payment 2 years from now = $0.30 / 1.142 = $0.23
 	$0.30 payment 3 years from now = $0.30 / 1.143 = $0.20
 	$1 annual payment to perpetuity 4 years from now = ( $1 / 0.14 ) / 1.144 = $4.82

Adding them all up get you the total PV

= $0.23 + $0.20 + $4.82

= $5.25

shanky · Answer

Isn't the calculation in the present value of $1 annuity incorrectly written, I got 4.23 everytime i tried?

Neil Harkness · Answer

Got a bit carried away compressing my steps and had a typo - it should be 1.143, not 1.144.

After the second payment, 3 years from now, the 'present' value of the $1 perpetuity payments is 1/0.14. So calculating the present value to year 0 would be:

( 1 / 0.14 ) / 1.143

= 4.82

Sorry! 😜