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Up6
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.
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Up4
Isn’t the calculation in the present value of $1 annuity incorrectly written, I got 4.23 everytime i tried?
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Up1
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! 😜
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Up3
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
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Up0
Thank you so much! I got it partially correct and now I see where I made the mistake. 🙂
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Up0
No problem. If you have any further questions just create a new topic!
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