Your parents recently retired and asked you to recommend one of the annuities so
ID: 2730509 • Letter: Y
Question
Your parents recently retired and asked you to recommend one of the annuities sold by Tramp insurance company and Hill investments company. You can earn 4 % on your money in other investments.
a) What is interest rate built into the annuity for both companies
b) What is the present value of the annuities
c) Which annuity will you recommend and why?
Annuity Cost today Payments per year Duration of Annuity
Tramp CO. $160,000 $10,754 20 years
Hill CO. $140,000 $10,635 22 years
Explanation / Answer
a) What is interest rate built into the annuity for both companies?
The cost today is the PV of the annuities discounted at the interest rate built into the annuities.
The interest rate is to solved from the following equation:
Tramp Co: 160000 = 10754*pvifa(i,20); 14.8782 = pvifa(I,20)
for 3% the factor is 14.8775
for 4% 13.5903
exact rate = 3 + 0.0007/1.2872 = 3.00054 = 3%
Hill Co: 140000/10635 = pvifa(i,22) = 13.1641
from the factor table it is close to the factor for 5%
Hence, interest rate for Hill Company is 5%
b) What is the present value of the annuities
Present value of the annuities is
Tramp company = 10754*pvifa(4,20) = 10754*13.5903 = $146,150
Hill company = 10635*pvifa(4,22) = 10635*14.4511 = $153,687
(NPV would be Tramp company = 146150 - 160000 = -$13,850; Hill company = 153687 - 140000 = $13,687)
c) Which annuity will you recommend and why?
Would recommend the annuity of Hill company as it gives a return of 5% (inbuilt interest rate) which is greater than the required rate of return of 4%, whereas in the case of Tramp company the inbuilt interest rate is only 3%, which is lower than the required rate of return of 4%. (NPV is positive for Hill company and negative for Tramp company)
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