To determine: Whether the policy is worth purchasing.
Introduction:
The
Answer to Problem 60QP
The policy is not worth purchasing.
Explanation of Solution
Given information:
An insurance company offers a new policy to their customers. The children’s parents or grandparents will buy the policy at the time of the child’s birth. The parents can make 6 payments to the insurance company. The six payments are as follows:
- On the 1st birthday, the payment amount is $800.
- On the 2nd birthday, the payment amount is $800.
- On the 3rd birthday, the payment amount is $900.
- On the 4th birthday, the payment amount is $900.
- On the 5th birthday, the payment amount is $1000.
- On the 6th birthday, the payment amount is $1000.
After the 6th birthday of the child, the payment will not be made. At the time when the child is 65 years, he or she gets $150,000. The interest rate for the first 6 years is 9% and for the rest of the years is 5.5%.
Note: From the given information, it is essential to compute the future value of the premiums for the comparisons of the promised cash payments at 65 years. Thus, it is necessary to determine the premiums’ value at 6 years first, as the rate of interest varies at that time.
Time line of the payments:
Formula to calculate the future value is as follows:
Note: PV denotes the present value, r denotes the rate of discount and t denotes the number of years.
Compute the future value for the five years is as follows:
Hence, the future value of 1st year is $1,230.90.
Hence, the future value of 2nd year is $1,129.27.
Hence, the future value of 3rd year is $1,165.53.
Hence, the future value of 4th year is $1,069.29.
Hence, the future value of 5th year is $1,090.
Compute the value of 6th year is as follows:
Note: The value of 6th year is calculated by adding all the computed future values and the 6th year’s value, that is, $1,000.
Hence, the value of 6th year is $6,684.98.
Compute the future value of the lump sum at the 65th birthday of the child is as follows:
Note: The number of years is 59, because after the 6th birthday of the child the payments will not be paid.
Hence, the future value of the lump sum at the 65th birthday of the child is $157,396.57.
From the above calculation of the future value, it can be stated that the policy is not worth purchasing as the deposit’s value in the future is $157,396.57, but the contract will pay off at $150,000. The premium’s amount to $7,396.57 is more than the payoff of the policy.
Note: The present value of the two cash flows can be compared.
Formula to calculate the present value of the premiums is as follows:
Compute the present value of the premiums as follows:
Hence, the present value of the premiums is $3,986.04.
The today’s value of the $150,000 at the age of 65 is as follows:
The cash flow of the premiums is still higher. At the time of zero, the difference is $187.32
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Chapter 5 Solutions
ESSENTIALS OF CORPORATE FINANCE (LL)
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