Question

Your client would like a $1 million life insurance policy with the following relevant information: § Premium: $10,000 per year Expected dividends per year: $800 Cash value 20 years from now: $125,000 Discount rate: 5% a. Given this information, compute the Net Cost of the policy over the next 20 years. Compute the cost per year, per $1,000 of coverage. b. Compute the policy’s Interest-Adjusted Cost over the next 20 years, per year, per $1,000 of coverage. c. Suppose the cash value at the end of the most recent (previous) year is $2,300, and the cash value at the end of the current year will be $5,000. Compute the policy’s cost per $1,000 of coverage using the Benchmark Method.

Answer 1

Calculating the present discounted value of a two-year bond with a principal of $3,000 requires adjusting the future cash flows by the current discount rate. If interest rates rise, the present value is recalculated with the higher discount rate, resulting in a lower present value for the bond's future payments.

Step-by-step explanation:

Calculating Present Discounted Value

When considering a simple two-year bond with a principal of $3,000 and an annual interest rate of 8%, the bond will pay $240 in interest each year. If the discount rate is also 8%, the present discounted value (PDV) of the bond's payments can be calculated using the formula for PDV, which considers both the yearly interest payments and the principal repayment at the end of the second year.

Now, if interest rates rise and the new discount rate becomes 11%, the present discounted value needs to be recalculated, which will be lower compared to when the discount rate was 8% due to the higher discount applied to future cash flows.

Example Calculation with an 8% Discount Rate

The bond pays $240 at the end of the first year and an additional $240 plus the $3,000 principal at the end of the second year. The present value of the first payment is:

PV1 = $240 / (1 + 0.08)1

And the present value of the second payment is:

PV2 = ($240 + $3,000) / (1 + 0.08)2

The total PDV is the sum of PV1 and PV2.

Example Calculation with an 11% Discount Rate

If the discount rate increases to 11%, the present value of the payments decreases:

• Premium: $10,000 per year
• Expected Dividends per year: $800
• Cash Value 20 years from now: $125,000
• Discount rate: 5%
• Cash Value at the end of the most recent year: $2,300
• Cash Value at the end of the current year: $5,000
• Coverage Amount: $1,000,000
• Calculate each of the three scenarios using the provided formulas.