Question

John met his insurance agent to discuss the purchase of an insurance plan to fund his 8- year-old daughter’s university education in 11 years’ time. The payout from the insurance company is as follows: • Receive $30,000 at the beginning of each year for 4 years with the first receipt starting 11 years from today. The insurance company had 3 payment proposals:

Proposal 1: • Pay $35,000 today.

Proposal 2: • Beginning 2 years from today, pay $8,000 each year for the next 8 years.

Proposal 3: • Beginning 2 years from today, make payments each year for the next 8 years. • The first payment is $7,000 and the amount increases by 5% each year.

(a) Calculate the present value of each proposal. Use a 10% discount rate

(b) Which proposal should John choose? Explain

(c) If the discount rate is not given to you, what would be an appropriate discount rate to use?

Answer 1

John wants to receive 30,000 after 11 years, i.e., from the beginning of the 12 th year for 4 years.

First let us bring all future cash flows to time 0, for easy comparison between the proposals.

Year 2 3 4 5 6 7 8 9 10 11 12 13 14 15 30000 30000 30000 30000 PV $ -36,663.61 $ 1,04,605.56

Considering PMT= 30000 at beginning of year, rate= 10%, N= 4 yrs, FV = 0, PV at the end of 11th year = 104,605.56 dollars. Now discounting this, to t=0, PV=36,663.61 dollars. Now let us compare this value with the 3 proposals.

a). we just need to pay 35,000 dollars

Proposal 1: Pay $35,000 today. PV $ -35,000.00

Proposal 2: • Beginning 2 years from today, pay $8,000 each year for the next 8 years. Year 0 3 - 4 5 6 8000 8000 8000 8000 11 12 13 14 15 7 8000 8 8000 9 8000 10 8000 PV $ -38,799.46 $ 46,947.35

In proposal 2,John has to pay 8000 from the beginning of year 3, for 8 years. Using PV function: rate = 10%, N= 8, PMT=8000, FV=0, we get PV @ end of yr 2 = 46,947.35. Discounting this to time 0, we get PV @ Time 0=38,799.46 dollars

5 Proposal 3: • Beginning 2 years from today, make payments each year for the next 8 years. The first payment is $7,000 and the amount increases by 5% each year. Year 0 4 6 10 11 12 13 14 15 7000 7350.00 7717.50 8103.38 8508.54 8933.97 9380.67 9849.70 PV $ -35,955.25 $ 43,505.86

In proposal 3,John has to make payments as shown above from the beginning of year 3, for 8 years. Using NPV function: rate = 10%, N= 8, &above cash flows, we get PV @ end of yr 2 = 43,505.86. Discounting this to time 0, we get PV @ Time0 =35,955.25 dollars

b). John should choose proposal 1: Pay 35,000 dollars now, as he ends up paying the lowest among the 3 proposals

c). Discount rate = Risk free rate + Risk premium. Risk free rate can be taken from the US treasury bond rates. Risk premium is assumed according to the perceived risk of the investment/ product. Otherwise, rates of similar insurance product with the perceived risk in the market can be chosen.