Question

John met his insurance agent to discuss the purchase of an insurance plan to fund his 8year-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

A)

Case 1: Present value is to be found net of receipts

1.
=-35000+30000/1.1^11+30000/1.1^12+30000/1.1^13+30000/1.1^14=1663.61053703549

2.
=-8000/1.1^2*(1-1/1.1^8)/(1-1/1.1)+30000/1.1^11+30000/1.1^12+30000/1.1^13+30000/1.1^14=-2135.85272043845

3.
=-7000/1.1^2*(1-(1.05/1.1)^8)/(1-(1.05/1.1))+30000/1.1^11+30000/1.1^12+30000/1.1^13+30000/1.1^14=-2887.16984095516

Case 2: Present value is to be found only of payments

1.
=-35000

2.
=-8000/1.1^2*(1-1/1.1^8)/(1-1/1.1)=-38799.4632574739

3.
=-7000/1.1^2*(1-(1.05/1.1)^8)/(1-(1.05/1.1))=-39550.7803779906

B)
Choose Proposal 1 as it leads to lowest present value of payments

C)
Rate earned by John in other investments