Question

John is looking at several options to fund his son’s 4-year university degree. The university fees of $45,000 a year will have be paid starting 11 years from today. He is analysing an insurance plan that pays out $45,000 a year for 4 years with the first payout 11 years from today. The insurance plan has several payment options:

Option 1 Pay $60,000 today.

Option 2 Beginning 1 year from today, pay $12,000 a year for the next 8 years.

Option 3 Beginning 1 year from today, make payments each year for the next 8 years. The first payment is $11,000 and the amount increases by 5% each year. Answer the following questions regarding the options above:

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

(b) Analyse which option John should choose.

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

Answer 1

(a) Calculation of present value under 3 options:-

Opton 1: Pay $ 60,000 today i.e the present value for today.

Option 2:Beginning 1 year from today, pay $12,000 a year for the next 8 years.

Formula for present value=Future value/(1+r)^n

=12000/(1+10%)^8+12000/(1+10%)^7+12000/(1+10%)^6+12000/(1+10%)^5+12000/(1+10%)^4+12000/(1+10%)^3+12000/(1+10%)^2+12000/(1+10%)^1

=$64,019.11

Option 3:Beginning 1 year from today, make payments each year for the next 8 years. The first payment is $11,000 and the amount increases by 5% each year

Payments to be made @5% increase each year

Year	1	2	3	4	5	6	7	8
Payments	11000	11550	12127.50	12733.88	13370.57	14039.10	14741.05	15478.10
Increases by 5%		5%	5%	5%	5%	5%	5%	5%

Formula for present value=Future value/(1+r)^n

=11000/(1+10%)^8+11550/(1+10%)^7+12127.5/(1+10%)^6+12733.88/(1+10%)^5+13370.57/(1+10%)^4+14039.1/(1+10%)^3+14741.05/(1+10%)^2+15478.1/(1+10%)^1

=$71,744.70

b) John should go ahead with option 1 where the present value is comparatively less compared to option 2 & 3..Hence, option 1 of $60,000 is better.

c) It can be thought of as the opportunity cost of making the investment. The opportunity cost, would be the cost related to the next best investment.If we know that the cash-on-cash return for the next best investment (opportunity cost) is 8%, then we should use a discount rate of 8%.