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

In the given case, John will accept that option which will provide lesser cost from the given options.

A. Calculation of Present value (PV) of each option

Option 1 Present value is $60000

Option 2 PV = Principal(1/(1+r)^n)

i.e Principal is 12000, r is 10%, n(No. of period) = 8 Years

Thus PV calcualation as below

Years

Years	Principal	Rate factor @10%	PV $
1	12000	0.909	10908
2	12000	0.826	9912
3	12000	0.751	9012
4	12000	0.683	8196
5	12000	0.621	7452
6	12000	0.564	6768
7	12000	0.513	6156
8	12000	0.466	5592
		Total	63996

Option 3

PV is calculated as follow

Years	Principal	Rate factor @10%	PV $
1	11000	0.909	9999
2	11550	0.826	9540
3	12127	0.751	9107
4	12734	0.683	8697
5	13371	0.621	8303
6	14039	0.564	7918
7	14741	0.513	7562
8	15478	0.466	7213
		Total	68340

(B) Thus as per above solution, John should choose Option 1 is suitable with payment of $60000.

(C) The appropriate discount rate will as per IRR ( Internal rate of return) i.e Pv of Cash inflow = Pv of cash outflow.

As per above solution in B part,

Pv of Cash inflow is 60000

Pv of Cash outflow is as follow

Principal ( 1/(1+r)^n) i.e

As per IRR 60000=45000 (1/(1+r)^4)

r = 6.9%