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 8 years. The first Beginning 1 year from today, make payments each year for the 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

Answer A : Calculation of Present value
Option 1
Since $60,000 has to be paid today only its present value shall be $60,000
Option 2
Year	PV Factor	Payout	Present value
1	0.91	12000	10,909.09
2	0.83	12000	9,917.36
3	0.75	12000	9,015.78
4	0.68	12000	8,196.16
5	0.62	12000	7,451.06
6	0.56	12000	6,773.69
7	0.51	12000	6,157.90
8	0.47	12000	5,598.09
	Total		64,019.11
PV factor formula = 1/(1+R)^N
Whereas:
R = Rate of interest
N = No. of years
Option 2
Year	PV Factor	Payout	Present value
1	0.91	11,000	10,000.00
2	0.83	11,550	9,545.45
3	0.75	12,128	9,111.57
4	0.68	12,734	8,697.41
5	0.62	13,371	8,302.07
6	0.56	14,039	7,924.70
7	0.51	14,741	7,564.49
8	0.47	15,478	7,220.65
	Total		68,366.35
Answer B
option A should be choosen by John since, the present value is minimum amongest all the optiones available.
Answer C
Appropriate discount rate shall be the rate when present value of inflow is equal to present value of outflow
Let us assume discount rate is 10%
Present value of inflow shall be as under
Year	PV Factor	Payout	Present value
11	0.35	45,000	15,772.23
12	0.32	45,000	14,338.39
13	0.29	45,000	13,034.90
14	0.26	45,000	11,849.91
	Total		54,995.42
Net present value = 54995.42-60000 = -5004.58
Let us assume discount rate is 8%
Present value of inflow shall be as under
Year	PV Factor	Payout	Present value
11	0.38	45,000	16,936.66
12	0.40	45,000	17,870.12
13	0.37	45,000	16,546.41
14	0.34	45,000	15,320.75
	Total		66,673.93
Net present value = 69037-60000= 9037
IRR formula	Lower discount rate + (NPV lower discount rate*(Higher rate-Lower rate))/(NPV at Higher value-NPV at Lower value)
		=8%+((9037*(10%-8%))/((9037-(-5004.58))))
		= 9.29%
Appropriate discount rate shall be 9.29%