Question

An investment pays $2,050 per year for the first 3 years, $4,100 per year for the next 3 years, and $6,150 per year the following 7 years (all payments are at the end of each year). If the discount rate is 8.75% compounding quarterly, what is the fair price of this investment?

Answer 1

Value of investment = Sum of the present values of future cash flows

Value of investment = 2050/(1+8.75%)^1 + 2050/(1+8.75%)^2 + 2050/(1+8.75%)^3 + 4100/(1+8.75%)^4 + 4100/(1+8.75%)^5 + 4100/(1+8.75%)^6 + 6150/(1+8.75%)^7 + 6150/(1+8.75%)^8 + 6150/(1+8.75%)^9 + 6150/(1+8.75%)^10 + 6150/(1+8.75%)^11 + 6150/(1+8.75%)^12 + 6150/(1+8.75%)^13

Fair value of investment = $32,187.90

OR can be done as below:

Year	Cash flow	Discounting = Df	Present value
Y	CF	Df =1/(1+8.75%)^Y	CF x Df
1	2050	0.91954	1,885.06
2	2050	0.84555	1,733.39
3	2050	0.77752	1,593.92
4	4100	0.71496	2,931.34
5	4100	0.65744	2,695.49
6	4100	0.60454	2,478.61
7	6150	0.55590	3,418.77
8	6150	0.51117	3,143.70
9	6150	0.47004	2,890.76
10	6150	0.43222	2,658.17
11	6150	0.39745	2,444.29
12	6150	0.36547	2,247.63
13	6150	0.33606	2,066.78
		Total = PV =	32,187.90