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

The fair price of investment can be calculated as present value of future cashflows.

Year	Cashflow	[email protected]%	Cashflow*PVAF
1-12	512.50	10.45*	5355.63
13-24	1025	8.06**	8261.50
25-52	1537.50	12.30***	18911.25

Fair Price = $32,528.38 (5355.63+8261.5+18911.25)

PVAF for 1-12years @2.1875% =  (1-(1+r)^-n)/r = (1-1.021875^-12)/.0.021875 = 10.45

PVAF for 13-24 years @ 2.1875%=  (1-(1+r)^-n)/r - PVAF for 1-12years @2.1875% = (1-1.021875^-24)/.0.021875 -10.45 = 18.51 -10.45 = 8.06

PVAF for 25-52 years @ 2.1875% = (1-(1+r)^-n)/r - PVAF for 13-24 years @ 2.1875% = (1-1.021875^-52)/.0.021875 -18.51 = 30.81-18.51 = 12.30