Question

Calculate the value of T which makes the two cash flow diagrams economically equivalent (i.c. have the same present value) at an effective annual interest rate of 8%. 1,000 $1000 2T $500 $500 EOY EOY 3T

Answer 1

Present value of a cash flow is given as:

$PV = \frac{FV}{(1+r)^n}$

where PV = present value, FV = future value, r = annual rate of interest and n = no. of years

Present value of first cash flow:

$PV_1= \sum \frac{FV}{(1+r)^n} = 1000 + \frac{500}{(1+0.08)^2}+ \frac{1000}{(1+0.08)^4} + \frac{500}{(1+0.08)^6}$

$= 1000 + 428.67+ 735.03 + 352.48 = 2516.18$

Present value of second cash flow:

$PV_2= \sum \frac{FV}{(1+r)^n} = \frac{T}{(1+0.08)^1}+ \frac{2T}{(1+0.08)^3} - \frac{3T}{(1+0.08)^6}$

$= 0.93T +1.59T- 1.89T = 0.63T$

By the equivalence of two cash flows,

0.63T = 2516.18 => T = 3993.94