Question

Consider the cash flow series shown below. What value of C makes the inflow series equivalent
to the outflow series at an interest rate of 6% compounded annually?

Answer 1

We will calculate the present value of all inflow cash series and equate it with the present value of all outflow cash series.

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

where PV = present value

FV = future value

r = rate of interest

and n = no. of years.

Using this and -

PV of cash inflows = PV of cash outflows

$\frac{150}{(1+0.06)^1} + \frac{150}{(1+0.06)^2} + \frac{150}{(1+0.06)^3}+ \frac{150}{(1+0.06)^7}+ \frac{150}{(1+0.06)^8}+ \frac{150}{(1+0.06)^9} = \frac{C}{(1+0.06)^4}+\frac{C}{(1+0.06)^5}+\frac{C}{(1+0.06)^6}+\frac{3C}{(1+0.06)^{10}}$

$\Rightarrow 141.51+ 133.50 +125.94+ 99.76+94.11+ 88.78 = \frac{C}{1.26}+\frac{C}{1.34}+\frac{C}{1.42}+\frac{3C}{1.79}$

$\Rightarrow 683.60 = 0.79C+0.75C+0.70C+1.68C$

$\Rightarrow 3.92C = 683.60 \Rightarrow C = 683.60 /3.92 = 174.39$