Question

1. 7-17

Compute the rate of return represented by the cash flow.

Year	Cash Flow
0	-$20,000
1	$6,000
2	$6,500
3	$7,000
4	$7,500

This is Question 7-17 from Engineering Economic Analysis

Answer 1

Let,

Rate of return = R

Uniform annuity from year 1 to 4 = $6000

Arithmetic gradient = $500

Time = 4 years

So,

20000 = 6000*(P/A, R, 4) + 500*(P/G, R, 4)

At R = 12%

PW of cash inflows = 6000*3.03735 + 500*4.127

PW of cash inflows = $20287.6

At R = 13%

PW of cash inflows = 6000*2.97447 + 500*4.009

PW of cash inflows = $19851.32

Now, using the method of interpolation,

R = 12% + ((20287.6 - 20000)/(20287.6 - 19851.32))*(13% - 12%)

R = 12.66%

So, the rate of return is 12.66%  

( slight variation can be there due to the use of factor table and rounding off)