Question

1. Calculate the rate of return for an investment with the following characteristics.

Initial cost	$20,000
Project life	10 years
Annual receipts	$6000
Annual disbursements	$3000

Answer 1

Let the rate of return be i

AW of project=-20000*(A/P,i,10)+6000-3000=-20000*(A/P,i,10)+3000

We will first find the close range of i and then we can interpolate to get the value of i

We know that if discount rate is equal to rate of return, AW will be zero.

Let us try at i=6%, 7% and 8%

Take i=6%

AW of project=-20000*0.1359+3000=$282

Take i=7%

AW of project=-20000*0.1424+3000=$152

Take i=8%

AW of project=-20000*0.1490+3000=$20

Take i=9%

AW of project=-20000*0.1558+3000=-$116

We can say that i lies between 8% and 9%

Let us try at i=8.5%

AW of project=-20000*0.1524+3000=-$48

Now we can say that i lies between 8% and 8.5%

Let us interpolate

We have x1=20 and y1=0.08

x2=-48 and y2=0.085

We need y such that x=0

y-0.08=0.00147059

or y=0.08147059 or say 8.147%

(We can use Excel or any other software to get the rate of return. It gives it as 8.144%)