Answer to Question #266972 in Computer Networks for freshy

Question

Supply of laptops to a customer and maintenance agreement of three years costs GH¢ 16,000.  The annual cash flows are: 8,000, 7,000 and 6,000. If , what is the IRR (). 

Answer 1

Initial investment =16000

cash flow in year 1 = 8000

cash flow in year 2 = 7000

cash flow in year 3 = 6000

0=NPV= $\displaystyle\sum_{t=0}^T \frac{c_t}{(1+IRR)^t}$

Substitutes the values in the above equation

$0=- \frac{16000}{(1+IRR)^0}+\frac{8000}{(1+IRR)^1}+ \frac{7000}{(1+IRR)^2}+\frac{8000}{(1+IRR)^3}$

Using the plug and chug approach;

we can assume $IRR=20\%=0.2$

so the equation becomes

$0=- \frac{16000}{(1+0.2)^0}+\frac{8000}{(1+0.2)^1}+ \frac{7000}{(1+0.2)^2}+\frac{8000}{(1+0.2)^3}$

$0=-16000+6666.67+4861.111+3472.222-1000$

Hence as the RHS is negative we will decrease the value of IRR.

let us use IRR = 15%;

the equation becomes

$0=- \frac{16000}{(1.15)^0}+\frac{8000}{(1.15)^1}+ \frac{7000}{(1.15)^2}+\frac{8000}{(1.15)^3}$

$0=-16000+6956.52+5293.00+3945.09=194.61$

Now the RHS is positive so we will increase IRR.

Let us use IRR=15.7%

$0=- \frac{16000}{(1.157)^0}+\frac{8000}{(1.157)^1}+ \frac{7000}{(1.157)^2}+\frac{8000}{(1.157)^3}$

$0=-16000+6914.43+5229.15+3873.92=17.50$

So we can conclude $IRR=15.7\%$