Answer to Question #185046 in Financial Math for RKP

Question

Org Pvt. Ltd. is considering two mutually exclusive capital investments. The project’s expected net cash flows are as follows:

Expected Cash Flows

Year Project A Project B

0 -400 -575

1 95 150

2 110 200

3 118 250

4 125 275

5 140 230

6 150 180

a. If you were told that each project’s cost of capital was 10%, which project should be selected using the NPV criteria?

b. What is each project’s IRR?

c. What is the regular payback period for these two projects?

d. What is the profitability index for each project if the cost of capital is 12%?

Note - Proper calculations required in each step

Answer 1

(a)

Select project B as the NPV is more when compared to project A.

(b)

PROJECT A

initial investment =Present value of cash flow 

$400=95/(1+r)+110/(1+r)^{2}+118/(1+r)^{3}+125/(1+r)^{4}+140/(1+r)^{5}+150/(1+r)^{6}$

try r=15%

Present value of cash flow

$=95/(1.15)+110/(1.15)^{2}+118/(1.15)^{3}+125/(1.15)^{4}+140/(1.15)^{5}+150/(1.15)^{6}$

Present value of cash flow =454.27

Try r=20%

Present value of cash flow =390.62

Try r=19%

Present value of cash flow =401.35

Interpolation 

$r=19+(401.35-400)/(401.35-390.72)$

$r=19+1.35/=19.13$

r=19.13%

PROJECT A

IRR=19.13%

PROJECT B

initial investment =575

Present value of cash flow

$=150/(1+r)+200/(1+r)^{2}+250/(1+r)^{3}+275/(1+r)^{4}+230/(1+r)^{5}+180/(1+r)^{6}$

r=20%

Present value of cash flow

$=150/(1.2)+200/(1.2)^{2}+250/(1.2)^{3}+275/(1.2)^{4}+230/(1.2)^{5}+180/(1.2)^{6}$

Present value of cash flow =693.89

r=25%

Present value of cash flow =611.19

r=27%

Present value of cash flow =582.38

r=28%

Present value of cash flow =568.78

By interpolation 

$r=28 - (575-568.78)/(582.38-568.78)$

$r=28-6.22/13.60=27.54$

r=27.54%

PROJECT B 

IRR=27.54%

(c)

Payback period=First year +[( Initial cash outflow −First cumulative cash inflow )/Second cash inflow]

For Project A

From the above table, the Initial investment is recovered between 3^rd year and 4^th year,

Payback period$=3 + \frac{400- 323}{125 }$

$=3 + \frac{77}{125 }$

$=3 + 0.6160=3.6160$

the payback period of the project A is 3.62 years.

For Project B

   From the above table, the Initial investment is recovered between 2^nd year and 3^rd year,

 Payback period$=2 + \frac{575-350}{250}$  

$=2 +\frac{225}{ 250}$  

$=2 +0.90=2.90$

The payback period of the project B is 2.90 years.

(d)

The question is based on the concept of selection of mutual exclusive capital project by use of profitability index (PI).

$PI=\frac{NPV}{Initial Investment }$