Question

Solora Inc. is considering Projects X and Y, whose cash flows are shown below. These projects are equally risky. Firm;s WACC=10%.

Year	0	1	2	3	4
CF-X	−$1,100	$375	$375	$375	$375
CF-Y	−$2,200	$725	$725	$725	$725

a) Calculate Payback Period for these two projects. Which one do you choose if the Threshold is less than 3 years?

b) Calculate NPV for these two projects. Are they acceptable? Why? Which one do you choose if they are independent? What about if they are mutually exclusive?
c) Calculate IRR for these two projects. Are they acceptable? Why? Which one do you choose if they are independent? What about if they are mutually exclusive?
d) Do NPV & IRR reach to the same conclusion? If not, on what basis you choose any of these project and why?

Answer 1

a) Calculation of payback period:-

Here cash flows are same for all years for both project.

Payback period = Initial investment / Cash flows per year

Project X payback period = 1100 / 375 = 2.9333 years

project Y payback period = 2200 / 725 = 3.0345 years

Here Threshold limit is 3 years

So, Project X would be selected, it has payback period less than 3 years.

b) Calculation of NPV :-

here Cash flows are same, so we use present value of annuity factor to bring cash inflows into present value .

NPV of project = present value of cash inflows - initial investment

NPV of Project X = 375 * PVAF ( 10%,4 years) - 1100 = 375 * 3.1699 - 1100

NPV of Project X = $ 88.71

NPV of Project Y = 725 * PVAF ( 10%,4 years) - 2200 = 725 * 3.1699 - 2200

NPV of Project Y = $ 98.1775

NPV of project Y is higher than project X .So, Project Y is Selected.

C) Calculation of the IRR :-

IRR of Project X:-

AT, IRR , NPV = 0

375 / (1+i) + 375 / ( 1+i)2 +375 / ( 1+i)3 +375 / ( 1+i)4 - 1100 = 0

Let Us assume 1+i = x

375 / x + 375/x2 +375/x3 +375/x4 -1100 = 0

-1100x4 +375x3 +375x2 + 375x +375 =0

by using maths equation solver

x= 1.189765

1+i = 1.189765

i = 18.9765%

IRR of project X = 18.9765%

IRR of Project Y:-

AT, IRR , NPV = 0

725 / (1+i) + 725 / ( 1+i)2 +725 / ( 1+i)3 +725 / ( 1+i)4 - 2200 = 0

Let Us assume 1+i = x

725 / x + 725/x2 +725/x3 +725/x4 -2200 = 0

-2200x4 +725x3 +725x2 + 725x +725 =0

by using maths equation solver

x= 1.120448

1+i = 1.120448

i = 12.0448%

IRR of project Y = 12.0448%

IRR of project X is higher than project Y .So, Project X is Selected.

4) As per NPV project Y is selected.

As per IRR ,project X is selected.

Here PRoject Y is selected.

On basis of

NPV is absolute measure where IRR is relative measure.

NPV indicates profitability of company.