Question

Zayas has identified the following two mutually exclusive projects.

Year	Cash Flow (A)	Cash Flow (B)
0	-$78,500	-$78,500
1	$43,000	$21,000
2	$29,000	$28,000
3	$23,000	$34,000
4	$21,000	$41,000

a. What is the IRR for each project and if you apply the IRR decision rule which project would you accept

b. If the required return is 11% what is the NPV for each of these projects? Which project would you choose?

If possible, please show formula and do not use excel. Thanks!

Answer 1

a.

Project A

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

78,500 = 43,000/(1.0x) +29,000/ (1.0x)^2 +23,000/(1.0x)^3+ $ 21,000/(1.0x)^4      

Or x= 20.705%

Hence the IRR is 20.705%

Project B

Let the IRR be y.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

78,500 =21,000/(1.0y) + 28,000/ (1.0y)^2  + 34,000 /(1.0y)^3 +  41,000 /(1.0y)^4

Or y= 18.728%

Hence the IRR is 18.728%

Since the IRR of Project A is higher than that of Project B, Project A will be accepted.

b. NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

For Project A :

NPV = [ $ 43,000 * 1/(1.11) ^ 1 + $ 29,000* 1/(1.11) ^2 + $ 23,000* 1/(1.11) ^3 + $ 21,000* 1/(1.11) ^4 ] - $ 78,500

= $ 14,426.54

For Project B :

NPV = [ $ 21,000 * 1/(1.11) ^ 1 + $ 28,000* 1/(1.11) ^2 + $ 34,000* 1/(1.11) ^3 + $ 41,000* 1/(1.11) ^4 ] - $ 78,500

= $ 15,012.82

Since the NPV of Project B is higher than that of Project A, Project B will be accepted.