Question

As the director of capital budgeting for EFG Corporation, you are evaluating two mutually exclusive projects with the following net cash flows:

                               Project E Project F

                  Year     Cash Flow     Cash Flow

                   0       -$100,000        -$100,000

                   1          50,000            10,000

                   2          40,000            30,000

                   3          30,000            40,000

                   4          10,000            60,000

If EFG’s cost of capital is 15 percent, What is the NPV and IRR of the better project, respectively??

Answer 1

a) Questiion requires to choose alternate proposal in between E and F.

NPV is sum total of discounted cashflows.

Let us first calculate Net Present value of both projects as follows:

Year	Actual Cashflows @15%	Discounted Cashflows@15%
Project - E	Project - F	Project - E	Project - F
0	-1,00,000	-1,00,000	-1,00,000	-1,00,000
1	50,000	10,000	43,478	8,696
2	40,000	30,000	30,246	22,684
3	30,000	40,000	19,725	26301
4	10,000	60,000	5,718	34,305
NPV (Sum of discounted cashflows)	-833	-8,014

Since a positive NPV determine option to be viable, but here we are asked to determine more feaseble option, therefore Project - E is a better option since NPV is less negative here.

Now Let us calculate IRR by using formula of interpolation as follows:-

IRR = Lower Discount Rate + [NPV at Lower rate (Higher Rate - Lower Rate) / (NPV at Lower Rate - NPV at Higher Rate)]

Formulae for IRR :-

First for Project E

At discounting rate of 15% NPV is -833. Let us calculate NPV at 14% rate(on hit and trial basis): -

Year	Actual Cashflow	Discounted Cashflow
0	-1,00,000	-1,00,000
1	50,000	43,859.65
2	40,000	30778.7
3	30,000	20249.14
4	10,000	5920.8
NPV	808.29

IRR = Lower Discount Rate + [NPV at Lower rate x (Higher Rate - Lower Rate) / (NPV at Lower Rate - NPV at Higher Rate)]

Therefore IRR will be = 14% + {808.29 x (15% - 14%) / [808.29 -(-833]}

= 14% + (0.49)

= 14.49%

Therefore NPV will be 0 at 14.49 discounting rate for project E.

Similarly now let us calculate IRR for Project - F

Here, since NPV is -8,014 we will try disounting with more lower rate, say at 12% and 11%

Year	Actual Cashflow	Discounted Cashflow @12%	Discounted Cashflow @11%
0	-1,00,000	-1,00,000	-1,00,000
1	10,000	8,928.57	9,009.01
2	30,000	23915.81	24348.67
3	40,000	28471.21	29247.655
4	60,000	38131.08	39523.85
NPV	-553.33	2,129.18

IRR = Lower Discount Rate + [NPV at Lower rate x (Higher Rate - Lower Rate) / (NPV at Lower Rate - NPV at Higher Rate)]

Therefore IRR will be = 11% + { 2,129.18 x (12% - 11%)/ [2129.18 - (-553.33)]}

= 11% + 0.792

= 11.79%