Question

The internal rate of return (IRR) refers to the compound annual rate of return that a project generates based on its up-front cost and subsequent cash flows. Consider this case:

Blue Llama Mining Company is evaluating a proposed capital budgeting project (project Delta) that will require an initial investment of $1,600,000.

Blue Llama Mining Company has been basing capital budgeting decisions on a project’s NPV; however, its new CFO wants to start using the IRR method for capital budgeting decisions. The CFO says that the IRR is a better method because percentages and returns are easier to understand and to compare to required returns. Blue Llama Mining Company’s WACC is 8%, and project Delta has the same risk as the firm’s average project.

The project is expected to generate the following net cash flows:

Year	Cash Flow
Year 1	$350,000
Year 2	$475,000
Year 3	$425,000
Year 4	$500,000

Which of the following is the correct calculation of project Delta’s IRR?

4.05%

3.34%

2.99%

3.52%

If this is an independent project, the IRR method states that the firm should (accept/reject)?

If the project’s cost of capital were to increase, how would that affect the IRR?

A. The IRR would decrease.

B. The IRR would not change.

C. The IRR would increase.

Answer 1

Project Delta’s Internal Rate of Return (IRR)

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 3.00%(R1)

Year	Annual Cash Flow ($)	Present Value factor at 3.00%	Present Value of Cash Flow ($)
1	3,50,000	0.9708738	3,39,806
2	4,75,000	0.9425959	4,47,733
3	4,25,000	0.9151417	3,88,935
4	5,00,000	0.8884870	4,44,244
TOTAL			16,20,718

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $16,20,718 - $16,000,00

= $20,718

Step – 2, NPV at 3.00% is positive, Calculate the NPV again at a higher discount rate, Say 4.00% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 4.00%	Present Value of Cash Flow ($)
1	3,50,000	0.9615385	3,36,538
2	4,75,000	0.9245562	4,39,164
3	4,25,000	0.8889964	3,77,823
4	5,00,000	0.8548042	4,27,402
TOTAL			15,80,928

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $15,80,928 - $16,00,000

= -$19,072 (Negative NPV)

The calculation of Internal Rate of Return using Interpolation method is as follows

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.03 + [$20,718 x (0.04 – 0.03)]

              $20,718 – (-$19,072)

= 0.03 + [$207.18 / $39,790]

= 0.03 + 0.0052

= 0.0352 or

= 3.52%

“Therefore, the Project Delta’s Internal Rate of Return (IRR) will be 3.52%”

If this is an Independent Project, The IRR Method States that the firm should “REJECT” Project Delta, since the IRR (3.52%) is less than the WACC (8.00%).

If the Project’s Cost of capital Increases, then the “IRR WOULD NOT CHANGE”

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.