Question

Internal rate of return (IRR)

Ziff Corp. is evaluating a proposed capital budgeting project that will require an initial investment of $1,550,000. The project is expected to generate the following net cash flows:

Year	Net Cash Flow
1	$350,000
2	$475,000
3	$400,000
4	$475,000

Ziff Corp. hasbeen basing capital budgeting decisions on a project’s NPV; however, its new CFO wants to start using the internal rate of return (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. Ziff Corp.’s desired rate of return is 5%.

Which of the following is the IRR of the project?

5.00%

3.66%

3.80%

108.68%

4.66%

If this is an independent project, the IRR method states that the firm should    the project.

If the project’s desired rate of return increased, how would that affect the IRR?

The IRR will increase.

The IRR will decrease.

The IRR will not change.

Answer 1

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 3% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 3%	Present Value of Cash Flow ($)
1	3,50,000	0.970874	3,39,805.83
2	4,75,000	0.942596	4,47,733.06
3	4,00,000	0.915142	3,66,056.66
4	4,75,000	0.888487	4,22,031.35
TOTAL			15,75,626.89

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

= $15,75,626.89 - $15,50,000

= $25,626.89

Step – 2, NPV at 3% is positive, Calculate the NPV again at a higher discount rate, Say 4% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 4%	Present Value of Cash Flow ($)
1	3,50,000	0.961538	3,36,538.46
2	4,75,000	0.924556	4,39,164.20
3	4,00,000	0.888996	3,55,598.54
4	4,75,000	0.854804	4,06,031.99
TOTAL			15,37,333.20

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

= $15,37,333.20 - $15,50,000

= -$12,666.80 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.03 + [$25,626.89 x (0.04 – 0.03)]

              $25,626.89 – (-$12,666.80)

= 0.03 + [$256.27 / $38,293.70]

= 0.03 + 0.0066

= 0.0366 or

= 3.66%

Therefore, the Internal Rate of Return (IRR) for the Project = 3.66%”

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.

DECISION

If this is an independent project, the IRR method states that the firm should “REJECT” the project, Since the IRR (3.66%) is less than the desired rate of return of 5%.

If the project’s desired rate of return increased, then the “IRR will not change”.