IRR of a Perpetuity

[SHoot85]

I don’t understand why the (negative NPV of 20 million) doesn’t seem to be needed in this calculation. So that figure could have said it had an NPV of 1 Billion, and still we’d get the same answer?

A firm is considering a project that would require an initial investment of THB270 million (Thai baht). The project will help increase the firm’s after-tax net cash flows by THB30 million per year in perpetuity, and it is found to have a negative NPV of THB20 million. The IRR (%) of the project is closest to:
10.3%.
12.0%.
11.1%.


Incorrect.
The IRR is the discount rate that makes the NPV = 0. Because the cash flow stream is in perpetuity, it can be solved as follows:
IRR = 11.1%
2014 CFA Level I
“Capital Budgeting,” by John D. Stowe and Jacques R. Gagné
Section 4.2

 

[joe35y]

It is asking for the projects IRR not the required rate of return for the project. The IRR for any project is what makes the present value of the future cash flows equal to 0. In this case the required rate of return would be higher than the IRR which is why the project has a negative NPV.
So the present value of a perpetuity is Cash Flow/Required Rate of return. So in this case we plug in the IRR for the required rate of return. 30M/.111 = gives us around 270.2703

 

[lawnm0wer]

Tricky.

 

[SHoot85]

joe35y wrote:
It is asking for the projects IRR not the required rate of return for the project. The IRR for any project is what makes the present value of the future cash flows equal to 0. In this case the required rate of return would be higher than the IRR which is why the project has a negative NPV.
So the present value of a perpetuity is Cash Flow/Required Rate of return. So in this case we plug in the IRR for the required rate of return. 30M/.111 = gives us around 270.2703

Thanks joe35y; I knew that to find IRR you set NPV = 0, but I guess the -20 confused me whether to include that in setting the NPV = 0. But I get it now; much appreciated.

 

[Scibus]

If you want to have your BA II Plus do the calculations in these perpetual-NPV-questions, just type C01=30 and F01=9999. Then hit IRR and CPT and you get the IRR

 

[DPBass88]

Easiest way to find IRR is to just divide the perpetual cash flow by the initial investment. (30/270). 11.1%. It makes sense because the rate of return is 11.1% per year on the initial investment.