Question

• How do net present value (NPV) and internal rate of return (IRR) relate to each other mathematically?
• How does modified internal rate of return (MIRR) compare to internal rate of return (IRR)?

Answer 1

Answer :- Net present value (NPV) and Internal rate of return (IRR) :-

IRR measures only the quality of investment while NPV takes into account both the quality and the scale of investment. This is because the IRR provide a relative measure of value while NPV provides an absolute measure of value in the finance.

Two investment proposal / project may give the different result as per Net present value (NPV) and Internal rate of return (IRR) method. Such different results may be explained in mathematical terms (for both NPV and IRR) in the following manner : -

1). Time Disparity: - Short term project have higher IRR whereas Long-term project have higher NPV.

2). Size Disparity: - Project uses high investment have high NPV and project uses low investment have high IRR.

3). Reinvestment rate assumption: - In IRR, it is assumed that intermediate cash inflow in a project is reinvested at IRR itself whereas in NPV it is assumed that intermediate cash flow is reinvested at the rate of cost of capital.

Modified internal rate of return (MIRR) and Internal rate of return (IRR) :-

The main comparison point MIRR and IRR is that cash flows of project are re-invested at the cost of capital itself in MIRR whereas in IRR, The project cash flows are re-invested at IRR only. Further, MIRR is always lesser than IRR.