NPV and IRR in Investment Projects: Key Differences
NPV and IRR in Investment Projects
Relationship Between NPV and IRR
We know that the Internal Rate of Return (IRR) of an investment in a project is the discount rate (k) that makes the Net Present Value (NPV) equal to zero (NPV = 0 when k = IRR). If the NPV calculated for an investment project at a rate k is positive, it means the project’s IRR is greater than k. If the NPV is negative, it indicates that the project’s IRR is lower than the alternative investment’s profitability or the company’s cost of capital (ke). Therefore, accepting the project would result in a loss.
Relationship Between Investment Recovery Time and NPV
- If the recovery time is greater than the investment’s time horizon, the project fails to recover its initial investment. Consequently, the NPV will be less than zero, and the investment will generate losses.
- If the recovery time is equal to the investment’s time horizon, the project recovers the initial investment but does not generate profits or losses.
- If the recovery time is less than the investment’s time horizon, it means that after recovering the initial investment, the monthly cash flow is positive, and the investment will generate profits.
NPV and IRR: Potential Discrepancies
Both NPV and IRR assume that the intermediate cash flows of the investment project are reinvested at the same discount rate (k in the case of NPV or the IRR in the case of IRR). However, in the case of NPV, if cash flows are reinvested at a rate different from the discount rate, it will affect the project’s profitability. This can lead to discrepancies between the two methods.
Cash Flow Scenarios
Consider a scenario where cash flow in year 0 is positive (e.g., receiving an initial sum of money), and cash flows in years 1 and 2 are negative (e.g., refunding money in subsequent periods). This represents a financing project rather than an investment project. Furthermore, if the IRR is now greater than the opportunity cost of capital, it means that the financing has a higher cost than the project’s cost of capital. Therefore, it would not be wise to take on debt with a higher cost than the market rate. This is the opposite of a normal investment, and we should, in principle, accept the project when the IRR is lower than the discount rate.
Decision-Making with NPV and IRR
When NPV and IRR criteria lead to inconsistent decisions, it’s because investment projects have different elasticity concerning the discount rate. A change in the discount rate affects each project differently. This occurs due to differences in scale or a different temporal distribution of cash flows. When discrepancies arise, consider using Fisher’s analysis.
Sum of Investment and Financing Projects (VFN)
When evaluating a combined investment and financing project, calculate the VFN (Value of the Firm with the Net investment) for each project and choose the project with the largest VFN.
Estimated Capital Cost
Calculate the estimated capital cost of financing the project. If the results are positive (greater than 0), they are beneficial for the company. Choose the option with the highest positive value.
Internal Rate of Return (IRR)
If the cost of capital equals the IRR, the project does not add any value to the company. If the project’s cost exceeds the IRR, the project will be deficient. For example, if we have options with IRRs of 30.01% and 23.79%, we would choose the first option.
Payback Period
Calculate the payback period (without updating) using the investment project’s cash flow. Choose the shortest payback period. Then, calculate the updated payback period using the project’s cash flow discounted at the cost of capital. Again, choose the shortest payback period.