Higher IRR, Lower NPV? Why Investment Rankings Disagree
With equal initial outlays, earlier cash recovery gives A a higher IRR while B can create more net present value. Follow the two-year cash flows and see how the cost of capital changes the choice.
01 · Two investment projects
The same outlay, different recovery dates
A company can undertake one of two mutually exclusive projects: approving A rules out B. Both require US$100,000 today. A pays US$150,000 at the end of year one and nothing new in year two. B pays nothing in year one, then US$190,000 at the end of year two. A returns cash sooner; B asks the company to wait for a larger payment.
One manager favors A because its percentage return measure is higher. Another favors B because it creates more present value. Neither calculation has to be wrong. They are answering different questions. Before choosing a winner, the company needs to decide whether it is comparing a rate or the net value created at an appropriate cost of capital.
Year zero is today. A negative sign is a cash outlay; a positive sign is a receipt at year-end. A zero in year two means no new cash flow, not that money received in year one disappears.
Keep the comparison consistent
Use a common two-year horizon, USD cash flows and annual end-of-period payments. Assume comparable risk, the same effective annual cost of capital and the ability to undertake either project. The baseline discount rate is 10%. Taxes, inflation, additional residual value and capital rationing are excluded. The year-one receipt remains a year-one cash flow; we do not silently add a reinvestment payoff.
02 · Make a prediction
If you could approve only one, what would you check first?
Choose a line of reasoning before reading the analysis. This is not a right-or-wrong quiz. A useful answer needs a decision objective and a set of conditions.
03 · Two measures
IRR and NPV answer different questions
IRR is the discount rate that makes the present value of the entire cash-flow stream equal zero. It is determined by the project's own payments and gives a percentage break-even threshold. NPV begins with a specified discount rate and adds all cash inflows and outflows in today's money. It asks how much net value remains after the outlay and the opportunity cost of capital are accounted for.
A larger percentage is therefore not necessarily a larger amount of value. Nor is IRR a guaranteed annual return an investor can realize. At the common baseline cost of capital, B's larger later payment more than compensates for the wait. For a company seeking to increase value, that monetary difference is more directly relevant than the higher percentage alone.
NPV · USD
Net value at a specified cost of capital.
IRR · %
The rate at which each project's NPV is zero.
At 10.00%, B creates US$20,661.16 more NPV than A, although A has the higher IRR.
04 · Change the discount rate
Change the cost of capital, change the NPV ranking
The discount rate represents the required return used to price time and the opportunity cost of capital in this model. Raising it reduces the present value of a future receipt. B's later payment is exposed to an extra year of discounting. Move the rate below to see when the ranking reverses. Neither project's IRR changes with the comparison rate.
Below the crossover, B's larger later receipt outweighs the additional discounting. At the common cost of capital, B adds more present value even though A's IRR is higher.
Both NPVs are positive under the current assumptions.
The crossover means these particular cash flows have equal NPVs at that rate. It is not a forecast, and other project pairs need not have exactly one crossover. Above the zero line NPV is positive; below it NPV is negative.
05 · Explain the conflict
Why does earlier recovery not always win?
A's receipt is closer to today, so it loses less value to discounting. But it is also smaller. At a low cost of capital, the penalty for waiting is modest enough for B to retain more net value. As the required return rises, the extra delay becomes more expensive and A eventually has the higher NPV. Timing creates the conflict here; both projects have the same initial outlay.
Subtract A's NPV from B's to evaluate the switch: give up the earlier receipt and receive the larger payment later. A positive difference means that switch creates value at the current cost of capital. A negative difference means it destroys value relative to A. The crossover is where the difference reaches zero. In other cases, different project scales can also create disagreement between a percentage ranking and an amount-of-value ranking.
Receiving cash earlier gives the company flexibility, but this model does not specify how it will use those proceeds. In particular, A's IRR is not a promise that later reinvestments can earn that rate. Discounting at the cost of capital prices the cash flows' opportunity cost; it does not guarantee that every receipt can be reinvested at that rate either.
Put the dates into the equations
r is the effective annual discount rate in decimal form. A year-one receipt is divided by one growth factor; a year-two receipt by its square. Equating the two NPVs solves for this pair's crossover. Setting an individual NPV to zero solves for that project's IRR. These are different equations answering different questions.
06 · Decision conditions
How should the company choose?
When projects are mutually exclusive, risk is comparable, the discount rate is appropriate and no additional constraints apply, the higher acceptable NPV generally aligns better with increasing company value. That points to B in the baseline case. The choice should be reconsidered if the cost of capital changes. If both NPVs are negative and investment can be declined, rejecting both is an option; the company need not choose the smaller loss.
IRR remains useful for understanding how cash flows relate to a required return and for communicating a rate-based measure. With a limited capital budget, however, the best feasible portfolio may matter more than an isolated ranking. Different risks may also require different discount rates. Cash flows with repeated sign changes can produce multiple IRRs or no usable IRR, making one percentage an especially poor substitute for the complete analysis.
What the model captures—and what it leaves out
This is a teaching model with fixed annual cash flows. Actual receipts can be delayed, costs can rise and taxes, inflation and risk can change the estimates. A two-year horizon does not automatically capture every operating consequence. The discount rate should be consistent with the currency, timing and risk of the cash flows, not chosen to make a preferred project win. The model supplies a comparison method, not a guarantee of outcomes.
Further comparison
Change the cash flows and test the reasoning
What happens if B pays sooner, or the initial outlays differ? Bring the current case into the existing capital-budgeting comparator with its common discount rate and mutually exclusive setting, then edit the cash flows yourself. The useful lesson is not to remember a winner. It is to evaluate amounts, dates, the cost of capital and the decision objective together.
Explore further
Understand a concept, or calculate it on its own.
- Net present value
- Internal rate of return
- Modified internal rate of return
- Discounted payback