Return expressed as a rate
Net present value answers how much value a project adds. The internal rate of return (IRR) answers a different question: what annual rate does the project earn on the capital it consumes?
IRR is the discount rate at which a project's NPV is exactly zero. It is popular because a rate is easy to compare with a cost of capital, but it is a relative measure and can mislead when projects differ in size, timing, or cash-flow pattern.
Payback is simpler still: how long until the cash comes back. It measures speed and liquidity, never profitability, so it belongs in the analysis as a risk screen rather than the final word.
Key points
- IRR is the rate that makes NPV zero.
- NPV measures value; IRR measures return.
- Payback measures speed, not profit.
The capital-budgeting toolkit
0 = Σ [CFₜ ÷ (1 + IRR)ᵗ] − C₀
The discount rate at which the present value of inflows equals the outlay.
Accept when IRR > cost of capital
For a conventional project, IRR above the hurdle rate is equivalent to a positive NPV.
MIRR = (FV of inflows ÷ PV of outflows)^(1/n) − 1
Reinvests cash flows at the cost of capital, removing IRR's unrealistic reinvestment assumption.
Payback = Years before full recovery + Unrecovered ÷ Cash flow that year
Time until cumulative cash flow returns the initial investment.
Same as payback, using discounted cash flows
Payback measured in present-value terms, so it respects the time value of money.
PI = PV of inflows ÷ Initial investment
Value created per taka invested, useful when capital is rationed.
Conventional cash flows, one outflow followed by inflows, produce a single IRR. Projects with alternating signs can have several IRRs, which is why MIRR exists.
A five-year project
A project costs ৳120,000 and returns ৳45,000, ৳50,000, ৳50,000, ৳40,000, and ৳30,000 over five years. The cost of capital is 10%.
The IRR is 24.92%. Because that is well above the 10% cost of capital, the project earns more than the money it consumes. The NPV at 10% is ৳45,745, and the profitability index is 1.38, meaning each taka invested creates about ৳0.38 of value.
Payback is 2.5 years: ৳95,000 comes back in the first two years and the remaining ৳25,000 is recovered halfway through year three. Discounted payback stretches to about 3.01 years once the cash flows are valued properly.
Key points
- IRR 24.92% versus a 10% hurdle rate.
- NPV ৳45,745 and PI 1.38.
- Payback 2.5 years; discounted payback 3.01 years.
Where IRR misleads
IRR ignores scale. A 100% return on ৳1,000 adds less value than a 20% return on ৳1,000,000. When projects compete for a fixed budget, rank by NPV or profitability index, not by the highest rate.
IRR assumes cash flows are reinvested at the IRR itself. That is often unrealistic for a very high rate. MIRR fixes it by compounding inflows at the cost of capital and discounting outflows at the finance rate, which usually produces a lower and more defensible number.
IRR can also flip when cash flows change sign more than once. Use NPV as the primary rule and IRR as a communication tool. Payback narrows the field by flagging how long capital is exposed, but it should never be the reason a profitable project is rejected.
Key points
- Rank competing projects by NPV when scale differs.
- MIRR corrects the reinvestment assumption.
- Payback screens risk; NPV decides value.
Interactive experiment
IRR, MIRR, and payback
IRR is the discount rate that makes a project's NPV exactly zero. It is a rate, not an amount, so it must be read alongside NPV and payback.
0 = Σ [CFₜ ÷ (1 + IRR)ᵗ] − C₀
Your inputs
Cash committed at time zero.
The return available elsewhere at similar risk.
Result
- IRR
- 24.9%
- NPV at cost of capital
- ৳45,745
- MIRR
- 18.3%
- Payback periodYears to recover the outlay.
- 2.5
- Discounted payback
- —
- Profitability index
- 1.38×
- Total cash inflow
- ৳215,000
IRR of 24.9% is above the 10.0% cost of capital, and NPV is positive. The two measures agree.
03 / Apply
Two projects, one budget
A firm can fund only one of two projects. Project A costs ৳120,000 and returns the five-year stream above. Project B costs ৳1,000,000 and earns a 20% IRR, generating about ৳334,000 a year for five years. The cost of capital is 10%.
The assumptions
- Both projects carry similar risk and have five-year lives.
- Capital is limited this year, so only one can proceed.
- Cash flows are conventional: one outflow, then inflows.
What to take away
01
Project A has the higher IRR at 24.92%.
02
Project B likely creates more absolute value because of its scale.
03
Ranking by IRR alone would pick the smaller project.
Your turn
0 of 4 answered
01Question
An investment of ৳120,000 returns ৳45,000, ৳50,000, ৳50,000, ৳40,000, and ৳30,000. What is the payback period in years? Round to two decimals.
02Question
The same project has an IRR of 24.92% and the cost of capital is 10%. By how many percentage points does the IRR exceed the hurdle rate? Round to two decimals.
03Question
What does an IRR of 24.92% mean?
04Question
Two projects are mutually exclusive and differ greatly in scale. Which metric should decide?
Take it into the Lab
Experiment with the same idea.
The Lab turns this topic into a workspace: change the drivers, watch the statements move, and see the consequence before you commit to a decision.
What-if analysis
Change price, cost, and working capital. Watch margins, return, and risk move together.
Open the labFormula lab
Understand, manipulate, observe, solve, then apply the formula to a decision.
Walk the formulaStatement playground
See how one driver propagates through the income statement, balance sheet, and cash flow.
Open the playgroundSources & further reading
OpenStax · Principles of Finance, Capital Budgeting chapter ↗Educational sample content. Worked examples use hypothetical figures. Dates refer to the note's latest content update.