Advanced Financial Management · Discounted cash flow techniques

Modified IRR (MIRR) and Discounted Payback for ACCA AFM

Updated 11 October 2026 · Fact-checked

MIRR is the return you get when you compound all project inflows to the end at the cost of capital, then find the rate that turns the present value of the outlays into that terminal value. Discounted payback is the time needed for discounted cash inflows to recover the investment. Calculate both, then compare with NPV.

Understand Modified IRR and Discounted Payback

IRR is the discount rate that gives an NPV of zero. It is popular because managers like a percentage. But it has weaknesses. It assumes cash inflows are reinvested at the IRR itself, which is often unrealistic. It can give multiple answers when cash flows change sign more than once. It can also rank mutually exclusive projects differently from NPV.

The modified IRR (MIRR) fixes these problems. It assumes surplus cash is reinvested at the firm's cost of capital, a more believable rate. It also collapses the cash flows into just two figures: the present value of the outlays and the terminal value of the inflows. That gives one unique answer, so there is no multiple-IRR problem.

A project is acceptable if its MIRR is greater than the cost of capital. For a single project with conventional cash flows, this gives the same accept or reject decision as NPV. MIRR is also often a better guide than IRR when ranking mutually exclusive projects, but it can still differ from NPV when projects differ in scale. NPV remains the best measure of wealth created.

Payback is the time taken for cumulative cash inflows to equal the initial investment. It is simple and shows liquidity and risk exposure. But it ignores cash flows after the payback point and ignores the time value of money.

Discounted payback fixes the second weakness. You discount each cash flow at the cost of capital first, then find when the cumulative discounted inflows recover the outlay. It still ignores cash flows after the cut-off, so it can reject a project with a strongly positive NPV. If a project never recovers its outlay on a discounted basis, its NPV is negative.

Key rules to remember

MIRR (terminal value method): MIRR = (TV of inflows ÷ PV of outflows)^(1/n) − 1; TV of inflows = each inflow compounded to year n at the cost of capital (reinvestment rate). PV of outflows = outflows discounted to time 0 at the cost of capital. n = project life in years.
MIRR (ACCA present value form): MIRR = (PV of returns ÷ PV of investment)^(1/n) × (1 + re) − 1; PV figures are both discounted at the cost of capital. re is the reinvestment rate, normally the cost of capital. This gives the same answer as the terminal value method.
MIRR decision rule: Accept if MIRR > cost of capital; For a single project with conventional cash flows this agrees with a positive NPV.
Payback period: Years before full recovery + (unrecovered cost at start of year ÷ cash flow in that year); Uses undiscounted cash flows. Assumes inflows arise evenly through the year.
Discounted payback period: Same as payback, but using present values of cash flows at the cost of capital; Discount every cash flow first, build the cumulative PV column, then interpolate.
Discounted cash flow: PV = cash flow ÷ (1 + r)^t; Used for both discounted payback and the MIRR present value.

How to solve Modified IRR and Discounted Payback questions

Use this method for any MIRR or payback requirement. Set out clear workings so you earn method marks even if you make an arithmetic slip.

1Read the requirement. Note which measures are asked for and what cost of capital and reinvestment rate you are given.
2List the cash flows by year, with outflows negative. Include tax, working capital and so on only if the question has already built them into the cash flows.
3For MIRR, find the PV of all outflows at the cost of capital. If the only outflow is at time 0, this is just the initial investment.
4Compound each inflow to the end of the project at the cost of capital, then add them to get the terminal value. Or find the PV of inflows and use the present value form.
5Calculate MIRR = (TV ÷ PV of outflows)^(1/n) − 1. Use n as the number of years from time 0 to the last cash flow. Compare MIRR with the cost of capital.
6For discounted payback, discount each cash flow, build the cumulative column, find the year where it turns positive and interpolate within that year.
7State the decision. Compare with any company payback target and with NPV, and mention that discounted payback ignores later cash flows.
8Add a short comment on limitations or on how MIRR addresses IRR problems if the requirement asks for evaluation or advice.

Quickest way: Present value shortcut for MIRR

When to use it: Use when you have already calculated the NPV or the PV of inflows for the question, which is common in AFM. It saves compounding each cash flow separately.

Take the PV of the inflows at the cost of capital from your NPV working.
Divide by the PV of the outflows (the initial investment if it is the only outflow).
Raise the ratio to the power 1/n using the calculator, then multiply by (1 + cost of capital).
Subtract 1 to get MIRR and compare with the cost of capital.
For discounted payback, reuse the same PV column from the NPV table. Add a cumulative line and interpolate.

Common mistakes in Modified IRR and Discounted Payback

Compounding inflows at the IRR instead of the cost of capital
Students mix up the idea of MIRR with the assumption in IRR that cash is reinvested at the IRR.
Fix: MIRR uses the cost of capital (or the stated reinvestment rate) for compounding. Check the question for a different reinvestment rate.
Using the wrong n
Students count the number of cash flows rather than the number of years from time 0.
Fix: If the last inflow is at the end of year 4 and the investment is at time 0, n = 4. Draw a timeline.
Forgetting to discount the cash flows before finding discounted payback
Under time pressure students reuse the simple payback column.
Fix: Build a separate row of PVs and a separate cumulative row. Label it clearly.
Not interpolating within the recovery year
Students stop at the year in which payback occurs.
Fix: Divide the unrecovered balance by the PV of that year's cash flow and add it to the whole years. Convert to months if useful.
Saying discounted payback accounts for all cash flows
Students think discounting solves every weakness of payback.
Fix: Discounted payback fixes the time value of money only. It still ignores cash flows after the cut-off and does not measure total wealth created.
Claiming MIRR always agrees with NPV
Students overstate the advantage of MIRR.
Fix: Say MIRR agrees with NPV on accept or reject for a single project with conventional cash flows. For mutually exclusive projects of different scale, MIRR can still rank differently, so NPV is preferred.

Worked examples

Example 1

A project needs an investment of $100,000 now. Net cash inflows are $40,000 at the end of year 1, $50,000 at the end of year 2 and $60,000 at the end of year 3. The cost of capital, which is also the reinvestment rate, is 10%. Calculate the MIRR and advise whether the project is acceptable on this measure.

Show the solution

Outflows: only $100,000 at time 0, so PV of outflows = $100,000.
Compound each inflow to the end of year 3 at 10%. Year 1 inflow: 40,000 × 1.10² = 40,000 × 1.21 = $48,400.
Year 2 inflow: 50,000 × 1.10 = $55,000. Year 3 inflow: $60,000 with no compounding.
Terminal value = 48,400 + 55,000 + 60,000 = $163,400.
MIRR = (163,400 ÷ 100,000)^(1/3) − 1 = 1.634^(1/3) − 1.
1.634^(1/3) ≈ 1.1778, so MIRR ≈ 17.8%.
Check with the present value form: PV of inflows = 36,364 + 41,322 + 45,079 = $122,765. (1.22765)^(1/3) × 1.10 − 1 ≈ 1.0708 × 1.10 − 1 ≈ 17.8%. The answers agree.
17.8% is above the 10% cost of capital, so the project is acceptable. This agrees with the positive NPV of about $22,765.

Answer: MIRR ≈ 17.8%, which exceeds the 10% cost of capital, so the project is acceptable.

Example 2

A company with a 12% cost of capital is considering a project costing $200,000 now. Net cash inflows are $80,000 in year 1, $90,000 in year 2, $70,000 in year 3 and $60,000 in year 4, assumed to arise at each year end. Calculate the payback period and the discounted payback period, and comment.

Show the solution

Simple payback. Cumulative inflows: year 1 $80,000, year 2 $170,000, year 3 $240,000.
Payback occurs in year 3. Unrecovered at start of year 3 = 200,000 − 170,000 = $30,000. Fraction = 30,000 ÷ 70,000 = 0.43. Payback ≈ 2.43 years.
Discounted cash flows at 12%: year 1 = 80,000 ÷ 1.12 = $71,429. Year 2 = 90,000 ÷ 1.2544 = $71,747.
Year 3 = 70,000 ÷ 1.404928 = $49,825. Year 4 = 60,000 ÷ 1.573519 = $38,131.
Cumulative PV: year 1 $71,429, year 2 $143,176, year 3 $193,001, year 4 $231,132.
The outlay of $200,000 is not recovered by the end of year 3. Unrecovered = 200,000 − 193,001 = $6,999.
Fraction of year 4 = 6,999 ÷ 38,131 = 0.18. Discounted payback ≈ 3.18 years, about 3 years 2 months.
Total PV of inflows is $231,132, so NPV = $31,132, which is positive. The project creates value, but discounted payback is longer than simple payback because later cash flows are worth less.

Answer: Payback ≈ 2.43 years. Discounted payback ≈ 3.18 years (about 3 years 2 months). The NPV is positive at about $31,132.

Exam tips

In AFM, MIRR and discounted payback usually appear as part of a larger investment appraisal. Compute NPV first, then reuse the PVs for MIRR and discounted payback.
If the question gives a reinvestment rate different from the cost of capital, use it for compounding inflows. Discount outflows at the cost of capital.
Always conclude with advice. Compare each measure with its decision rule, then recommend using NPV as the main measure and say why.
When asked to evaluate, give balanced points. MIRR removes multiple IRRs and the unrealistic reinvestment assumption, but is still a percentage that ignores project scale. Discounted payback allows for the time value of money, but ignores cash flows after the cut-off.
Show the cumulative discounted cash flow row and the interpolation. Even if your arithmetic slips, the layout earns method marks, and professional skills marks reward a clear, usable conclusion.

Practice questions from Discounted cash flow techniques

Modified IRR and Discounted Payback in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Modified IRR and Discounted Payback: frequently asked questions

What is the MIRR formula in ACCA AFM?

MIRR = (terminal value of inflows ÷ present value of outflows)^(1/n) − 1. The terminal value compounds inflows at the cost of capital to the end of the project. ACCA also uses the form (PV of returns ÷ PV of investment)^(1/n) × (1 + re) − 1, which gives the same answer.

What is the difference between IRR and MIRR?

IRR implicitly assumes inflows are reinvested at the IRR itself and can give several answers when cash flows change sign more than once. MIRR assumes reinvestment at the cost of capital and always gives one answer. This makes MIRR a more realistic percentage return.

How do you calculate discounted payback?

Discount each year's cash flow at the cost of capital, then add them up cumulatively. Find the year when the cumulative PV first covers the initial outlay. Interpolate within that year using the unrecovered balance divided by that year's PV.

Is discounted payback always longer than simple payback?

Yes, for positive discount rates and positive inflows, discounting reduces each cash flow, so recovery takes at least as long. If the project never recovers its outlay on a discounted basis, it has a negative NPV.

Should I use MIRR or NPV to make the final decision?

NPV is the preferred measure because it shows the absolute wealth created for shareholders. MIRR is useful as a percentage return and for comparison with the cost of capital. For a single conventional project, both give the same accept or reject answer.