Method
NPV
Measures
Value created
Best use
Best overall decision anchor
Learning Hub · 9 methods explained
Learn investment appraisal
like a finance professor is sitting beside you.
A practical guide to NPV, IRR, MIRR, Payback Period, Discounted Payback, ARR, Profitability Index, Sensitivity Analysis, and Break-even Analysis — with examples, decision rules, and the traps each method can hide.
Learning Hub · 9 methods explained
Learn investment appraisal like
a finance professor is sitting beside you.
A practical guide to NPV, IRR, MIRR, Payback Period, Discounted Payback, ARR, Profitability Index, Sensitivity Analysis, and Break-even Analysis — with examples, decision rules, and the traps each method can hide.
Mock Project
Verdict
Luxury campus shuttle
neutralNPV
Barely positive
+GHS 3,200
IRR
Slightly above hurdle
12.6%
PP
Slow recovery
4.9 yrs
BEA
Tight margin
82% capacity
The numbers are not terrible, but the project has little room for error. Small changes in demand or cost could erase the value.
Mock Project
Verdict
Luxury campus shuttle
neutralNPV
Barely positive
+GHS 3,200
IRR
Slightly above hurdle
12.6%
PP
Slow recovery
4.9 yrs
BEA
Tight margin
82% capacity
The numbers are not terrible, but the project has little room for error. Small changes in demand or cost could erase the value.
NPVNet Present ValueIRRInternal Rate of ReturnMIRRModified Internal Rate of ReturnPPPayback PeriodDPPDiscounted Payback PeriodARRAccounting Rate of ReturnPIProfitability IndexSASensitivity AnalysisBEABreak-even AnalysisNPVNet Present ValueIRRInternal Rate of ReturnMIRRModified Internal Rate of ReturnPPPayback PeriodDPPDiscounted Payback PeriodARRAccounting Rate of ReturnPIProfitability IndexSASensitivity AnalysisBEABreak-even Analysis
The Big Idea
Each method answers a different business question.
Weak appraisal happens when people expect one method to answer every question.
Strong appraisal combines methods:
NPV for value, IRR and MIRR for return, Payback for liquidity, ARR for accounting profitability...
1
Value
Does the project increase wealth after considering risk and time?
NPV · PI
2
Return
What rate of return does the project appear to generate?
IRR · MIRR · ARR
3
Risk & survival
How fast is cash recovered, and what assumptions can break the project?
PP · DPP · SA · BEA
Quick Comparison
The nine methods
at a glance.
Discounted
Method
IRR
Measures
Percentage return
Best use
Easy to communicate
Method
MIRR
Measures
Adjusted percentage return
Best use
More realistic than IRR
Method
PP
Measures
Speed of cash recovery
Best use
Simple liquidity lens
Method
DPP
Measures
Discounted recovery time
Best use
Risk-aware liquidity lens
Method
ARR
Measures
Accounting profitability
Best use
Useful for profit reporting
Method
PI
Measures
Value per unit invested
Best use
Great under capital rationing
Method
SA
Measures
Assumption risk
Best use
Finds fragile assumptions
Method
BEA
Measures
Minimum required sales
Best use
Tests operating viability
| Method | Measures | Uses time value? | Best use |
|---|---|---|---|
| NPV | Value created | Yes | Best overall decision anchor |
| IRR | Percentage return | Yes | Easy to communicate |
| MIRR | Adjusted percentage return | Yes | More realistic than IRR |
| PP | Speed of cash recovery | No | Simple liquidity lens |
| DPP | Discounted recovery time | Yes | Risk-aware liquidity lens |
| ARR | Accounting profitability | No | Useful for profit reporting |
| PI | Value per unit invested | Yes | Great under capital rationing |
| SA | Assumption risk | Depends on output | Finds fragile assumptions |
| BEA | Minimum required sales | No | Tests operating viability |
Full Guide
The nine investment appraisal methods explained.
Read this section like a decision toolkit. Each
method has a job.
01 / Value creation
Net Present Value
Formula idea
PV of future cash flows — Initial investment
Best for
Knowing whether a project adds real value after considering the time value of money.
Decision rule
Accept if NPV is positive. Choose the project with the highest positive NPV when projects are mutually exclusive.
The theory
NPV is the gold-standard investment appraisal method because it translates all expected future cash flows into today's money. A cedi, dollar, or pound received next year is not worth the same as one received today, so NPV discounts future cash flows using a required rate of return.
Practical example
Suppose a project costs GHS 100,000 today and is expected to generate discounted cash inflows worth GHS 128,000. The NPV is GHS 28,000. That means the project is expected to create GHS 28,000 of value after covering the required return.
Interpretation
A positive NPV means the project earns more than the required return. A negative NPV means it fails to compensate investors for risk and time.
Watch out
NPV depends heavily on the discount rate and cash-flow estimates. A beautiful NPV built on unrealistic assumptions is still financial fiction wearing a suit.
Professor's note
“When in doubt, let NPV lead. Other methods are useful, but NPV speaks the language owners care about most: value added.”
02 / Return percentage
Internal Rate of Return
Formula idea
The discount rate that makes NPV equal to zero
Best for
Expressing a project's return as a percentage that is easy to compare with a hurdle rate.
Decision rule
Accept if IRR is higher than the required rate of return or cost of capital.
The theory
IRR answers a simple question: what annualised return does this project appear to generate? Instead of entering a discount rate to calculate NPV, IRR works backwards to find the rate at which the project's NPV becomes zero.
Practical example
If a project has an IRR of 18% and the business requires 12%, the project appears attractive because it clears the hurdle by 6 percentage points.
Interpretation
The higher the IRR above the required return, the more comfortable the margin of safety appears. But percentage returns can mislead when project sizes differ.
Watch out
IRR can produce confusing results for non-normal cash flows, and it may favour a small project with a high percentage return over a larger project that creates more total value.
Professor's note
“Use IRR for communication. Use NPV for final judgement. Percentages are catchy; value is decisive.”
03 / Adjusted return
Modified Internal Rate of Return
Formula idea
Return adjusted for finance cost and reinvestment rate
Best for
A more realistic return estimate when reinvested cash flows may not earn the same rate as the IRR.
Decision rule
Accept if MIRR exceeds the required return.
The theory
MIRR improves on IRR by separating two assumptions: the cost of financing the investment and the rate at which interim cash flows can be reinvested. This makes MIRR more realistic in many business situations.
Practical example
A project may show an IRR of 24%, but if interim cash inflows can only be reinvested at 10%, the MIRR might fall to 15%. That 15% may be a better picture of economic reality.
Interpretation
MIRR gives a smoother, often more conservative view of return. It is especially helpful when cash flows arrive before the project's final year.
Watch out
MIRR still depends on assumptions, especially the reinvestment rate. If that rate is poorly chosen, the result can still be misleading.
Professor's note
“MIRR is IRR after it has had coffee, slept well, and stopped pretending every cash inflow can be reinvested at a heroic rate.”
04 / Liquidity
Payback Period
Formula idea
Time required to recover the initial investment
Best for
Understanding how quickly cash is recovered, especially when liquidity and risk exposure matter.
Decision rule
Accept if the payback period is within management's target period.
The theory
Payback period measures the number of years or months needed for cumulative cash inflows to recover the initial cost. It is simple, intuitive, and popular because managers like knowing when the business gets its money back.
Practical example
A project costs GHS 60,000 and generates GHS 20,000 per year. The payback period is 3 years. If management's maximum payback target is 4 years, the project passes this test.
Interpretation
A shorter payback period means faster recovery and lower exposure to long-term uncertainty.
Watch out
Traditional payback ignores the time value of money and ignores cash flows after the payback date. A project that pays back quickly is not always the project that creates the most value.
Professor's note
“Payback is excellent for survival questions. It is weak for wealth-maximisation questions.”
05 / Risk-aware liquidity
Discounted Payback Period
Formula idea
Time required to recover initial investment using discounted cash flows
Best for
Measuring cash recovery while respecting the time value of money.
Decision rule
Accept if discounted payback is within the target period.
The theory
Discounted payback fixes one major weakness of ordinary payback by discounting future cash flows before accumulating them. This recognises that money received later is worth less than money received now.
Practical example
A project may recover its nominal cost in 3 years, but after discounting the inflows at 12%, it may take 4.2 years to recover the investment in present-value terms.
Interpretation
Discounted payback is stricter than ordinary payback. If a project passes discounted payback, its cash recovery is more financially meaningful.
Watch out
Like ordinary payback, it may still ignore valuable cash flows that occur after the recovery point.
Professor's note
“Discounted payback is payback with financial manners. Still not perfect, but definitely better dressed.”
06 / Accounting profitability
Accounting Rate of Return
Formula idea
Average accounting profit ÷ Average investment × 100
Best for
Connecting project appraisal to accounting profit, especially for non-finance audiences.
Decision rule
Accept if ARR exceeds the target accounting return.
The theory
ARR evaluates an investment using accounting profit rather than cash flow. It compares average annual profit with average investment to estimate an accounting-based return.
Practical example
If a machine produces average annual accounting profit of GHS 18,000 and the average investment is GHS 90,000, ARR is 20%. If the company's target ARR is 15%, the project passes.
Interpretation
A higher ARR suggests stronger accounting profitability, which can matter for reported performance and managerial evaluation.
Watch out
ARR ignores the time value of money and uses accounting profit, which can be affected by depreciation policies and accounting choices.
Professor's note
“ARR is useful when accountants are in the room. But for investment value, cash flow still wears the crown.”
07 / Value per unit invested
Profitability Index
Formula idea
PV of future cash inflows ÷ Initial investment
Best for
Choosing among projects when the business has limited capital.
Decision rule
Accept if PI is greater than 1. Rank projects by PI when capital is rationed.
The theory
Profitability Index measures how much present value is generated for every unit of money invested. It is closely related to NPV but expresses attractiveness as a ratio.
Practical example
If a project costs GHS 50,000 and the present value of its future inflows is GHS 65,000, PI is 1.30. That means every GHS 1 invested creates GHS 1.30 in present value.
Interpretation
PI above 1 means value is created. PI below 1 means the project destroys value.
Watch out
PI can favour smaller projects with high ratios even when larger projects create more total value.
Professor's note
“PI is excellent when money is scarce. But when choosing one major project, always check the actual NPV too.”
08 / Risk diagnosis
Sensitivity Analysis
Formula idea
Change one input at a time and observe the effect on NPV or return
Best for
Understanding which assumptions matter most: sales volume, price, cost, discount rate, tax, or inflation.
Decision rule
Investigate variables that cause the largest change in project value.
The theory
Sensitivity analysis tests how fragile a project's result is. Instead of pretending one forecast is certain, it asks: what happens if sales fall by 10%, costs rise by 15%, or the discount rate changes?
Practical example
If a project's NPV is positive at GHS 40,000 but becomes negative when selling price falls by just 5%, pricing is a critical risk. Management should investigate demand, competition, and pricing power before approving.
Interpretation
The most sensitive variables deserve the most research, monitoring, and contingency planning.
Watch out
Traditional sensitivity analysis changes one variable at a time, but in real life, bad things often arrive as a group project.
Professor's note
“Sensitivity analysis turns assumptions into suspects. The guilty ones are the variables that can destroy value fastest.”
09 / Operating viability
Break-even Analysis
Formula idea
Fixed costs ÷ Contribution margin per unit
Best for
Knowing the minimum sales volume needed to avoid losses.
Decision rule
The project is safer when expected sales are comfortably above break-even sales.
The theory
Break-even analysis estimates the sales level at which total revenue equals total cost. At break-even, the project has not made a profit yet, but it has covered its fixed and variable costs.
Practical example
If fixed costs are GHS 80,000, selling price is GHS 50, and variable cost is GHS 30, contribution per unit is GHS 20. Break-even volume is 4,000 units.
Interpretation
If expected demand is 7,000 units, there is a margin of safety of 3,000 units. If expected demand is 4,200 units, the project is breathing through a straw.
Watch out
Break-even analysis assumes stable prices, stable variable costs, and a clear separation between fixed and variable costs. Reality is often messier.
Professor's note
“Break-even does not tell you whether a project is excellent. It tells you where the floor is.”
Assay Verdict Framework
Do not ask “is the number good?” Ask “what story do the numbers tell together?”
A project with positive NPV, IRR above the hurdle rate, and fast payback is usually a winner.
1
Start with NPV
Does the project create wealth?
2
Check IRR/MIRR
Is the return comfortably above the hurdle rate?
3
Review payback
How long is capital exposed?
4
Use PI for capital rationing
Which project gives more value per unit?
5
Stress-test assumptions
Which variable can destroy the project?