QF5213 Chap.4 NPV, IRR and Payback Appraisal Techniques
NPV, IRR and Payback Appraisal Techniques
Three questions every appraisal method answers
Capital budgeting asks one thing of a manager: will this investment leave shareholders richer than the next best use of their money? The appraisal techniques in this topic attack that question from different angles. Payback and discounted payback ask how long it takes to recover the money spent. Net present value asks how many dollars of value the project adds today.
The internal rate of return asks what percentage return the project earns. The profitability index asks how much benefit each dollar of outlay buys. Every method starts from the same inputs: forecast cash flows, a required return set by the risk of the project, and a start date for the outlay.
The course judges a technique by two tests.
First, it must respect the time value of money, so that a dollar received in year five counts for less than a dollar today. Second, it must tell you how much value the project creates. Simple payback fails both tests, and discounted payback repairs only the first.
Both stop counting once the outlay has been recovered, so a very large late cash flow cannot change their answer, and the cutoff period is a company convention rather than a market price.
Why net present value carries the final say
Net present value discounts every expected cash flow at the cost of capital and subtracts the initial cost.
A positive result means the project more than covers what investors demand for bearing its risk, and the surplus is the wealth created in present-value terms. Because the benchmark is zero, the rule needs no arbitrary cutoff. For independent projects, any positive NPV is acceptable.
For mutually exclusive projects, where choosing one rules out another, the higher NPV is the better choice because it adds more to firm value.
The internal rate of return is the discount rate that drives NPV to zero, and for a normal project with one outlay followed by inflows it gives the same accept or reject verdict as NPV. Trouble appears in two places.
When two mutually exclusive projects have different cash flow timing, their NPV profiles can cross, and below the crossover rate the project with the higher IRR can have the lower NPV.
When cash flows change sign more than once, a project can have two or more IRRs, and the only sensible statement is the band of discount rates over which NPV is positive.
Ranking under a budget and across different lives
The profitability index equals the present value of inflows divided by the initial cost, so it exceeds one exactly when NPV is positive.
Its practical role is capital rationing: when funds are capped, ranking independent projects by PI and funding down the list usually delivers more total NPV than picking the single largest project. Projects with unequal lives need one more adjustment. If the shorter project can be repeated, compare NPVs over a common life or convert each NPV into an equivalent annual annuity. If it cannot be repeated, plain NPV decides.
Surveys cited in class show that larger firms rely most on NPV, while smaller firms still lean on payback, and most managers report several measures side by side.
What this chapter covers
- 01
The valuation steps that sit under every appraisal method
- 02
Payback and discounted payback, and the cash flows they ignore
- 03
Net present value as the dollar measure of value created
- 04
Internal rate of return and when it agrees with NPV
- 05
NPV profiles, crossover rates and multiple IRRs
- 06
Profitability index under rationing, and projects with unequal lives
- 07
Building cash flows from forecasts and setting the WACC hurdle
Worked example · free
Testing a borderline project with NPV, IRR and PI
- 2Discount each inflow at 12% to find its present value
- 1Sum the present values and subtract the $50,000 outlay to get NPV
- 2Compute the profitability index and solve for the IRR
- 1State the decision and check that all three rules agree
Key terms
- Payback Period
- Counts the years needed for undiscounted cash inflows to recover the initial investment, compared against a cutoff set by the firm.
- Discounted Payback Period
- Counts the years needed for the present values of cash inflows to recover the outlay, so it reflects the cost of capital.
- Net Present Value
- Measures the value a project adds today by discounting all expected cash flows at the cost of capital and netting off the initial cost.
- Internal Rate of Return
- Gives the discount rate at which a project's NPV equals zero, accepted when it exceeds the required return.
- Crossover Rate
- Marks the discount rate at which two projects have equal NPV, found as the IRR of their yearly cash flow differences.
- Profitability Index
- Expresses benefit per dollar of cost as the present value of inflows divided by the initial investment, with acceptance above one.
- Capital Rationing
- Describes a budget cap that prevents a firm from funding every positive NPV project, so projects must be ranked to maximise total NPV.
- Equivalent Annual Annuity
- Converts a project's NPV into a level yearly amount over its life so that projects with different lives can be compared fairly.
- WACC Hurdle Rate
- Sets the project hurdle rate by blending the after-tax cost of debt and the cost of equity in proportion to the firm's financing mix.
NPV, IRR and Payback Appraisal Techniques FAQ
What is the difference between payback and discounted payback?
Simple payback adds raw cash flows until the outlay is recovered, so a dollar in year three counts the same as a dollar today. Discounted payback first converts each cash flow to present value at the cost of capital, which makes the recovery take longer. Neither method looks at cash arriving after the cutoff.
Why do NPV and IRR sometimes rank projects differently?
Rankings can diverge for mutually exclusive projects whose cash flows differ in timing or scale. A project with large early inflows tends to show a higher IRR, while one with large late inflows can have the higher NPV at a low cost of capital. Below the crossover rate the two methods disagree, and NPV should decide.
How do you find the crossover rate between two projects?
Subtract one project's cash flow from the other's year by year, then solve for the discount rate that makes the NPV of those differences zero. That rate is the IRR of the difference stream. At this rate both projects have identical NPV, and on either side one project dominates.
Can a project have more than one IRR?
Yes. When the cash flow stream changes sign more than once, for example an outlay, then inflows, then a large clean-up cost, the NPV profile can cross zero several times. Each crossing is a valid IRR, so the useful answer is the range of discount rates over which NPV stays positive.
When should I use the profitability index instead of NPV?
Use PI when a fixed budget stops you from funding every positive NPV project. Ranking independent projects by benefit per dollar of outlay and funding down the list usually produces a larger combined NPV than choosing the single biggest project. Without a budget limit, the PI verdict simply matches NPV.
How do you compare projects with different lives?
If the shorter project can be repeated, either chain it to a common horizon and compare total NPVs, or divide each NPV by the annuity factor for its own life to get an equivalent annual annuity. The higher annual figure wins. If repetition is not realistic, compare the ordinary NPVs directly.
Exam move
Build one small spreadsheet with a row of cash flows and a discount rate cell, then add formulas for payback, discounted payback, NPV, IRR and PI. Enter two rival projects with different timing, chart NPV against rates from 0% to 30%, and read off each IRR and the crossover. Change one late cash flow and note which measures move and which stay fixed.
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