Lesson 4.4 35 min
Payback and capital rationing
Payback and discounted payback, what they miss, and ranking projects when the budget is fixed.
Payback is the time it takes for a project's cash flows to repay the outlay. It is the measure many owners reach for first because it needs no discount rate and answers a question they feel: when do I get my money back?
Payback
Add up the cash flows year by year until the total reaches zero. If the total passes zero partway through a year, the fraction is the shortfall at the start of that year divided by that year's cash flow.
Payback = Years before recovery + (Unrecovered cost at start of year ÷ Cash flow in that year)
The usual rule is to accept projects that pay back within a set number of years, say three.
What payback ignores
It has two weaknesses. It ignores the timing of cash within the payback period, treating $1 in year 1 the same as $1 in year 3. And it ignores everything after the payback date. A project that pays back in two years and stops can look better than one that pays back in three and runs for five.
Two $24,000 projects show it.
| X cash flow $ | X cumulative $ | Y cash flow $ | Y cumulative $ | |
|---|---|---|---|---|
| Year 0 | (24,000) | (24,000) | (24,000) | (24,000) |
| Year 1 | 14,000 | (10,000) | 6,000 | (18,000) |
| Year 2 | 10,000 | 0 | 8,000 | (10,000) |
| Year 3 | 2,000 | 2,000 | 10,000 | 0 |
| Year 4 | 0 | 2,000 | 12,000 | 12,000 |
| Year 5 | 0 | 2,000 | 14,000 | 26,000 |
| Payback, years | 2.00 | 3.00 | ||
| Discounted payback, years | never | 3.54 | ||
| NPV at 10% | (1,505.63) | 12,468.32 |
Project X pays back in 2.00 years and Y in 3.00. A three-year rule accepts both. Look beyond payback: X's cash flows stop in year 3, Y's carry on. Discounted at 10%, X never recovers its cost, with an NPV of −$-1,505.63. Y has an NPV of $12,468.32. A payback rule that stops at "which is faster" picks the project that loses value.
Discounted payback
Discounted payback uses present values, so it corrects the timing problem: Y's discounted payback is 3.54 years, longer than its simple payback, and X has none. It still ignores what comes after, so it can reject a project with a long payback and a large NPV. Treat payback as a measure of risk and liquidity, how long cash is exposed, and use NPV to decide.
Capital rationing
A business often has more good projects than money. When the budget is fixed, the aim is to get the largest total NPV from the money available, and ranking by NPV alone can mislead, because a large project uses up the budget. The profitability index divides the present value of inflows by the cost, so it shows value per dollar.
Profitability index = (NPV + Cost) ÷ Cost
Some textbooks define the index as NPV ÷ cost, which is this figure minus 1. The two give the same ranking. Rank projects by index and fund them in order until the budget is spent. This works when projects cannot be split and fit the budget neatly. Where a project does not fit, check the combinations directly, since a small number of projects can be checked by hand or in a spreadsheet.
Worked case
Four projects, one budget
Between them Northside and Hartley have four candidate projects and $60,000 to spend this year, discounted at 10%.
| Project | Cost $ | NPV $ | Index |
|---|---|---|---|
| Second espresso machine | 18,000 | 6,081.39 | 1.338 |
| Hydro-jetting unit | 30,000 | 9,789.63 | 1.326 |
| Online ordering and card-reader refit | 12,000 | 2,264.39 | 1.189 |
| Shop racking and parts stock room | 30,000 | 4,117.08 | 1.137 |
All four have a positive NPV, and together they cost $90,000. Ranking by index and funding in order gives the espresso machine ($18,000), the hydro-jetting unit ($30,000) and the online ordering refit ($12,000), which uses $60,000 and adds $18,135.41 of NPV. The racking project ($30,000) does not fit.
Checking every combination that fits in $60,000 confirms nothing beats that: the best total NPV is $18,135.41. Racking plus the espresso machine, for example, totals $10,198.47. Where a good project is left out, it is worth asking whether its cost can be split, financed in a different way, or delayed to next year.
Template
Payback and ranking workbook
A payback sheet with cumulative cash flow, simple and discounted payback and NPV for two projects, and a ranking sheet that computes NPV and profitability index for up to eight projects and funds them in index order against a budget. The case figures are loaded.
The full working file, 4-4-payback-and-ranking.xlsx, is in the Accounting and Finance Toolkit, Complete Track 1. The lesson above teaches the method and shows the worked numbers, so you can build it yourself in any spreadsheet.
Exercises
Work these, then open the answers
Project Y has an outlay of $24,000 and inflows of $6,000, $8,000, $10,000, $12,000 and $14,000. How many years does it take to recover the cost?
Answer
After 2 years the total is $14,000, leaving $10,000. Year 3 brings in $10,000, so payback is exactly 3.00 years.
A project has an NPV of $2,264.39 and costs $12,000. What is its profitability index?
Answer
(2,264.39 + 12,000) ÷ 12,000 = 1.189.
Explain why a payback rule can reject a good project.
Answer
It ignores cash flows after the payback date. A project that pays back slowly and then earns for years can have a high NPV and still fail a short payback hurdle.
Check
4 questions
Sources
Sources
- Principles of Finance, OpenStax, Rice University