Five Measures, $500,000, and a Five-Year Payback Rule
The plant has $500,000 of capital available this year and a 12% real discount rate. Five measures are on the table: (A) LED and lighting controls, $180,000, $60,000/yr, 10-year life; (B) compressed-air leak repair and master controls, $90,000, $45,000/yr, 7-year life; (C) boiler plant replacement with condensing boilers, $320,000, $55,000/yr, 20-year life; (D) VSDs on four AHU supply fans, $70,000, $22,000/yr, 15-year life; (E) roof insulation, $150,000, $12,000/yr, 25-year life. The roof membrane is already scheduled for replacement in 24 months at $180,000; adding insulation at that time would cost $95,000 extra instead of $150,000. The CFO's rule is 'nothing with a payback over five years.'
1. Build the project portfolio. Show the NPV and payback for each measure and justify the package you recommend.
Read the worked answer
Annuity factors at 12%: 7 yr = 4.564, 10 yr = 5.650, 15 yr = 6.811, 20 yr = 7.469, 25 yr = 7.843.
| Measure | CapEx | $/yr | Life | Simple PB | NPV @12% |
|---|---|---|---|---|---|
| A Lighting | $180k | $60k | 10 | 3.0 | +$159k |
| B Compressed air | $90k | $45k | 7 | 2.0 | +$115k |
| C Boilers | $320k | $55k | 20 | 5.8 | +$91k |
| D AHU VSDs | $70k | $22k | 15 | 3.2 | +$80k |
| E Roof insulation | $150k | $12k | 25 | 12.5 | −$56k |
Packages within $500k:
- A + B + D = $340k, savings $127k/yr, NPV $354k ← best
- B + C + D = $480k, NPV $286k
- A + C = $500k exactly, NPV $250k
- A + B = $270k, NPV $274k (leaves $230k idle)
Recommendation: A + B + D. It produces the highest NPV and the highest annual savings per dollar committed, and it preserves $160k of unspent budget. Note that ranking by simple payback would have put C last - yet C is strongly NPV-positive because of its 20-year life. Payback is a liquidity test, not an economic one.
2. How should measure E be handled, given the roof replacement in 24 months?
Read the worked answer
Defer it, and re-frame it as an incremental decision.
The $150,000 is not the relevant cost.
- Standalone now: NPV = (12 × 7.843) − 150 = −$56k. Reject.
- Bundled with the scheduled roof: incremental cost $95,000 → NPV = 94.1 − 95 = ≈ −$1k, i.e. an IRR of roughly 12.6% - right at the hurdle, essentially a wash.
- Doing it now also risks wasting work if the membrane replacement disturbs it.
What to do
- Remove E from this year's portfolio and issue it as a conditional recommendation tied to the 24-month roof project.
- Re-estimate the savings before the roof decision - the $12k/yr is almost certainly gas-only. Insulation also reduces summer cooling load, and that electricity saving has a higher value per unit and a demand component. If the combined saving reaches $18–20k/yr, the $95k incremental spend clears the hurdle comfortably.
- Verify structural capacity for the added insulation and check the dew-point/condensation risk of the proposed assembly - a 25-year measure must not create a moisture problem.
Saying 'no, but here is the trigger and the price' is more useful to the client than either a bare rejection or bundling a marginal item into an attractive package.
3. The CFO says any measure with payback over five years is out. Evaluate that rule using measure C, and state what you would tell him.
Read the worked answer
The rule contradicts the hurdle rate.
- C's payback is 5.8 years on a 20-year asset - IRR is roughly 16.5%, well above the 12% hurdle, and NPV is +$91k. Rejecting it destroys value.
- A 5-year payback cutoff on a 20-year life is an implicit IRR requirement of ~19–20%. If that is genuinely the company's cost of capital, say so - but then the 12% discount rate in the analysis is wrong and the hurdle must be restated. The two cannot both be true.
- Payback also ignores everything after the payback date, which is exactly where C's value lives; and it ignores interactions: D lowers cooling load, E lowers both heating and cooling, so the measures are not independent.
Also test the escalation assumption: boiler savings are gas savings. At 2%/yr real gas escalation against a 12% discount rate, the effective discount rate is 1.12/1.02 = 9.8%, the 20-year factor rises to ~8.63, and C's NPV becomes ≈ +$155k. Under any energy-price scenario, C is the measure most exposed to being wrongly cut.
Message to the CFO: 'Your rule and your discount rate disagree. Pick one. If 12% is right, C is your third-best project and should be funded in the next cycle.'