Whole-Life Heating Choice for a New Secondary School
A local education authority is choosing between two heating systems for a new secondary school. Option A uses gas boilers: capital cost $1.20 million, annual energy $180,000, annual maintenance $25,000 and a major replacement in year 15 costing $400,000. Option B uses electric heat pumps: capital cost $2.10 million, annual energy $110,000, annual maintenance $40,000 and a major replacement in year 18 costing $350,000. The appraisal period is 25 years. The authority uses a real discount rate of 6%. The finance team has supplied these factors: 25-year annuity factor at 6% = 12.783; single-payment discount factor at year 15 = 0.417; at year 18 = 0.350. No residual values are to be included. The authority has a limited capital budget and is under political pressure to choose the lower-capital-cost option. A carbon tax of $35 per tonne of CO2 is being considered but is not yet approved. Option A emits about 320 tonnes of CO2 per year; Option B about 150 tonnes. The QS is asked to advise.
1. Calculate the whole-life NPV of each option and recommend on financial grounds. State the assumptions you use.
Read the worked answer
Assume all costs are stated in constant prices, so the real discount rate and real cash flows are consistent. Annual costs are treated as end-of-year annuities; replacement costs occur at the stated years.
Option A:
- Capital: $1,200,000
- Energy: $180,000 x 12.783 = $2,300,940
- Maintenance: $25,000 x 12.783 = $319,575
- Replacement: $400,000 x 0.417 = $166,800
- NPV: $3,987,315
Option B:
- Capital: $2,100,000
- Energy: $110,000 x 12.783 = $1,406,130
- Maintenance: $40,000 x 12.783 = $511,320
- Replacement: $350,000 x 0.350 = $122,500
- NPV: $4,139,950
Option A is cheaper by about $152,600 over 25 years. That is only about 3.8% of A's whole-life cost, so the result is not overwhelming. The recommendation should be for Option A on the stated financial assumptions, subject to sensitivity testing of energy prices, maintenance inflation and replacement timing. The QS should also note that the lower-capital-cost option is not automatically the lower whole-life cost option, even though here it happens to be.
2. Calculate the effect of the proposed $35 per tonne carbon tax and the tax rate at which the two options become financially equal. Advise how the QS should present the carbon-tax uncertainty to the authority.
Read the worked answer
At $35 per tonne, the present value of the carbon tax is:
- Option A: 320 tonnes x $35 x 12.783 = $143,170
- Option B: 150 tonnes x $35 x 12.783 = $67,111
Adding these to the NPVs gives A $4,130,485 and B $4,207,061. A remains cheaper by about $76,600.
The break-even tax rate is the NPV difference divided by the discounted emissions difference: $152,635 / ((320 - 150) x 12.783) = $152,635 / 2,173 = about $70 per tonne.
At a carbon tax above roughly $70 per tonne, Option B becomes cheaper on the stated assumptions. The QS should not include an unapproved tax in the base-case recommendation, but should present it as a sensitivity. A short table showing NPV at $0, $35 and $70 per tonne would make the decision transparent. The authority should also weigh non-financial factors: carbon exposure, resilience to gas price shocks, maintenance skills, plant space, noise and the risk that heat-pump performance is lower than assumed. If the authority expects carbon pricing to rise, Option B has an option value that the base-case NPV understates. The advice should distinguish the financial recommendation from the strategic risk judgement.