Northgate Logistics: Fleet Replacement under Inflation
Northgate Logistics is evaluating the replacement of 40 diesel delivery vans with electric vans. The electric fleet costs £2,400,000 and has an expected life of four years with no residual value. Annual operating cash savings (fuel, servicing and road tax) are estimated at £820,000 in current prices, before any allowance for inflation, and these savings are expected to rise with inflation. The company's nominal after-tax cost of capital is 10% and inflation is expected to be 3% per year. Northgate is profitable and pays tax at 25%, one year in arrears. For simplicity the finance team intends to appraise the project using the £820,000 savings as a constant nominal amount and a four-year annuity factor of 3.170. The operations director argues for a five-year appraisal because battery technology is improving and a second-hand market for the vans should exist; she estimates a £300,000 residual value at the end of year 5 and a year-5 saving of £700,000 before inflation. The board has a four-year payback guideline.
1. Calculate the NPV and payback under the finance team's constant-nominal assumption and comment on the consistency of the approach.
Read the worked answer
NPV as proposed
PV of savings = 820,000 × 3.170 = £2,599,400
NPV = 2,599,400 − 2,400,000 = £199,400 positive
Payback = 2,400,000 ÷ 820,000 = 2.93 years, inside the four-year guideline.
The inconsistency. The 10% cost of capital is a nominal rate, built from a real return plus expected inflation (roughly 1.10 ÷ 1.03 − 1 = 6.8% real). A nominal rate must be applied to nominal cash flows. The £820,000 is stated in current prices, so it is a real amount, and treating it as constant nominal cash flow omits the 3% annual growth the company actually expects. The analysis therefore understates the project's value.
There are two correct routes and they should give the same answer:
- Inflate the savings at 3% and discount at the 10% nominal rate.
- Leave the savings in current prices and discount at the 6.8% real rate.
Mixing the two is a common error. It is not automatically conservative, because the direction of the error depends on which rate and which cash flows have been mismatched. The tax calculation has also been ignored: Northgate pays 25% one year in arrears, and capital allowances on £2,400,000 would provide relief, so the true NPV is not simply 75% of the operating PV.
2. Recalculate the NPV and payback with the 3% inflation applied to the savings, and advise the board.
Read the worked answer
Inflated savings and discount factors at 10%
| Year | Savings (£) | DF 10% | PV (£) |
|---|---|---|---|
| 1 | 844,600 | 0.909 | 767,800 |
| 2 | 869,900 | 0.826 | 718,500 |
| 3 | 896,000 | 0.751 | 672,900 |
| 4 | 922,900 | 0.683 | 630,300 |
PV of savings ≈ £2,789,500; NPV = 2,789,500 − 2,400,000 = £389,500 positive, roughly £190,000 better than the uncorrected figure.
Payback with inflation: cumulative savings reach 844,600 in year 1, 1,714,500 by year 2 and 2,610,500 by year 3, so payback occurs in year 3 at 2 + (2,400,000 − 1,714,500) ÷ 896,000 = 2.76 years.
Advice to the board
- The project clears the 10% hurdle by a comfortable margin on a consistent nominal basis and meets the payback guideline, so the decision is not marginal.
- Sensitivity: the constant-nominal break-even saving is 2,400,000 ÷ 3.170 = £757,100, a fall of 7.7% from £820,000. On the inflated basis the margin for error is larger, but the savings estimates remain the critical variable and should be validated against actual fuel and maintenance data from a pilot fleet.
- Tax: at 25% paid one year in arrears, with capital allowances on £2,400,000, the after-tax NPV will be materially lower than £389,500. The board should not approve the project until the after-tax, after-allowance figure is produced; it is possible that the tax timing effect reduces the surplus to a modest amount.
- Payback is a liquidity screen, not a value measure; NPV should be the primary criterion.
3. Evaluate the operations director's five-year extension, including the residual value, and explain the limitations of the revised appraisal.
Read the worked answer
Extension calculation
Inflated year-5 saving = 700,000 × 1.03⁵ = £811,500. Add the £300,000 residual value = £1,111,500, discounted at 0.621 = £690,200.
Revised NPV ≈ 389,500 + 690,200 = £1,079,700.
Limitations
- The savings assumption changes. Her own figures have the saving falling from £922,900 in year 4 (inflated) to £811,500 in year 5, a real decline from £820,000 to £700,000. That is an admission of deteriorating economics, probably battery degradation, not a reason to extend the project. The extension's value depends on an assumption that contradicts the earlier forecast.
- Missing cash outflows. Replacing batteries at the end of year 4 or 5 is a large capital cost not included. If a battery pack costs several hundred thousand pounds, it could absorb the entire residual value and more.
- Residual value risk. The second-hand electric van market is immature and the £300,000 is an estimate, not a contract. Sensitivity should be run at zero and at £150,000.
- Comparability distorted. Extending one option's life without extending the alternative's makes the comparison invalid. The diesel alternative should be appraised over the same horizon, or the two should be compared on an equivalent annual annuity basis.
- Tax still ignored. Capital allowances on the extra year and the tax on the residual value (a balancing charge is likely) both affect the figure.
Conclusion: the extension is worth modelling properly, but the headline £1,080,000 should not be presented to the board as a like-for-like improvement. The defensible position is that the four-year project already clears the hurdle, and the extension is an option whose value depends on battery replacement cost and residual value - both of which should be tested explicitly before the investment decision is taken.