Crane Replacement: NPV Against Divisional ROI
Harbor Logistics Inc. evaluates divisional managers on return on investment (ROI) and pays bonuses on that measure. The Voyage Division is considering replacing its crane. The existing crane is fully depreciated and has no resale value; it costs ₱24,000,000 a year to operate. A new crane costs ₱40,000,000, has a four-year life, a ₱4,000,000 terminal salvage value, and would cut annual cash operating costs to ₱10,000,000. Depreciation is straight-line over four years to salvage value. The division's current investment base is ₱120,000,000 and its operating income is ₱18,000,000; acquiring the new crane would raise the investment base to ₱160,000,000. Harbor's cost of capital is 12%: the four-year annuity factor is 3.0373 and the present value factor at year 4 is 0.6355. The company allocates ₱6,000,000 of head-office overhead to the division; ₱500,000 of that amount is additional overhead that would be triggered only by the acquisition. Ignore income taxes.
1. Compute the net present value of replacing the crane, identifying each relevant cash flow and each item deliberately excluded.
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Relevant cash flows are those that differ between replacing and not replacing:
- Initial outlay: ₱(40,000,000). The old crane has no resale value, so there is no disposal proceeds offset and no tax effect to consider.
- Annual operating savings: 24,000,000 − 10,000,000 = ₱14,000,000 for years 1–4, an annuity of 14,000,000 × 3.0373 = ₱42,522,200.
- Terminal salvage: 4,000,000 × 0.6355 = ₱2,542,000.
NPV = 42,522,200 + 2,542,000 − 40,000,000 = ₱5,064,200 positive - accept.
Excluded: the old crane's book value (nil here, and in any case a sunk cost), the ₱6,000,000 allocated head-office overhead (a reallocation of existing cost that does not change with the decision), and all depreciation, which is a non-cash allocation - note the ₱9,000,000 annual depreciation (40,000,000 − 4,000,000)/4 is not a cash flow, which is why it is absent from the computation, though it matters to the ROI analysis below.
The decision is not sensitive: the NPV would turn negative only if annual savings fell to roughly ₱12.4 million or if the outlay rose by about ₱5 million.
2. Compute the division's ROI and residual income before and after the acquisition and explain the behavioural problem the incentive creates.
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Divisional operating income after the acquisition: 18,000,000 + 14,000,000 cash savings − 9,000,000 additional depreciation = ₱23,000,000. (No depreciation on the old crane, which is fully depreciated.)
| Measure | Before | After |
|---|---|---|
| ROI | 18,000,000 ÷ 120,000,000 = 15.00% | 23,000,000 ÷ 160,000,000 = 14.375% |
| Residual income | 18,000,000 − 14,400,000 = ₱3,600,000 | 23,000,000 − 19,200,000 = ₱3,800,000 |
The project has a positive NPV, so it creates shareholder value. But it lowers the manager's ROI from 15.00% to 14.375% - below the division's current average - so a manager rewarded on ROI and measured against a 15% target will reject it. This is the classic under-investment problem: ROI penalises any investment whose return, though above the 12% cost of capital, is below the existing average return.
Residual income resolves the conflict: it rises by ₱200,000, so a manager charged 12% on the investment base accepts. The residual income charge equals the cost of capital, so any positive-NPV project increases residual income. Harbor should shift the bonus metric to residual income or economic value added, or apply ROI only to assets in place, to align the manager's interest with the company's.
3. The controller proposes deducting the full ₱6,000,000 overhead allocation. Recompute and advise on the correct treatment and on the final decision.
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Deducting the full allocation would give: 42,522,200 + 2,542,000 − 40,000,000 − (6,000,000 × 3.0373 = 18,223,800) = ₱(13,159,600), which would lead to rejection. That is wrong.
The ₱6,000,000 is an allocation of costs the company already incurs; it does not change with the decision, so it is irrelevant to incremental analysis. Only the ₱500,000 that is triggered by the acquisition is a differential future cash flow and belongs in the analysis:
NPV = 5,064,200 − (500,000 × 3.0373 = 1,518,650) = ₱3,545,550 positive. Accept.
The distinction is between an allocated cost, which merely redistributes existing spend and would be incurred anyway, and an incremental cost, which arises only because of the decision. The presence of the allocation in the division's reported operating income also means the ROI figures above already absorb it in both scenarios, so it does not distort the comparison.
Final advice: acquire the crane, since value is created on a relevant-cash-flow basis; but recognise that the ROI bonus will still cause the manager to resist. Fix the measure rather than the analysis, and separately verify that the ₱500,000 incremental overhead estimate is complete.