Meridian Components: The Bottleneck Machine and a Marginal NPV
Meridian Components runs a single machining cell that is the plant's bottleneck. A replacement machine costs $1,200,000, has a five-year life and no residual value, and would cut labour and rework costs by $440,000 a year while adding $40,000 a year in maintenance. Straight-line depreciation over five years is used for tax, the tax rate is 25% payable in the year incurred, and the after-tax cost of capital is 10%. An extra $150,000 of working capital (spares and inventory) is needed at the outset and is released at the end of year five. The plant accountant has already expensed a $25,000 feasibility study and proposes to charge $60,000 a year of existing head-office overhead to the project. The old machine carries $300,000 of book value and would be scrapped for no proceeds.
1. Decide which figures belong in the incremental cash flow and compute the project NPV. Explain each exclusion.
Read the worked answer
In / out test - does the item change because we do the project?
| Item | Treatment | Reason |
|---|---|---|
| $1,200,000 machine | t0 outflow | Incremental cash |
| $150,000 working capital | t0 outflow, t5 inflow | Recoverable, not an expense |
| $440,000 savings less $40,000 maintenance = $400,000 | Annual, pre-tax | Incremental operating cash |
| $25,000 feasibility study | Exclude | Sunk; incurred whatever we decide |
| $60,000 allocated overhead | Exclude | Reallocation of existing cost; no extra cash leaves the firm |
| $300,000 book value of old machine | Exclude | Non-cash; no proceeds means no tax consequence |
| Depreciation | Tax shield only | Non-cash, but reduces tax |
| Interest | Exclude | Captured in the 10% discount rate |
Annual after-tax cash flow (years 1–5)
Pre-tax net 400,000 − depreciation 240,000 = taxable 160,000; tax at 25% = 40,000. Cash flow = 400,000 − 40,000 = $360,000 (equivalently 400,000 × 0.75 + 240,000 × 0.25).
NPV
- t0: (1,200,000) + (150,000) = (1,350,000)
- Years 1–5: 360,000 × 3.7908 = 1,364,688
- Year 5 release: 150,000 × 0.6209 = 93,138
NPV = 1,364,688 + 93,138 − 1,350,000 = +$107,800 (approx.)
2. The finance director wants a three-year payback hurdle applied to all capital requests. Test this project against that rule and advise the board on which measure should govern.
Read the worked answer
Payback = 1,350,000 ÷ 360,000 = 3.75 years, so the project fails a three-year hurdle even though it creates value.
Why the two measures disagree:
- Payback ignores the time value of money entirely; a dollar in year 3 is discounted at 10% in the NPV.
- It truncates the stream at 3.75 years and so ignores roughly 1.25 years of $360,000 plus the $150,000 working-capital release - precisely the $108k of value the NPV detects.
- The three-year cut-off is arbitrary: it is not derived from the cost of capital or from the life of the asset, and it systematically biases the firm against long-lived, efficiency-generating assets and towards quick, low-return ones.
Recommendation: NPV is the decision rule because it is the only measure that consistently ranks projects by change in shareholder value. Keep payback as a secondary liquidity screen on projects where capital is rationed or cash is tight - used as a filter it can veto value, but that veto should be an explicit, owned policy decision, not a default.
Note the honest caveat: +$108k is about 8% of the outlay, so the margin is thin and the decision should hang on the reliability of the $440,000 savings estimate (see next task).
3. How far can the annual savings fall before the project destroys value, and what does that tell you about the decision?
Read the worked answer
Break-even annual after-tax cash flow
Required PV of operating flows = 1,350,000 − 93,138 = 1,256,862. Divided by the 5-year annuity factor: 1,256,862 ÷ 3.7908 = $331,556.
Versus the forecast $360,000, that is a fall of $28,444, or 7.9%. In pre-tax terms: 331,556 = 0.75 × X + 60,000, so X = $362,075, i.e. net savings of $362k rather than $400k - a fall of about 9.5%.
Interpretation
- A ~10% shortfall in savings wipes out the entire return, and a 10% error on a cost-saving forecast is unremarkable. The project is therefore conditional, not comfortably positive.
- The conventional savings case also understates the benefit. This cell is the bottleneck: an hour of extra capacity is worth its throughput contribution, not just the labour and rework saved. If a machine-hour at the constraint earns, say, $90 of contribution and the new machine frees the equivalent of 1,500 hours, that is $135,000 a year of value the NPV above omits.
- Conversely, the NPV omits the risk of disruption during installation.
What to do: validate the rework and labour savings with a trial on a comparable cell, quantify bottleneck throughput per hour so the business case reflects the real constraint value, and approve on the corrected case rather than on the marginal one.