FIN.6:5 - Archetypal Grounding
With qualified supplied flows. A constructed project pays 1,000 now and receives 600 at the end of each of the next two years. These are complete incremental after-tax operating cash flows; no terminal value remains. At a matching annual rate of 10%, NPV = −1,000 + 600/1.10 + 600/1.10² = 41.32. Equal annual receipts of 576.19 would give zero NPV. At a required return of 15%, the same 600 receipts give −24.57. Thus the result supports the project on the stated 10% basis, and the relevant return assumption can reverse it. The 41.32 is a value estimate; it does not supply the initial 1,000.
Construct the flows from the alternatives. A separate constructed two-year project requires equipment costing 900 and operating working capital of 100 now. The baseline continues the existing business and rents the available room for 40 per year. The project uses that room, generates annual revenue 1,100 and incurs operating costs 400. It also reduces the existing business’s annual contribution after avoided costs by 60. There are no other operating changes. A study costing 30 was paid already and has no differing future tax effect; allocated headquarters expense of 50 per year would be incurred under either alternative.
Assume nominal amounts, a matched supplied annual return of 10%, and no debt. All operating receipts, payments and taxes occur at each year end; the initial working capital stays at 100 until its complete cash recovery at year 2. Under the stipulated tax rules, all the relevant income and deductions use 25% in the same year, tax depreciation is 450 each year, and no other noncash charge exists. At year 2, equipment with zero tax basis sells for 100, taxable in full, and closure costs 20 are deductible and paid. These are case assumptions, not jurisdictional tax rules.
| Incremental cash construction | Now | End of year 1 | End of year 2 |
|---|---|---|---|
| Operating margin before depreciation: 1,100 − 400 − 60 − 40 | 0 | 600 | 600 |
| Cash tax on that margin after depreciation: (600 − 450) × 25% | 0 | −37.50 | −37.50 |
| Equipment payment | −900 | 0 | 0 |
| Working-capital investment and recovery | −100 | 0 | +100 |
| Equipment sale after tax: 100 − 25 | 0 | 0 | +75 |
| Closure payment after tax: −20 + 5 | 0 | 0 | −15 |
| Incremental free cash flow | −1,000 | +562.50 | +722.50 |
The annual operating cash can also be recovered as taxable operating income 150 × 75% + depreciation 450 = 562.50. The 900 equipment payment is counted once; the 30 study and unchanged 50 allocation cancel. At 10%, NPV = −1,000 + 562.50/1.10 + 722.50/1.10² = 108.47.
Change the baseline. A credible alternative tenant offers 150 per year instead of 40. Holding the other case grounds fixed, the extra forgone rent is 110 before tax, or 82.50 after tax each year. The revised flows are −1,000, +480, +640 and NPV is −34.71. The rent that makes the project indifferent to this baseline is 40 + 108.471074/[0.75 × (1/1.10 + 1/1.10²)] = 123.33 per year. If the obtainable rent is unresolved across that threshold, obtain firmer terms or give a conditional comparison. The tax and timing assumptions are part of that threshold.