Estimating project cash flows

When the cohort reconvenes, Dr. Varga puts the press-line figures from lesson 5 back on the screen and admits that he simplified them. A real proposal does not arrive with a tidy row of after-tax cash flows. It arrives with an engineering estimate of the equipment cost, a production manager's guess at the labour saved, a purchasing estimate of scrap reduction, and a spreadsheet from the accounting team showing the project's effect on reported earnings. Turning those into the cash flows that belong in an NPV calculation is where most of the judgment in capital budgeting lies, and where most of the errors are made.

The incremental principle

The cash flows that matter are incremental: the difference between the firm's cash flows with the project and without it. Everything follows from that principle. A cost that will be incurred whether or not the project goes ahead is irrelevant. A benefit that the firm would enjoy anyway is irrelevant. What counts is how the decision changes the firm's future cash.

Four kinds of item commonly trip up analysts. Sunk costs, money already spent, should be ignored; Northfield's 400,000 dollars of engineering studies for the press line are gone whatever the board decides. Opportunity costs, the value of resources the project uses that could be used elsewhere, should be included even when no cash changes hands; if the press line occupies floor space that could otherwise be leased to a neighbouring firm for 250,000 dollars a year, that forgone rent is a cost of the project. Side effects on the firm's other products count: a new product that takes sales from an existing one, called cannibalization, reduces the incremental benefit, while one that helps sell other products adds to it. And allocated overhead counts only to the extent that it actually changes; if head office costs are spread across projects by a formula but would not rise, they are not incremental.

Cash flow, not profit

The NPV calculation uses after-tax cash flows, not accounting profit. Three adjustments turn one into the other. First, depreciation is not a cash outflow; the cash was spent when the equipment was bought. But depreciation for tax purposes reduces the taxes the firm pays, and that tax saving, the depreciation tax shield, is a real cash benefit. Second, investment in working capital, such as inventory, receivables and spare parts, ties up cash at the start and releases it when the project ends. Third, interest is excluded from project cash flows, because the cost of financing is captured in the discount rate; including it would count the cost of debt twice.

In this formula, revenue minus cash operating costs is taxed at the tax rate, the depreciation deduction saves tax equal to the tax rate times the deduction, and capital spending and increases in working capital are subtracted. An equivalent form starts with operating profit after tax and adds back depreciation, the same structure as free cash flow to the firm in lesson 4. Project analysis and company valuation use the same building blocks.

Depreciation for tax

In Canada, tax depreciation is called capital cost allowance, CCA. Assets are grouped in classes, each with a prescribed rate, and most classes use the declining-balance method: each year the firm may deduct the class rate times the undepreciated capital cost, UCC, the balance not yet deducted. Under the half-year rule, only half the normal rate may be claimed in the year an asset is acquired. To encourage investment, the federal government introduced the accelerated investment incentive in 2018, which for eligible property suspends the half-year rule and allows one and a half times the normal first-year rate, and for some classes, such as manufacturing and processing machinery and clean energy equipment, allowed full expensing for several years. The incentive began phasing out from 2024, and the November 2025 federal budget, under its productivity super-deduction, proposed restoring the enhanced first-year write-off for most capital assets and allowing immediate expensing of eligible manufacturing and processing buildings acquired from Budget Day and available for use before 2030. Because the rules change often, an analyst should confirm the class, the rate and the first-year treatment for each asset before building the model.

When CCA continues indefinitely on a declining balance, the present value of all the tax savings from an asset has a closed form. With the half-year rule, a capital cost C, a CCA rate d, a tax rate T and a discount rate k, the present value of the CCA tax shield is the expression below, less a similar term for the salvage value removed from the class when the asset is sold. The formula is a compact way to see why faster write-offs matter: they move tax savings closer to the present.

Northfield's press line in full

The press line costs 14 million dollars. Engineering expects it to save enough in labour and scrap to add 3.4 million dollars a year after tax, which at Northfield's combined federal and Ontario tax rate of 26.5 per cent is about 4.63 million before tax. It requires 0.8 million dollars of spare parts and tooling, recovered at the end of eight years, when the line can be sold for about 1.5 million. Assume it falls in a class with a 30 per cent declining-balance rate, and for simplicity that the remaining balance is deducted when the asset is sold. The general federal corporate rate is 15 per cent, and provincial rates add between about 8 and 16 points; Canadian-controlled private corporations pay a lower combined rate, with a federal small business rate of 9 per cent, on the first 500,000 dollars of active business income, which Northfield, with taxable income well above that, mostly does not benefit from.

# Northfield press line: incremental after-tax cash flows with CCA (millions)
cost, life, salvage = 14.0, 8, 1.5
savings, tax, r = 3.4 / (1 - 0.265), 0.265, 0.09   # pre-tax savings giving 3.4 after tax
nwc = 0.8                                           # spare parts and tooling, recovered at the end
d = 0.30                                            # declining-balance CCA rate for the class

def cca_schedule(cost, d, years, first_year_factor):
    ucc, out = cost, []
    for t in range(1, years + 1):
        rate = d * first_year_factor if t == 1 else d
        claim = ucc * rate
        out.append(claim)
        ucc -= claim
    return out, ucc

def project(first_year_factor):
    cca, ucc_end = cca_schedule(cost, d, life, first_year_factor)
    flows = [-cost - nwc]
    for t in range(1, life + 1):
        cf = savings * (1 - tax) + cca[t - 1] * tax
        if t == life:
            cf += salvage + nwc
            cf += (ucc_end - salvage) * tax      # terminal loss treated as fully deductible here
        flows.append(cf)
    return sum(f / (1 + r) ** t for t, f in enumerate(flows)), cca

for label, factor in [("half-year rule", 0.5), ("accelerated incentive", 1.5)]:
    v, cca = project(factor)
    print(f"{label:22s} first-year CCA {cca[0]:5.2f}  NPV {v:5.2f}")

half-year rule         first-year CCA  2.10  NPV  7.74
accelerated incentive  first-year CCA  6.30  NPV  7.96

Two lessons emerge. First, once the tax shield, working capital and salvage value are included, the NPV rises to about 7.7 million dollars, well above the simple figure of 4.8 million in lesson 5, which treated 3.4 million a year as the whole after-tax cash flow and left out the tax value of the CCA deductions. Second, the accelerated incentive adds about 0.2 million dollars of value by moving tax deductions forward. For a capital-intensive firm making many such investments, the incentive changes which projects clear the hurdle, which is exactly what the policy intends.

Working capital and terminal values

Working capital is easy to forget and can change a decision. A new store needs inventory before it makes its first sale; a new product line needs receivables because customers pay on credit. These investments are cash outflows at the start and, if the project ends, cash inflows when the inventory is sold off and receivables are collected. Grace's estimate for a new Fairway store includes 1.1 million dollars of inventory, partly offset by 0.7 million of supplier credit, so the net working capital investment is 0.4 million. Cedarline, the cohort's case company, shows what happens when working capital is ignored: its inventory grew from 58 to 128 million dollars over four years, absorbing cash that its reported profits never revealed.

At the end of the forecast, a project may have a salvage value, or it may continue indefinitely, in which case a terminal value is needed, usually a growing perpetuity of the final year's cash flow. When an asset is sold, the tax consequences depend on how its sale price compares with its remaining tax value: a sale above that value creates a taxable recapture or gain, a sale below it a deductible loss. These end-of-life effects are small for long projects at high discount rates but can matter for short ones.

Inflation, scenarios and forecasting bias

Forecasts should be consistent about inflation. If the discount rate is nominal, as rates observed in markets are, the cash flows should include expected inflation in prices, wages and materials. A common mistake is to hold revenues flat in today's dollars and discount at a nominal rate, which understates the NPV of every long project. Tax depreciation, by contrast, is fixed in nominal terms at the original cost, so its real value falls with inflation.

Forecasts are also systematically optimistic. Studies of large capital projects, notably by Bent Flyvbjerg, find that cost overruns and benefit shortfalls are the norm, not the exception, and that the cause is less often bad luck than a combination of optimism and strategic misrepresentation by project sponsors. Dr. Varga recommends three defences. Reference-class forecasting compares a project's estimates with the actual outcomes of similar past projects. Scenario analysis builds a pessimistic, base and optimistic case with internally consistent assumptions, rather than flexing one variable at a time. And break-even analysis asks how far a key assumption, such as annual savings, could fall before the NPV reaches zero; for the press line, after-tax savings could fall by about two fifths before the project destroys value.