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 labor 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 neighboring 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 the United States, tax depreciation uses the Modified Accelerated Cost Recovery System, MACRS. Each asset is assigned a recovery period, such as five years for computers and vehicles or seven years for most machinery, and the IRS publishes the percentage of the cost that may be deducted each year, using a half-year convention so that the first and last years get half a year's deduction. On top of MACRS, bonus depreciation lets firms deduct a large part of the cost of qualifying property immediately. The Tax Cuts and Jobs Act of 2017 allowed 100 percent bonus depreciation and scheduled it to phase down from 2023; the 2025 budget reconciliation law, the One Big Beautiful Bill Act, made 100 percent bonus depreciation permanent for qualifying property acquired after January 19, 2025. Firms can elect out and use ordinary MACRS, for example when they expect higher tax rates later or have losses that make deductions less valuable now.

The value of faster depreciation comes from timing. Over the life of an asset, total deductions equal its cost whether they are taken over seven years or in the first year. But a dollar of tax saved in the first year is worth more than a dollar saved in the eighth. Bonus depreciation therefore does not reduce the total tax a firm pays on a project so much as defer it, and the value of the deferral rises with the discount rate.

Northfield's press line in full

The press line costs 14 million dollars. Engineering expects it to save enough in labor and scrap to add 3.4 million dollars a year after tax, which at a combined federal and state rate of 25 percent, the federal rate of 21 percent plus a typical state tax net of its federal deduction, is about 4.53 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. The line is seven-year MACRS property, and because it is acquired well after January 19, 2025, it qualifies for 100 percent bonus depreciation unless Northfield elects out.

# Northfield press line: incremental after-tax cash flows with MACRS (millions)
cost, life, salvage = 14.0, 8, 1.5
savings, tax, r = 3.4 / (1 - 0.25), 0.25, 0.09     # pre-tax savings giving 3.4 after tax
nwc = 0.8                                          # spare parts and tooling, recovered at the end
macrs7 = [0.1429, 0.2449, 0.1749, 0.1249, 0.0893, 0.0892, 0.0893, 0.0446]

def project(bonus):
    dep = [cost] + [0.0] * (life - 1) if bonus else [cost * p for p in macrs7]
    flows = [-cost - nwc]
    for t in range(1, life + 1):
        cf = savings * (1 - tax) + dep[t - 1] * tax
        if t == life:
            book = cost - sum(dep)
            cf += salvage + nwc - (salvage - book) * tax   # tax on gain over remaining basis
        flows.append(cf)
    return sum(f / (1 + r) ** t for t, f in enumerate(flows)), dep

for label, bonus in [("7-year MACRS", False), ("100% bonus", True)]:
    v, dep = project(bonus)
    print(f"{label:14s} first-year deduction {dep[0]:5.2f}  NPV {v:5.2f}")

7-year MACRS   first-year deduction  2.00  NPV  7.59
100% bonus     first-year deduction 14.00  NPV  8.20

Two lessons emerge. First, once the tax shield, working capital and salvage value are included, the NPV rises to about 7.6 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 depreciation. Second, bonus depreciation adds about 0.6 million dollars of value by moving all the deductions into the first year. For a capital-intensive firm making many such investments, that 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 defenses. 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.