12.3 Capex and Depreciation

The PP&E Schedule Is a Fourth Statement in Disguise

Revenue, COGS, and SG&A in 12.1 produced Year 1 EBIT of $7,761,000 with existing D&A of $6,000,000. Working capital in 12.2 produced a $578,783 cash use. This section adds the property, plant, and equipment (PP&E) roll-forward that CFI treats as mandatory in Operational Modeling: capex, disposals, and depreciation. Without it, D&A on the income statement, the add-back on the cash flow statement, and net PP&E on the balance sheet will be three different numbers — the most common three-statement break after retained earnings and cash.

Ending net PP&E = Beginning net PP&E + Capex − Disposals (at net book value) − Depreciation and amortization

Gross PP&E and accumulated depreciation can be rolled separately:

• Ending gross PP&E = Beginning gross + Capex − Gross cost of disposals
• Ending accumulated D&A = Beginning accumulated + D&A − Accumulated D&A on disposals
• Net PP&E = Gross − Accumulated

Both presentations must give the same net. Compact FMVA cases often roll net only and skip gross unless a disposal or a revaluation is in the prompt.

Northstar Year 0 (historical):

Remaining depreciable life on the existing net book, assuming zero salvage: $40,000,000 / $6,000,000 = 6.7 years. Remaining useful life is remaining depreciable base (net book − salvage) divided by remaining annual straight-line. If the case gives salvage of $4,000,000 on the old assets, remaining life = ($40,000,000 − $4,000,000) / $6,000,000 = 6.0 years. Do not take historical cost / original life and call it remaining life; that ignores already-depreciated years.

Capex: Percent of Sales Versus Maintenance and Growth

Two forecast methods, both legal:

1. Capex % of sales. Historical capex / historical sales becomes the driver. Fast. Smooth. Wrong in a year with a discrete plant.
2. Maintenance versus growth capex. Maintenance capex keeps current capacity (often close to D&A, or a stated % of sales). Growth capex expands capacity for volume. Lumpy. Right when the case describes a project.

Northstar historical maintenance has run at 4% of sales = 0.04 × $50,000,000 = $2,000,000, well below the $6,000,000 D&A charge — the fleet is aging. Year 1 the firm spends $10,000,000 of total capex: $2,000,000 maintenance plus $8,000,000 growth for a new line that supports the 5% volume increase and future mix. In the workbook that $10,000,000 is one blue input (or two, if you split maintenance and growth). It is not 4% × $54,075,000 = $2,163,000. Using the percent-of-sales rule in a project year understates PP&E, understates future D&A, and overstates UFCF by about $8 million.

Capex is a cash-from-investing outflow. It is not an income-statement expense. Expensing $10,000,000 in SG&A and putting it in CFI subtracts it twice from cash and once from net income. Capitalizing it on the PP&E schedule and forgetting CFI leaves cash too high.

Worked: Five-Year Straight-Line on $10 Million

The new line costs $10,000,000, useful life 5 years, placed in service at the start of Year 1, full-year convention, salvage $0 for book purposes.

Straight-line D&A per year = (Cost − Salvage) / Useful life = ($10,000,000 − $0) / 5 = $2,000,000

With $1,000,000 salvage, annual SL = ($10,000,000 − $1,000,000) / 5 = $1,800,000, and Year 5 net book = salvage. Salvage is not cash until you sell; it only changes the depreciable base.

Half-year convention (common in tax, optional in book policy) would take $1,000,000 of book D&A in Year 1 and Year 6 on a 5-year asset. If the case does not say half-year, do not invent it. Northstar's policy in this chapter is full-year in the year of acquisition, none in the year of disposal unless the prompt says otherwise.

Year 1 total D&A = existing $6,000,000 + new $2,000,000 = $8,000,000. That is the number that must appear in three places: income statement, cash-flow add-back, PP&E roll-forward.

Year 1 net PP&E roll-forward

Gross roll-forward check: beginning gross $70,000,000 + $10,000,000 = $80,000,000. Accumulated D&A $30,000,000 + $8,000,000 = $38,000,000. Net $42,000,000. Tied.

Revisit the P&L with the new charge:

EBIT falls even though contribution rose, because $2,000,000 of extra depreciation more than ate the operating-leverage gain versus a $6,000,000 D&A freeze. Section 12.1's $7,761,000 EBIT was the right number before the project. After the schedule, $5,761,000 is the articulated EBIT. A model that keeps D&A at 12% of sales ($6,489,000) is still wrong: D&A is a function of the asset base and remaining life, not of this year's revenue.

Straight-Line Versus Declining-Balance

Straight-line (SL) spreads (cost − salvage) evenly. Declining-balance applies a constant rate to remaining net book. Double-declining balance (DDB) uses 2 / useful life. On a 5-year asset, DDB rate = 2/5 = 40%. Salvage is usually ignored until the floor: you do not depreciate below salvage.

Five-year schedule on the $10,000,000 asset, salvage $0:

Year 5 DDB takes the remaining book so the asset reaches salvage (here zero). Many textbooks switch to straight-line when SL on the remaining book exceeds DDB. At the start of Year 4, remaining DDB book is $2,160,000 over 2 years = $1,080,000 SL, which is greater than 40% × $2,160,000 = $864,000, so a switch would book $1,080,000 in Year 4 and $1,080,000 in Year 5. If the case does not mention a switch, either policy is defensible if you apply it consistently and do not go below salvage.

Sum-of-years-digits and tax MACRS tables are the same idea: more depreciation early, less later. Total depreciation over the life still equals cost minus salvage. Timing is what changes taxes and net book.

Book D&A Versus Tax D&A and Deferred Tax

Book depreciation follows the accounting policy (Northstar: SL, 5 years, full-year). Tax depreciation follows the tax authority (often accelerated). They do not have to match. The income statement still shows book D&A. Cash tax is computed on taxable income, which uses tax D&A.

Year 1 on the new asset only: book D&A $2,000,000, tax D&A $4,000,000 (DDB). Extra tax deduction = $2,000,000. At a 25% tax rate, cash tax is $500,000 lower than book tax expense. That $500,000 is a deferred tax liability (DTL) — tax you postponed, not tax you cancelled. Over the life of the asset the extra early deductions reverse (Years 4–5 book D&A exceeds remaining tax D&A), and the DTL unwinds.

Conceptual links, not a full tax provision:

• Book tax expense ≈ 25% × book EBT (ignore permanent differences unless given).
• Cash tax ≈ 25% × (book EBT − extra tax D&A + other timing items).
• Deferred tax expense = book tax − cash tax. Year 1: $500,000, credited to DTL on the balance sheet.

CFI's core UFCF formula does not add ΔDTL: UFCF = EBIT × (1 − t) + D&A − Capex − ΔNWC, with book D&A and a marginal tax on EBIT. Some interview variants add ΔDTL (or subtract a ΔDTA) to move from book NOPAT toward cash tax. On the FMVA final, unless the case hands you a DTL roll-forward, stay with the official formula and keep the DTL discussion as why the depreciation method still matters for cash even though D&A itself is non-cash.

Disposals

A disposal removes net book value, not original cost, from the net roll-forward. Proceeds are a CFI inflow. The difference is a gain or loss on the income statement.

Example (not in Year 1, so Northstar's $42,000,000 close is undisturbed): sell a machine with cost $2,000,000, accumulated D&A $1,500,000, NBV $500,000, proceeds $400,000. Loss = $100,000. Net PP&E falls $500,000. CFI shows +$400,000 proceeds (and still −capex for new assets). The $100,000 loss is already in net income, so the cash flow statement adds it back (or starts from the $400,000 proceeds in CFI and never puts the NBV through CFO twice). Exam trap: subtracting original cost $2,000,000 from net PP&E. That double-removes $1,500,000 already in accumulated D&A and will not balance.

Depreciation Is Non-Cash — and the Schedule Still Has to Be Right

D&A does not use cash in the period you record it. Cash was used when you spent capex. The income statement still needs the expense so that EBIT, tax, and net income are accrual-correct. The cash flow statement adds D&A back because the indirect method started at net income. The balance sheet needs the contra-asset so net PP&E is not stuck at historical cost. Three-statement integrity is the same D&A number in all three places, sourced from this schedule, not from a free percent of sales.

That non-cash expense does change cash through taxes. Higher book D&A lowers book EBT and book tax expense. Higher tax D&A lowers cash tax even if book D&A is unchanged. Skip the schedule, and both the tax line and net PP&E are fiction, which means UFCF is fiction.

Worked UFCF Using All Three Operational Schedules

Year 1 EBIT after the $10 million project = $5,761,000. Tax rate 25%. NOPAT = 5,761,000 × (1 − 0.25) = $4,320,750. Book D&A = $8,000,000. Capex = $10,000,000. ΔNWC from 12.2 = +$578,783.

UFCF = $4,320,750 + $8,000,000 − $10,000,000 − $578,783 = $1,741,967

This is why Operational Modeling sits between 3-statement work and DCF in CFI's core list. Volume × price, days, and the PP&E roll-forward are not extra credit. They are the operating forecasts inside the three statements and inside unlevered free cash flow. Change volume from 5% to 6% and, if the model is built correctly, units, revenue, COGS, variable SG&A, AR, inventory, AP, ΔNWC, and UFCF all move. Capex moves only if you linked growth capex to volume; Northstar's $10 million was a discrete project, so it stays $10 million until you change that input.

Exam Traps on Capex and Depreciation

• D&A as a percent of sales. Year 1 D&A is $8,000,000 from the schedule, not 12% × $54,075,000.
• Forgetting Year 1 D&A on new capex (or taking a half-year when the case is full-year). The $10 million project is $2,000,000 of SL, not zero and not $4,000,000 unless you are on DDB for tax.
• Capex % of sales in a project year. $2,163,000 is the 4% rule; the case spent $10,000,000.
• Roll-forward with the wrong sign on D&A or disposals. End = begin + capex − disposals − D&A.
• Treating D&A as optional because it is non-cash. Skip it and you miss tax, net PP&E, the CFS add-back, and UFCF.
• Subtracting capex on the income statement. Capex is CFI, not SG&A.
• Book versus tax. Accelerated tax D&A does not change book EBIT; it changes cash tax and DTL. UFCF on the CFI formula still uses book D&A and tax on EBIT unless the case adds a DTL schedule.