Bonds, returns and business math Updated November 2026

Depreciation methods

Depreciation spreads an asset's cost minus salvage value over its useful life. Straight-line charges (cost - salvage) / life each year. Double-declining balance charges 2 / life times the opening book value, front-loading the expense. Sum-of-the-years-digits charges (cost - salvage) x remaining life / sum of the years. All methods total the same amount.

Syntax

SL = (cost - salvage) / life   DDB_t = book value x 2 / life   SYD_t = (cost - salvage) x (life - t + 1) / (life x (life + 1) / 2)

Part	What it is
`cost`	Purchase cost including installation
`salvage`	Expected value at the end of the useful life
`life`	Useful life in years
`book value`	Cost minus accumulated depreciation

Examples

Straight-line: cost 10,000, salvage 1,000, life 5
(10,000 - 1,000) / 5

Result: 1,800 per year; book value after year 2 = 6,400

Excel: =SLN(10000, 1000, 5)

Double-declining: cost 10,000, life 5, rate 40%
Year 1: 10,000 x 0.4 = 4,000 (book 6,000)
Year 2: 6,000 x 0.4 = 2,400 (book 3,600)
Year 3: 3,600 x 0.4 = 1,440 (book 2,160)

Result: Expense falls each year; stop when book value reaches salvage

Excel: =DDB(10000, 1000, 5, 2) returns 2,400 for year 2

Sum-of-the-years-digits: cost 10,000, salvage 1,000, life 5
Sum = 1+2+3+4+5 = 15
Year 1: 9,000 x 5/15; Year 2: 9,000 x 4/15; Year 3: 9,000 x 3/15

Result: 3,000; 2,400; 1,800; then 1,200 and 600

Excel: =SYD(10000, 1000, 5, 1) returns 3,000

Common mistakes

Subtracting salvage value before applying the declining-balance rate; DDB uses full book value and instead stops when book value hits salvage (year 5 above is capped at 296, not 518.40).
Letting declining-balance depreciation take the book value below salvage, or never reaching it; many firms switch to straight-line in later years.
Depreciating land, which is not depreciated, or depreciating a full year for an asset bought mid-year when a partial-year convention applies.

Practice Depreciation methods

These drills check your answer on live data, free, no account needed.

Straight-line book valueEquipment costs $15,000, has a salvage value of $3,000 and a useful life of 3 years. Using straight-line depreciation, what is its book value at the end of year 2?
Double-declining depreciationA delivery van costs $13,000, with a salvage value of $1,000 and a 10-year life. Using double-declining balance (no switch to straight line), what is the depreciation expense in year 3?
Sum-of-the-years'-digitsA machine costs $13,000, has a salvage value of $2,000 and a 3-year life. Using sum-of-the-years'-digits, what is the depreciation expense in year 3?

Questions

Which depreciation method should I use?

Straight-line for simplicity and most financial reporting; an accelerated method (DDB or SYD) when the asset loses value or productivity faster early on, or when tax rules allow it to defer tax.

What is the Excel formula for depreciation?

=SLN(cost, salvage, life) for straight-line, =DDB(cost, salvage, life, period) for double-declining balance, =SYD(cost, salvage, life, period) for sum-of-the-years-digits, and =DB for fixed-rate declining balance.

Break-even pointBreak-even units = fixed costs / (price - variable cost per unit); break-even revenue = fixed costs / contribution margin ratio. Examples, margin of safety.
NPV (net present value)Net present value is the sum of discounted cash flows minus the initial investment. Examples at 10% and 8%, the accept rule, Excel NPV and the sign mistake.
After-tax cost of debtThe after-tax cost of debt is the interest rate times one minus the tax rate, because interest is deductible. Examples, finding the pre-tax rate, mistakes.
Margin vs markupMargin is profit divided by price; markup is profit divided by cost. How to convert between them, set a price from a target margin, examples and the error.