Equipment, depreciation and payback
capital cost formulaswhen does it pay for itselfasset write-down
Straight-line and declining-balance depreciation plus simple payback — how a purchase looks on paper and in cash.
Straight-Line Depreciation
Equal annual write-down of an asset: cost minus salvage value, spread evenly over its useful life.
Declining-Balance Depreciation (Book Value)
Book value of an asset after k years when a fixed fraction d of the remaining value is written off every year.
Simple Payback Period
Years for an upgrade to repay its own capital cost out of the money it saves each year, ignoring interest and inflation.
Future Value of an Annuity (Regular Deposits)
What an equal deposit made at the end of every period grows to after n periods at rate i — the replacement-fund and savings-plan formula.
How they fit together
A capital purchase gets measured two different ways and they rarely agree. Depreciation is an accounting story about how value is written down over a useful life; payback is a cash story about when the thing has returned what it cost. A boiler upgrade can pay back in four years while still carrying book value for ten.
Straight-line spreads the loss evenly and suits assets that wear steadily. Declining balance front-loads it and better matches things that lose most of their value early, vehicles above all. Tax authorities usually dictate which is allowed, so the choice is rarely free.
Simple payback is the one every efficiency proposal leads with, and it deserves a warning label: it ignores the time value of money entirely, and it says nothing about what happens after the payback date. A two-year payback on equipment that dies in year three is a worse deal than a four-year payback on equipment that runs for twenty.