Depreciation Models

Business Calculus · Axiom Academy

Comparing linear and exponential depreciation methods A company purchases a delivery truck for 45,000 . They need to model its depreciation for tax and replacement planning purposes. The truck has an expected useful life of 10 years and a salvage value of 5,000 . Alternatively, it loses approximately 20% of its value each year through exponential depreciation. Compare both depreciation methods and determine when the truck's value drops below 10,000 under each model. Linear (straight-line) depreciation assumes the asset loses the same dollar amount each year. V_0 = \ 45,000 (initial value) D = annual depreciation amount Using the linear model, what is the truck's value after 3 years? Exponential depreciation assumes the asset loses a fixed percentage of its current value each year. With 20% annual depreciation, the truck retains 80% of its value each year: Or using continuous depreciation: We can find k from the annual rate: e^ -k = 0.80 , so k = - (0.80) 0.223 Using the discrete exponential model V(t) = 45000(0.80)ᵗ, what is the value after 3 years? Exponential depreciation drops faster in early years, then slows down. This often matches reality better—a new car loses more value in year 1 than in year 10. Take the natural log of both sides: How much sooner does the truck value drop below 10,000 under exponential depreciation? Use linear depreciation for accounting and tax records Use exponential depreciation to estimate actual resale value

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