A factory owner installs a new machine costing 60,000 . Its...

A factory owner installs a new machine costing $\$ 60,000 .$ Its expected lifetime is five years, and at the end of that time the machine has no salvage value. (a) Find a formula for the value of the machine after $t$ years, where $0 \leq t \leq 5$ (b) Complete the following depreciation schedule. $$\begin{array}{cccc} \begin{array}{c} \text { End of } \\ \text { year } \end{array} & \begin{array}{c} \text { Yearly } \\ \text { depreciation } \end{array} & \begin{array}{c} \text { Accumulated } \\ \text { depreciation } \end{array} & \begin{array}{c} \text { Value } \\ V \end{array} \\ \hline 0 & 0 & 0 & 60,000 \\ 1 & & \\ 2 & & \\ 3 & & \\ 4 & & \\ 5 & & 60,000 & 0 \\ \hline \end{array}$$

A factory owner installs a new machine costing $\$ 60,000 .$ Its expected lifetime is five years, and at the end of that time the machine has no salvage value.
(a) Find a formula for the value of the machine after $t$ years, where $0 \leq t \leq 5$
(b) Complete the following depreciation schedule.
$$\begin{array}{cccc}
\begin{array}{c}
\text { End of } \\
\text { year }
\end{array} & \begin{array}{c}
\text { Yearly } \\
\text { depreciation }
\end{array} & \begin{array}{c}
\text { Accumulated } \\
\text { depreciation }
\end{array} & \begin{array}{c}
\text { Value } \\
V
\end{array} \\
\hline 0 & 0 & 0 & 60,000 \\
1 & & \\
2 & & \\
3 & & \\
4 & & \\
5 & & 60,000 & 0 \\
\hline
\end{array}$$

Key Concepts

Depreciation

Depreciation is an accounting method used to allocate the cost of a tangible asset over its useful life. It reflects how the asset loses value over time due to factors such as wear and tear, obsolescence, or usage. This process is essential for accurately representing the asset’s value on the balance sheet and matching expenses with revenue generated by the asset.

Straight-Line Depreciation

Straight-line depreciation is a method where the asset’s cost, less any salvage value, is evenly spread over its useful life. This results in the same amount of depreciation expense each period. It is one of the simplest and most commonly used methods of depreciation because it reflects a constant rate of value reduction over time.

Depreciation Schedule

A depreciation schedule is a table that details the reduction in an asset’s book value over time by listing periodic depreciation expenses, accumulated depreciation, and the remaining asset value at the end of each period. This schedule is a useful tool for tracking the depreciation process, planning for asset replacement, and ensuring accurate financial reporting.

Salvage Value

Salvage value, also known as residual value, is the estimated amount that an asset is expected to be worth at the end of its useful life. In depreciation calculations, it is subtracted from the asset’s initial cost to determine the total amount that will be depreciated over the asset’s lifetime. A zero salvage value indicates that the asset is expected to have no remaining worth at the end of its useful life.

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