MACRS depreciation: how does it work?

Answering the second part of your question first: If you’re asked to calculate depreciation at the end of the first year with modified accelerated cost recovery system (MACRS) depreciation and the half-year convention, there is a formula to be followed:

$Depreciation in 1st year=Cost\times \frac{1}{Depreciation Period}\times A\times Depreciation Convention$

$Depreciation in Later Years=(Residual Value)\times \frac{1}{Depreciation Period}\times A$

A and Depreciation Periods are standard assumed values:

A is 100% or 150% or 200%

Useful Life = 3, 5, 7, 10, 15, 20, 25 … depending on asset class

So depreciation in first year, assuming 200% declining balance method, using half-year convention:

$$\begin{gathered} =\cos t\times \frac{1}{3}\times 200\%\times \frac{1}{2} \\ =33\% \end{gathered}$$

In other words, if you’re looking up from a table (or given a value) that says this assumes a half-year convention, the given value should already incorporate the half year calculation, i.e. the number is already divided by 2, so don’t divide it by 2 again.

—

The first part of your question, I’m not sure if there’s enough info included.

Assuming your example assumes a double-declining balance method (A = 200%) and half-year convention, there’s depreciation in year 4 (the remaining half year) so book value is not zero if your project ends at end of year 3.

Terminal Net Operating Cash Flow (TNOCF) = Salvage Value + Net Working Capital _Inv – Tax (Salvage Value – End Book Value)

So TNOCF is calculable at the end of year 3, I’m not following why TNOCF ‘would not be needed’ if the project is only 3 years.

Thoughts?