Question

Your Company is considering a new project that will require $1,040,000 of new equipment at the start of the project. The equipment will have a depreciable life of 8 years and will be depreciated to a book value of $388,000 using straight-line depreciation. The cost of capital is 14%, and the firm's tax rate is 40%. Estimate the present value of the tax benefits from depreciation (closest to).

$81,500

$48,900

$32,600

$151,227

Answer 1

Depreciation per year = (Cost of equipment - Salvage value) / Life of equipment

or, Depreciation per year = ($1,040,000 - $388,000) / 8 = $81,500

Depreciation tax shield per year = $81,500 x 40% = $32,600

These will equal in all in the year. To find the present value of equal annual cash inflows, we have to multiply the equal annual inflows with the present value interest factor annuity of $1 (PVIFA) which can be computed as follows -

$PVIFA = \frac{1-[\frac{1}{(1+r)^{n}}]}{r}$

where, r is the rate of interest and n being the no. of years

In our case, r = 14% or 0.14, n = 8

$PVIFA = \frac{1-[\frac{1}{(1+0.14)^{8}}]}{0.14}=4.63886389392$

Present value of tax benefits of depreciation = Depreciation tax shield x PVIFA (14%, 8) = $32,600 x 4.63886389392 = $151,226.962941 or $151,227