Like all companies, Exco has to pay taxes on its profits. However, for each additional dollar in depreciation Exco claims, Exco taxes are reduced bv t, since the depreciation expense offsets income, thus reducing profits subject to tax. Exco is required bv tax law to use declining-balance depreciation to calculate the depreciation of assets on a year-by-year basis, with a depreciation rate of d. This depreciation calculation continues forever, even if the asset is sold or scrapped.
The actual depreciation for a particular asset is best represented as straight-line over y years, with zero salvage value. If the asset costs P dollars, and interest is i, what is the present worth of all tax savings Exco will incur by purchasing the asset? (Hint: The depreciation savings in the first year is Ptd.)