Question 2 of 7: Depreciation

Question 2: Depreciation (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

What depreciation is, in a tax sense. A capital asset — reactors, columns, buildings — is bought once but delivers service over many years, so its cost cannot be expensed in the year of purchase. Depreciation is the systematic, book-keeping allocation of that capital cost over the asset's useful life. Crucially for the corporation, depreciation is a non-cash, tax-deductible expense: it is subtracted from revenue when computing taxable income, so it lowers the income-tax liability without any cash actually leaving the company that year. The cash saved equals the depreciation amount multiplied by the corporate tax rate, and this "depreciation tax shield" is why depreciation matters so directly to on-going finances. In Canada, tax depreciation is not the straight-line figure carried on the financial statements but the Capital Cost Allowance (CCA) prescribed by the Canada Revenue Agency: assets are grouped into classes, each with a declining-balance rate, and only the class rate may be claimed for tax.

Current value versus salvage value. The current value (book value; in the CCA system the undepreciated capital cost, UCC) is the original installed cost minus the depreciation accumulated to date — what the asset is "worth" on the books at a given moment. The salvage value is the estimated proceeds recoverable when the asset is finally retired and disposed of at the end of its service — its market or scrap value at disposal, independent of the book calculation. The two need not agree: an asset can be fully written down (low book value) yet still fetch a meaningful salvage price, or vice-versa; any gain or loss on disposal relative to book value has its own tax treatment.

Recovery period. The recovery period is the length of time (number of years) over which the capital cost is written off for tax — the depreciable service life assigned to the asset's class. Under a declining-balance system such as CCA, the recovery period is expressed through the class rate rather than a fixed number of years, but it plays the same role: it sets how quickly the capital cost, and therefore the tax shield, is recovered.

Illustration — a Canadian CCA schedule (Check assumptions below). Consider installed process equipment of capital cost $C=\$500{,}000$ in a class with a declining-balance CCA rate of $30\%$, subject to the half-year rule in the year of acquisition, at a corporate tax rate $t=25\%$.

1. Year 1 — half-year rule. Only half the normal allowance may be claimed in the acquisition year: $$CCA_1 = C\,r\,(0.5) = (\$500{,}000)(0.30)(0.5) = \boxed{\$75{,}000}$$ leaving an undepreciated capital cost $UCC_1 = \$500{,}000-\$75{,}000 = \$425{,}000$.
2. Year 2 — full declining balance. The full rate now applies to the remaining UCC: $$CCA_2 = UCC_1\,r = (\$425{,}000)(0.30) = \$127{,}500,\qquad UCC_2 = \$297{,}500.$$
3. Year 3. Continuing the declining balance, $$CCA_3 = UCC_2\,r = (\$297{,}500)(0.30) = \$89{,}250,\qquad UCC_3 = \$208{,}250.$$
4. Tax shield. The cash saved by the Year-2 allowance is $CCA_2\,t = (\$127{,}500)(0.25) = \$31{,}875$ — real money kept in the business purely because depreciation reduced taxable income.