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11-CS-1 Engineering Economics · December 2013

Question 3 of 5: Testing Device — After-Tax Analysis

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — December 2013 — 11-CS-1 Engineering Economics. Open book; non-communicating calculator permitted. Any four of the five questions constitute a complete paper; all questions are of equal value. Fully worked solutions to all five questions are given below; standard compound-interest factors are used and minor rounding is immaterial.

Question 3: Testing Device — After-Tax Analysis (25 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.

After-Tax Cash Flows

Depreciation $=20000/7=\$2{,}857$/yr (years 1–7). After-tax savings $=3700(0.60)=\$2{,}220$/yr (years 1–9). Depreciation shield $=2857(0.40)=\$1{,}143$/yr (years 1–7). Salvage after tax (book value $0$, fully taxed) $=3000(0.60)=\$1{,}800$ at year 9.

Three separate time spans therefore have to be carried, and mixing them up is the commonest way to get this question wrong. The $20,000 purchase is not deductible in itself, so it sits at $t=0$ untouched by tax. The quality-improvement savings are ordinary taxable income and run for the full nine-year service life, so they are reduced by the 40% tax rate and discounted over nine years. The capital allowance runs only over the seven-year depreciation life the tax rules impose, so the shield stops at year 7 even though the device keeps saving money for two more years. Finally, because straight-line depreciation over seven years to a zero salvage writes the book value down to nothing, the entire $3,000 received on disposal is recaptured depreciation, taxed as ordinary income rather than treated as a tax-free return of capital. Each stream is then discounted at the after-tax MARR of 11%, which is the rate the question already states on an after-tax basis, so no further adjustment to the discount rate is needed.

(a) After-Tax Present Worth (i = 11%)

$$PW = -20000 + 2220(P/A,11\%,9) + 1143(P/A,11\%,7) + 1800(P/F,11\%,9)$$
$$= -20000 + 2220(5.5371) + 1143(4.7122) + 1800(0.39092)$$
$$= -20000 + 12{,}292 + 5{,}385 + 704 \approx \boxed{-\$1{,}619}$$

The after-tax PW is negative, so the investment should NOT be made at an 11% after-tax MARR.

(b) Approximate After-Tax IRR

Since $PW<0$ at 11%, the IRR is below 11%. Evaluating: $PW(8\%)\approx+\$719$ and $PW(9\%)\approx-\$110$. Interpolating:

$$\text{IRR} \approx 8\% + \frac{719}{719+110}(1\%) \approx \boxed{8.9\%}$$

(c) Decision by IRR

The after-tax IRR (~8.9%) is below the 11% MARR, so reject the investment—consistent with the negative present worth.