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11-CS-1 Engineering Economics · May 2014

Question 3 of 5: Independent Projects — Rate of Return

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

Notes on this paper

National Exams — May 2014 — 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 follow; standard compound-interest factors are used and minor rounding is immaterial.

Question 3: Independent Projects — Rate of Return (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.

(a) Rate-of-Return (Independent Projects)

Net annual = revenue − expenses: A = $54,000; B = $94,000. For independent projects, accept each whose IRR exceeds the MARR. Solving $Cost = A(P/A,i,10) + S(P/F,i,10)$:

$$\text{IRR}_A \approx 13.5\%\ (>10\%)\qquad \text{IRR}_B \approx 9.7\%\ (<10\%)$$

So invest in Project A only (A clears the 10% hurdle; B does not).

(b) MARR Making the Projects Equivalent

This is the incremental IRR of (B − A): extra cost $320,000, extra net $40,000/yr, extra salvage $45,000. Solving $320{,}000 = 40{,}000(P/A,i,10) + 45{,}000(P/F,i,10)$ gives $i \approx \boxed{6.0\%}$. Below ~6% Project B is preferred; above it, Project A.

(c) Future-Worth Analysis

Taking each project forward to the end of year 10 at the 10% MARR, with $(F/P,10\%,10)=2.59374$ and $(F/A,10\%,10)=15.93742$:

$$FW_A = -300{,}000(2.59374) + 54{,}000(15.93742) + 45{,}000 = \boxed{+\$127{,}500}$$
$$FW_B = -620{,}000(2.59374) + 94{,}000(15.93742) + 90{,}000 = \boxed{-\$20{,}000}$$

Equivalently, $FW = PW\times(F/P,10\%,10)$ with $PW_A \approx +\$49{,}200$ and $PW_B \approx -\$7{,}700$, so Future Worth gives exactly the same accept/reject signal as Present Worth: $FW_A > 0$ (accept), $FW_B < 0$ (reject). Hence FW analysis also says invest in A only.

(d) MARR = 4%, Choose One

Now the projects are mutually exclusive. Since 4% is below the ~6% break-even MARR from part (b), the increment to the larger Project B is justified—so choose Project B. (No new calculation needed: below the crossover rate, B dominates.)