Engineering Economics
This domain tests whether you can compare alternatives on a consistent after-tax basis, apply the Hong Kong tax rules correctly, and explain why the ranking changes when capital is limited.
Time value and comparison
- NPV = Σ CF_t/(1 + i)^t, discounted at the MARR or hurdle rate. A positive NPV at the MARR means accept.
- IRR is the rate at which NPV = 0; it can be multiple-valued with unconventional cash flows.
- For mutually exclusive options, use incremental analysis or incremental IRR, not the highest IRR. A small project with a 40% IRR may add less value than a large one at 18%.
- Payback is a liquidity screen only; discounted payback adds discipline but still ignores cash flows after the cut-off.
- Annual worth converts everything to an equivalent annual amount, which is convenient for unequal lives; repeatability assumptions must be stated.
Tax, depreciation and cash flow
- Accounting depreciation is not a cash flow. For decisions, use after-tax cash flow and the tax rules that apply.
- Hong Kong profits tax for corporations is 16.5%, with a two-tiered rate of 8.25% on the first HK$2 million of assessable profits for one nominated entity in a group.
- Capital expenditure on machinery and plant qualifies for initial and annual depreciation allowances under the Inland Revenue Ordinance, so the tax shield timing differs from book depreciation. Never mix book depreciation into a tax cash flow.
- Inflation: discount nominal cash flows at a nominal rate, or real flows at a real rate. Never mix.
Worked example
An automated line costs HK$1,000,000 and returns HK$300,000 net per year for five years; MARR is 10%. The five-year annuity factor is 3.7908, so PV = HK$1,137,240 and NPV = +HK$137,240 - accept. At 15% the factor is 3.3522, giving PV = HK$1,005,660, so IRR is just above 15%. Simple payback is 3.33 years. All three measures point the same way here, but the NPV is the decision, because it is the only one stated in today's money.
Traps that cost marks
- Using a monthly nominal rate and an annual cash flow without converting: effective annual = (1 + 0.12/12)^12 − 1 = 12.68%.
- Including sunk costs or allocated overhead that does not change between alternatives.
- Ranking mutually exclusive projects by IRR alone.
- Forgetting that the two-tiered profits tax rate applies to one entity only in a group.