Investment Appraisal and Risk
AdvancedCapital projects are large and long-lived, appraised by payback period, accounting rate of return and net present value: payback measures recovery speed, ARR the average accounting return, NPV the time value of money; decisions must also weigh risk and return plus non-financial factors.
- Capital investments are large, long-lived and hard to reverse — appraise systematically before deciding
- Payback = years to recover the cost; simple, but it ignores time value and post-payback flows
- ARR = average annual profit ÷ average investment, computed from accounting profit rather than cash flows
文體小知識：商業知識說明文——講解回收期、會計報酬率與淨現值三種資本投資評估方法的計算與優劣，並討論風險與非財務因素。
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1Capital investment means committing to long-term assets — plant, machinery or a new branch. Such decisions involve large sums over long periods, are hard to reverse once made, and shape the firm for years. Firms therefore appraise the financial viability of competing projects systematically, then combine risk and non-financial factors before the final call.
2The payback period method computes how many years of cumulative net cash inflows are needed to recover the investment. It is simple and liquidity-minded — the shorter the payback, the safer. But it ignores all cash flows after payback and the time value of money, so a project with slow early recovery but rich later returns may be wrongly rejected.
3The accounting rate of return divides average annual profit by average investment; being tied to accounting profit, it is easy to compare with a target return — but it uses profit rather than cash flows and ignores time value. The net present value method discounts each year's net cash inflows at a discount rate, subtracts the investment cost, and accepts a project when NPV is positive — the higher the NPV, the better.
4NPV rests on the time value of money: a dollar today is worth more than a dollar in a year, because today's money can be invested at once. The discount rate generally starts from the cost of capital, reflecting risk and inflation. For example, at 10% a year, $110 receivable in one year has a present value of about $100, since $100 invested for a year grows to exactly $110 with interest.
5No appraisal method is foolproof. Cash inflows are estimates — an over-optimistic sales forecast inflates returns; the discount rate is hard to pin down; and appraisals should not ignore non-financial factors such as environmental impact, staff safety and corporate image. The risk-return relationship matters too: projects promising higher returns usually carry higher risk, and management must choose within the firm's capacity to bear it.
1Summary 重點摘要
Capital projects are large and long-lived, appraised by payback period, accounting rate of return and net present value: payback measures recovery speed, ARR the average accounting return, NPV the time value of money; decisions must also weigh risk and return plus non-financial factors.
2Vocabulary cards Vocabulary
The decision to acquire long-term assets such as plant and machinery — large, long-lived and far-reaching.
The years of cumulative net cash inflows needed to recover the investment; the shorter, the lower the liquidity risk.
Average annual profit divided by average investment, expressed as a percentage.
The present value of future net cash inflows minus the investment cost; a positive figure marks a project worth considering.
A sum today is worth more than the same sum later, because it can be invested at once to earn returns.
The process of converting a future amount into present value at a discount rate.
The value today of an amount receivable in the future.
The coefficient derived from the discount rate; multiply a future amount by it to obtain present value.
The discount rate at which NPV equals zero; useful for comparing the returns of projects.
Higher expected returns usually come with higher risk; decisions must balance the two.
3Step by step Steps
- Step 1: The nature of capital investment decisionsCapital investments are large, long-lived and hard to reverse; a wrong call burdens the firm for years, so systematic appraisal is essential. For example, a bakery weighing a $200,000 automated line must forecast years of cash inflows, compare machine options and plans, then add risk and staffing effects — rather than deciding on instinct or a salesperson's pitch. Appraisal methods turn intuition into argument.
- Step 2: The payback period and its computationPayback = the number of years for cumulative net cash inflows to just recover the cost. For example, equipment costing $200,000 yields net inflows of $80,000, $60,000, $50,000 and $40,000 over four years: after two years $140,000 has accumulated, leaving $60,000; the third year brings $50,000, so payback = 2 + $60,000 ÷ $50,000 = 3.2 years. The usual rule: accept if payback is shorter than the target period; among mutually exclusive options, take the shortest.
- Step 3: Strengths and weaknesses of paybackPayback is simple, easily understood and liquidity-minded — especially useful to cash-strapped firms. But it ignores every cash flow after payback and the time value of money. For example, project A pays back in two years and earns nothing after; project B takes four years but then pours in cash yearly — payback alone would wrongly pick A. Use payback alongside other methods rather than on its own.
- Step 4: The accounting rate of return and its computationARR = average annual profit ÷ average investment × 100%, where average investment is often (initial cost + residual value) ÷ 2. For example, equipment costing $100,000 yields total net inflows of $180,000 over four years; straight-line depreciation to zero is $25,000 a year. Average annual inflow $45,000 less depreciation gives average profit $20,000; average investment $50,000; ARR = $20,000 ÷ $50,000 × 100% = 40% — compare with the target return to decide.
- Step 5: Time value of money and discountingMoney has time value: a dollar today beats a dollar next year, since today's money can earn returns at once, and future receipts carry inflation and uncertainty. Discounting converts future amounts into present value: PV = future amount × discount factor. For example, at 10%, $110 due in one year has PV = $110 × 0.909 = $100; due in two years, only about $90.9. In examinations the discount-factor table lists the coefficients — simply look them up.
- Step 6: Net present value and its computationNPV = the sum of the present values of future net cash inflows − investment cost. A positive NPV means the project's return beats the discount rate and it is worth considering. For example, a project costing $100,000 returns $60,000 in each of two years at a 10% discount rate, with factors 0.909 and 0.826: PV total = $60,000 × (0.909 + 0.826) = $104,190; NPV = $104,190 − $100,000 = +$4,190 — acceptable. Among mutually exclusive projects, pick the highest NPV.
- Step 7: Comparing the three methodsPayback stresses liquidity and speed of calculation but ignores time value and post-payback flows; ARR rests on profit and is easy to compare with a target return, yet also ignores time value; NPV covers the whole life of cash flows and the time value of money — theoretically the soundest — though the discount rate is hard to set and estimates-sensitive. The internal rate of return — the discount rate that zeroes NPV — helps compare return levels. For example, when asked which method to adopt, argue for NPV and explain the others' limits.
- Step 8: Risk and non-financial factorsEvery appraisal rests on estimates: small errors in sales forecasts, costs or the discount rate can flip the conclusion. Mind the risk-return relationship — higher returns usually mean higher risk, so gauge the firm's capacity to absorb setbacks, and watch inflation eroding the real value of future cash. Non-financial factors count too: environmental impact, staff safety, corporate image and regulation all shape the final decision. For example, a financially attractive project that badly pollutes a neighbourhood may invite fines and boycotts — a long-run loss.
5Worked example Example
Hong Wah Manufacturing Company Limited has $300,000 and can invest in only one of two projects. Expected net cash inflows over four years: Project A, $100,000 each year; Project B, $160,000 in year 1, $100,000 in year 2, $60,000 in year 3 and $40,000 in year 4. The discount rate is 10%, with discount factors 0.909, 0.826, 0.751 and 0.683 for years 1 to 4. Appraise both projects by the payback period and the net present value methods, and recommend which to choose.
- Payback (A): $100,000 a year, so $300,000 ÷ $100,000 = 3 years.
- Payback (B): $260,000 after two years, leaving $40,000; year 3 brings $60,000, so payback = 2 + $40,000 ÷ $60,000 = 2.67 years — shorter than A.
- NPV (A): $100,000 × (0.909 + 0.826 + 0.751 + 0.683) = $100,000 × 3.169 = $316,900; NPV = $316,900 − $300,000 = +$16,900.
- NPV (B): $160,000 × 0.909 + $100,000 × 0.826 + $60,000 × 0.751 + $40,000 × 0.683 = $145,440 + $82,600 + $45,060 + $27,320 = $300,420; NPV = $300,420 − $300,000 = +$420.
- Compare: B pays back sooner, but A's NPV is far higher; NPV considers the whole life of cash flows and the time value of money, and among mutually exclusive projects the higher NPV wins — so recommend Project A.
- Answer: Payback: A 3 years; B about 2.67 years — B recovers its cost sooner. NPV: A = $316,900 − $300,000 = +$16,900; B = $300,420 − $300,000 = +$420. Both NPVs are positive, so either alone would merit acceptance, but the firm can choose only one. The NPV method accounts for both the time value of money and cash flows after payback, making it theoretically sounder; A's NPV is clearly higher, so Project A should be chosen. If liquidity were tight and quick recovery paramount, B's shorter payback would still carry weight; and the final decision should also weigh each project's risks and non-financial factors.
6Common mistakes Mistakes
7Quick check Quick check
Q1Name two main limitations of the payback period method.
Q2A project costs $120,000 and yields $40,000 of net cash inflow each year. What is its payback period?
Q3What does a positive net present value indicate?
Q4Why is a dollar today worth more than a dollar in a year?
Q5Besides financial measures, what non-financial factors should investment decisions consider?
8Recap Recap
- Capital investments are large, long-lived and hard to reverse — appraise systematically before deciding
- Payback = years to recover the cost; simple, but it ignores time value and post-payback flows
- ARR = average annual profit ÷ average investment, computed from accounting profit rather than cash flows
- NPV = present value of net inflows − investment cost; positive is acceptable, and the highest NPV wins among rivals
- Weigh risk and return, inflation, and non-financial factors — environment, safety, image — in the final decision