5.6 Capital Investment Appraisal (Payback, ARR, NPV)

1. Real-World Case Dilemma

Case Context: The board of directors of a Singapore shipping and logistics company must choose between two mutually exclusive capital investment projects costing S$1,000,000 upfront:

• Project Alpha (Short-Term Truck Fleet): Generates fast cash inflows, paying back the full S$1,000,000 in 2 years, but produces zero cash after Year 3. Total 5-year accounting profit is S$200,000.
• Project Beta (Automated Robotic Warehouse): Takes 4.5 years to pay back, but produces massive, compounding cash inflows in Years 5 through 10, delivering a Total Net Accounting Profit of $1,800,000 and a Net Present Value (NPV) of +$450,000.

Payback says: “Choose Project Alpha (it’s faster and less risky)!”
NPV says: “Choose Project Beta (it creates over double the shareholder wealth)!”
How does management reconcile these conflicting quantitative signals to make the optimal long-term strategic decision?

2. Key Terms & Jargon Decoder

3. Concept & Visual Anchor

Overview of the 3 Investment Appraisal Techniques

1. Payback Period (Liquidity & Risk Screen)

• Core Focus: “How fast do I get my initial capital cash back?”
• Decision Rule: Shorter is better (e.g. 2.5 years beats 4.0 years).
• Critical Flaw: Ignores all cash flows earned after the payback point.

2. Accounting Rate of Return [ARR] (Accounting Profitability %)

• Core Focus: “What is the average annual accounting profit return percentage?”
• Decision Rule: Higher is better (must exceed company’s target hurdle rate e.g. 15%).
• Critical Flaw: Uses accounting profit (distorted by depreciation) and ignores cash timing.

3. Net Present Value [NPV] (Discounted Cash Flow / True Wealth)

• Core Focus: “What are all future cash inflows worth in TODAY’s dollars?”
• Decision Rule: Accept if \text{NPV} > 0; choose the highest positive NPV.
• Theoretical Superiority: Accounts for the time value of money, cash timing, and risk.

Master Quantitative Calculation Formula Bank

\text{Payback Period (Constant Inflows)} = \frac{\text{Initial Capital Cost}}{\text{Annual Net Cash Inflow}}

\begin{gathered} \text{Payback (Uneven Inflows)} = \text{Years before full recovery} \\ + \left( \frac{\text{Unrecovered Cost at start of year}}{\text{Net Cash Inflow during that year}} \times 12\text{ months} \right) \end{gathered}

\text{Average Annual Profit} = \frac{\text{Total Cumulative Net Cash Inflows over Life} - \text{Initial Capital Cost}}{\text{Project Lifespan in Years}}

\text{Accounting Rate of Return (ARR \%)} = \frac{\text{Average Annual Net Profit}}{\text{Initial Capital Cost}} \times 100

\text{Present Value of Year } t = \text{Net Cash Flow in Year } t \times \text{Discount Factor at rate } r\%

\text{Net Present Value (NPV)} = \sum \text{Present Values of all Future Cash Inflows} - \text{Initial Capital Outlay}

4. Check Your Understanding

5. Exam Error Surgery: Fix the Weak Answer

Paper 1 Section B Prompt (10 marks): Evaluate why Net Present Value (NPV) is considered theoretically superior to the Payback Period method for capital investment appraisal.

6. Strategic Evaluation Matrix

Non-Financial / Qualitative Factors in Capital Decisions

A positive NPV is not enough on its own. Executive boards must evaluate 5 qualitative pillars:

7. “I Do / We Do / You Do” Exam Scaffolds

“I Do” Annotated Model Answer (12 marks)

Question: Project X has an NPV of +S$80,000 and a payback of 4.5 years. Project Y has an NPV of +S$60,000 and a payback of 2.0 years. Recommend which project the business should choose. Justify your decision.

[AO1/AO2 Framing the Decision Conflict]

Management faces a classic financial trade-off: Project X maximizes long-term shareholder wealth (higher NPV by +S\$20,000), but Project Y provides rapid cash liquidity recovery (payback in 2.0 years vs 4.5 years).

[AO3 Analysis: The Financial Trade-Off]

From a pure wealth-maximization perspective (§5.1), Project X is superior. Its Net Present Value (+S$80,000) discounts all future cash flows at the firm’s cost of capital, proving that it adds S$20,000 more net present enterprise value to shareholders than Project Y over its full operating lifespan.

However, Project X carries substantial liquidity and duration risk. Tying up capital for 4.5 years before recovering the initial outlay exposes the firm to severe vulnerability if market demand shifts, interest rates spike, or the technology becomes obsolete in Year 4. If the business is currently highly geared (§5.2) or facing working capital shortages (§5.4), waiting 4.5 years for payback could trigger a fatal cash flow crisis. In contrast, Project Y’s rapid 2-year payback replenishes liquid cash reserves quickly, allowing the firm to repay bank debt or reinvest in secondary projects.

[AO4 Evaluative Recommendation]

I recommend that the decision depends strictly on the company’s current financial liquidity position:

1. If the business possesses strong cash reserves, low gearing (<0.5), and secure long-term bank lines, it should choose Project X to maximize long-term shareholder wealth.
2. If the business is capital-constrained, highly geared, or operating in a fast-disrupting tech market, it should choose Project Y, prioritizing short-term liquidity security and lower risk over the marginal S$20,000 NPV difference.

“We Do” Guided Practice Scaffold

Question: Explain how an increase in market interest rates impacts the Net Present Value (NPV) calculation of a long-term capital investment project (6 marks).

Complete the analytical sentences using the provided sentence frames:

1. [Higher Discount Rate] When central bank interest rates rise, the firm’s cost of capital increases, which forces management to use a [ higher / lower ] discount rate in the NPV model \dots (Hint: explain why investors demand higher returns when baseline interest rates rise).
2. [Compression of Present Value] A higher discount rate applies a steeper discount penalty to future cash inflows (especially in Years 4–10), which causes the total Present Value of inflows to fall, meaning that the project’s net NPV will \dots (Hint: explain why marginal projects may turn from positive NPV to negative NPV, leading to project cancellation).

“You Do” Independent Exam Practice

8. Self-Diagnosis & Retrieval Matrix