Unit 5: Investment Decisions - Subjective Questions

Capital budgeting is the process of evaluating and selecting long-term investments that are expected to generate benefits over several years.

Its principal characteristics are:

• Long-term commitment: Funds are invested in assets such as plants, machinery, technology, or new projects for an extended period.
• Large initial investment: Capital projects generally require substantial expenditure at the beginning.
• Future benefits: Returns are expected through future cash inflows, cost savings, or strategic advantages.
• Risk and uncertainty: Future costs, cash flows, useful life, and market conditions must be estimated.
• Irreversibility: Capital expenditure decisions are difficult or costly to reverse.
• Strategic importance: These decisions influence the firm's growth, profitability, competitiveness, and value.

Thus, capital budgeting helps a firm allocate scarce financial resources to investments that contribute to its long-term objectives.

Capital budgeting is important because it ensures that long-term funds are invested efficiently. Its rationale includes:

• Wealth maximization: Appropriate projects increase future cash flows and shareholder value.
• Efficient resource allocation: Since capital is limited, firms must select projects offering the best returns.
• Long-term impact: Investment decisions determine the future production capacity, operating costs, and growth of a business.
• Risk management: Systematic evaluation identifies the risks associated with uncertain future cash flows.
• Cost control: Capital budgeting prevents excessive or unproductive expenditure.
• Strategic planning: Decisions regarding expansion, replacement, modernization, and diversification support corporate strategy.
• Performance evaluation: Forecast cash flows and returns provide benchmarks against which actual performance can be assessed.

A poor capital budgeting decision can lock a firm into an unprofitable investment, whereas a sound decision can create a sustainable competitive advantage.

The capital budgeting process normally includes the following stages:

1. Identification of investment opportunities: Ideas may involve expansion, replacement, modernization, diversification, or regulatory requirements.
2. Preliminary screening: Proposals inconsistent with the firm's objectives, budget, or policies are eliminated.
3. Estimation of cash flows: The initial outlay, operating cash inflows and outflows, working capital, taxes, and terminal cash flows are forecast.
4. Evaluation of proposals: Appropriate techniques such as payback period, ARR, PI, or NPV are applied.
5. Risk analysis: The firm examines uncertainty through sensitivity analysis, scenario analysis, or other risk-assessment methods.
6. Selection and authorization: Projects meeting the decision criteria are ranked and approved, subject to the availability of funds.
7. Implementation: Funds are allocated, assets are acquired, and the project is executed.
8. Monitoring and post-completion audit: Actual costs and benefits are compared with forecasts to identify deviations and improve future decisions.

• Independent projects: Acceptance of one project does not affect the acceptance of another. Every project satisfying the required investment criterion may be accepted if funds are available.

• Mutually exclusive projects: Acceptance of one project requires rejection of another because the projects perform the same function or use the same resources. The firm must choose the project that creates the greatest value.

• Projects under capital rationing: The firm has a fixed investment budget and cannot accept every desirable project. Projects or project combinations must therefore be ranked to obtain the highest possible total return from the available funds.

For example, two machines designed for the same production process are mutually exclusive, while investments in an independent warehouse and a profitable delivery system may both be accepted. If the firm cannot finance both because of a budget limit, the decision becomes a capital-rationing problem.

Non-discounting techniques do not explicitly recognize the time value of money. The principal examples are the payback period and accounting rate of return.

Discounting techniques convert future cash flows into present values by applying a required rate of return. Examples include net present value, internal rate of return, and profitability index.

Key differences are:

• Non-discounting methods treat money received at different dates as equivalent, whereas discounting methods recognize that an earlier cash flow is more valuable.
• Payback focuses on liquidity and recovery of investment, while ARR focuses on accounting profit.
• Discounting techniques normally use cash flows and consider the cost of capital.
• Non-discounting techniques are simple but may produce incomplete decisions.
• Discounting techniques are theoretically superior for shareholder wealth maximization.

Although sometimes discussed alongside simple appraisal methods, the profitability index is a discounted cash-flow technique, not a non-discounting technique.

The payback period is the time required for a project's cumulative cash inflows to recover its initial investment.

When annual cash inflows are equal, it is calculated as:

Substituting the given values:

Therefore, the project will recover its initial investment in 4 years. If the firm's maximum acceptable payback period is at least four years, the project may be accepted under this criterion.

For unequal cash inflows, cumulative cash inflows must be calculated:

• End of Year 1: $100,000
• End of Year 2: $100,000 + $120,000 = $220,000
• End of Year 3: $220,000 + $140,000 = $360,000
• Amount remaining after Year 3: $400,000 - $360,000 = $40,000

The Year 4 cash inflow is $160,000. Therefore, the fraction of Year 4 required is:

Hence:

The investment is recovered in 3.25 years, or approximately 3 years and 3 months.

Under the payback period method, management establishes a maximum acceptable payback period, also called the cut-off period.

• For an independent project, accept the project if its payback period is equal to or shorter than the cut-off period. Reject it if recovery takes longer.
• For mutually exclusive projects, the project with the shortest payback period is generally preferred, provided it satisfies the cut-off requirement.

For example, if the cut-off period is four years, a project with a three-year payback is acceptable, while one with a five-year payback is rejected.

The rule emphasizes rapid recovery and liquidity. However, selecting the shortest-payback project may not maximize wealth because the method ignores cash flows received after payback and, in its basic form, does not discount future cash flows.

Advantages:

• It is simple to understand and calculate.
• It emphasizes liquidity by showing how quickly invested funds are recovered.
• It is useful when future conditions are highly uncertain.
• It favors projects with early cash inflows and may therefore provide a rough indication of risk.
• It is helpful for firms facing cash shortages or rapid technological obsolescence.

Limitations:

• The basic method ignores the time value of money.
• It ignores cash flows occurring after the payback date.
• The selection of the cut-off period is often arbitrary.
• It measures capital recovery rather than profitability.
• It may reject long-term projects that create substantial value after the payback period.
• It does not directly indicate the contribution of a project to shareholder wealth.

Consequently, payback is best used as a supplementary liquidity and risk measure rather than as the sole investment criterion.

The accounting rate of return measures the average annual accounting profit from an investment as a percentage of the investment amount.

Its common formula is:

If straight-line depreciation is used and working capital is ignored, average investment may be calculated as:

Average annual accounting profit is:

Some firms use the initial investment rather than average investment in the denominator. Therefore, the convention must be stated when comparing projects. A project is accepted if its ARR equals or exceeds management's minimum target accounting return.

First, calculate the average investment:

The ARR is then:

Therefore, the machine has an accounting rate of return of approximately . It would be accepted if the firm's required ARR is or lower.

Advantages:

• ARR is simple to calculate and communicate.
• It uses familiar accounting information from financial statements.
• It considers accounting profits over the project's entire life.
• It can be compared with management's target return or reported return on investment.
• It facilitates performance evaluation using accounting measures.

Limitations:

• ARR ignores the time value of money.
• It is based on accounting profit rather than cash flows.
• Accounting policies for depreciation and profit recognition can affect the result.
• Different definitions of investment, such as initial or average investment, may produce different rates.
• It does not directly measure the increase in shareholder wealth.
• It may fail to distinguish correctly between projects with different timing patterns or useful lives.

ARR is therefore useful as a supplementary accounting-performance measure but is weaker than discounted cash-flow methods for investment selection.

The payback period and ARR are both non-discounting techniques, but they emphasize different objectives.

• Measure used: Payback uses project cash flows, whereas ARR uses accounting profit.
• Objective: Payback measures the speed of capital recovery; ARR measures accounting profitability.
• Decision rule: Payback accepts projects within a specified cut-off period; ARR accepts projects meeting a target rate.
• Project life: Payback ignores cash flows after capital recovery, while ARR considers profits over the full project life.
• Time value: Neither method recognizes the time value of money in its basic form.
• Risk and liquidity: Payback provides a rough indication of liquidity and exposure to long-term uncertainty. ARR does not directly measure liquidity.
• Accounting influence: ARR is affected by depreciation and accounting policies, while payback is not.

Neither technique alone provides a complete wealth-maximizing decision, so firms commonly use them with discounted cash-flow methods.

The profitability index is the ratio of the present value of a project's future cash inflows to its initial cash outlay.

Since:

PI can also be written as:

The decision rules are:

• Accept when , because .
• Be indifferent when , because .
• Reject when , because .

PI is a discounted cash-flow technique and measures value created per unit of initial investment.

The profitability index is calculated as:

Substituting the values:

The project's net present value is:

Because , the project generates in present-value inflows for every invested. It also has a positive NPV of . Therefore, the project should be accepted, assuming it is independent and no overriding constraints apply.

PI and NPV may rank mutually exclusive projects differently because they measure different aspects of investment performance:

• PI is a relative measure: It reports present-value benefits per unit of investment.
• NPV is an absolute measure: It reports the total monetary value added by a project.

A small project may have a high PI but create less total value, while a large project may have a lower PI but a higher NPV. For example, a $100 investment producing a present value of $140 has a PI of and NPV of . A $1,000 investment producing a present value of $1,300$ has a PI of $1.30$ but NPV of $300$.

If the projects are mutually exclusive and capital is not constrained, the project with the higher NPV should generally be selected because it adds more total value. PI is especially helpful when capital is rationed, but it should not automatically replace NPV for mutually exclusive alternatives.

Calculate the PI of each project:

The ranking is therefore A, B, C.

Selecting A and B uses the entire budget:

Their combined NPV is:

Thus, based on PI ranking and the stated budget, the firm should select Projects A and B. This recommendation assumes that the projects are divisible only as specified, independent, and have comparable risk. For indivisible projects, all feasible combinations should ultimately be checked to confirm which one produces the highest total NPV.

Payback period:

• Measures the time needed to recover the initial investment.
• Accepts a project if payback is within the firm's cut-off period.
• Uses cash flows but normally ignores discounting and post-payback benefits.
• Is most useful for assessing liquidity and rapid capital recovery.

Accounting rate of return:

• Measures average accounting profit as a percentage of investment.
• Accepts a project if ARR meets or exceeds the target rate.
• Uses accounting profits and ignores the time value of money.
• Is useful for comparing a project with accounting-performance targets.

Profitability index:

• Measures the present value of inflows per unit of initial outlay.
• Accepts a project when .
• Uses discounted cash flows and incorporates the required return.
• Is useful for ranking projects when capital is limited.

PI is theoretically stronger because it recognizes timing and the cost of capital. Payback and ARR can still provide supplementary information about liquidity and reported profitability.

1. Payback period

Cumulative inflows after two years are:

The amount remaining is $400,000 - $290,000 = . The fraction of Year 3 required is:

Therefore:

2. Accounting rate of return

Annual depreciation is:

Annual accounting profits are $40,000, $50,000, $30,000, and $10,000. Average annual profit is:

Average investment is $400,000/2 = $200,000. Thus:

3. Profitability index

The project recovers its cost in approximately 2.85 years, earns an ARR of , and has a PI of approximately . Since PI exceeds 1, it is acceptable under the discounted criterion.

Financial techniques provide essential numerical evidence, but capital budgeting decisions should also consider qualitative factors, including:

• Alignment with corporate strategy
• Product quality and customer satisfaction
• Employee safety and morale
• Environmental and social effects
• Legal and regulatory compliance
• Technological change and obsolescence
• Competitive position and brand reputation
• Dependence on suppliers or key personnel

A post-completion audit compares the project's actual investment, cash flows, timing, and performance with the original forecasts.

Its benefits include:

• Identifying forecasting errors and operational problems
• Holding managers accountable for proposals and implementation
• Improving future cash-flow estimates
• Detecting cost overruns or delays
• Determining whether corrective action, expansion, or abandonment is appropriate

However, the audit should distinguish genuine managerial failures from unexpected external events. Capital budgeting is most effective when quantitative appraisal, strategic judgment, and subsequent performance review are combined.