Accounting (9615) | Capital investment appraisal

Welcome to Capital Investment Appraisal!

Hello future business strategists! This chapter is where management accounting gets really exciting. We are moving beyond recording past transactions and stepping into making huge, high-stakes decisions about the future.

Capital Investment Appraisal is the process businesses use to decide whether to buy an expensive, long-term asset (like a new factory, machinery, or a major IT system). These decisions involve large amounts of money and commitment for many years, so getting it right is crucial!

In these notes, we will look at the two main methods for appraising these projects: one simple approach (Payback Period) and one highly sophisticated approach (Net Present Value). Let's get started!

Section 1: The Foundation – Cash Flows and Terminology

1.1 What is Capital Investment?

A Capital Project (or investment) involves spending money now in the hope of generating significant returns (cash inflows) over many future years.

Example: Buying a new production machine that costs $500,000 but will save $100,000 in labour costs every year for the next seven years.

1.2 Cash Flow vs. Profit

This is the first and most critical rule: Investment Appraisal uses Cash Flows, NOT Accounting Profit.

Why? Accounting profit includes non-cash items, most notably Depreciation. Depreciation is an estimate of asset usage, not an actual movement of cash. Since capital appraisal is about tracking money in and money out, we ignore depreciation.

Therefore, when calculating the annual returns for appraisal, you must always use the Net Cash Flow.

Calculation and Use of Cash Flows

Cash flow includes:

• Initial Outlay: The amount paid immediately to buy and install the asset (a negative cash flow in Year 0).
• Future Annual Cash Flows (Inflows): The extra cash received or saved each year due to the project.
• Residual Value (Scrap Value): Any cash received from selling the asset at the end of its useful life (often in the final year).

1.3 Key Terminology for Appraisal

You must understand these terms before moving on:

• Payback Period: How quickly the initial investment is recovered.
• Net Present Value (NPV): The current value of all future cash flows compared to the initial investment (after adjusting for the time value of money).
• Cost of Capital (or Discount Rate): The minimum rate of return a company requires on an investment. This is often based on the interest rate the company has to pay to borrow money or the return expected by shareholders.
• Discount Factor: The multiplier used to convert a future cash amount into its present-day value.

Section 2: Payback Period (PBP)

2.1 Understanding Payback Period

The Payback Period (PBP) is the simplest appraisal method. It measures the length of time, usually expressed in years and months, required for the cumulative net cash flows from a project to equal the initial investment.

Analogy: If you pay for a new coffee machine for your shop, how long will it take for the extra profit (cash) generated by the machine to cover its original price?

2.2 Calculating the Payback Period

The calculation differs slightly depending on whether the annual cash flows are even or uneven.

Case 1: Even Annual Cash Flows

If the project generates the same cash flow every year, the calculation is straightforward:
$$ \text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Net Cash Flow}} $$

Case 2: Uneven Annual Cash Flows (More Common)

If cash flows vary (which they usually do), we calculate the Cumulative Cash Flow until the initial investment is recovered.

Step-by-Step Example:
A project costs $100,000.

1. Year 0: Initial outflow = \(\$-100,000\)
2. Year 1: Cash inflow = $\$40,000$. Cumulative cash flow = \(\$-60,000\) remaining.
3. Year 2: Cash inflow = $\$40,000$. Cumulative cash flow = \(\$-20,000\) remaining.
4. Year 3: Cash inflow = $\$50,000$. The investment is recovered during Year 3.

We know the payback is 2 years + a fraction of Year 3.

The amount needed at the start of Year 3 was $\$20,000$. The total inflow in Year 3 was $\$50,000$.

$$ \text{Fraction of Year 3} = \frac{\text{Amount needed}}{\text{Cash flow in Year 3}} = \frac{\$20,000}{\$50,000} = 0.4 \text{ years} $$ $$ \text{Payback Period} = 2 \text{ years } + (0.4 \times 12 \text{ months}) = 2 \text{ years and } 4.8 \text{ months} $$

2.3 Benefits and Limitations of Payback Period

Benefits (Why businesses use it)

• Simplicity: It is very easy to calculate and understand, even for non-accountants.
• Focus on Liquidity/Risk: It highlights projects that quickly return cash, which is important for companies that are short on funds or operating in unstable markets (high risk).

Limitations (Why it is often not the best method)

• Ignores Timing: It ignores the Time Value of Money (TVM). It treats money received in Year 1 the same as money received in Year 5.
• Ignores Total Profitability: It ignores all cash flows that occur after the payback period. A project might pay back quickly but produce very little money afterwards, while a slower project might generate huge returns later on.

Section 3: Net Present Value (NPV) – The Time Value of Money

3.1 The Time Value of Money (TVM)

Don't worry if this seems tricky at first—it's a fundamental concept in finance!

The principle of TVM: A dollar received today is worth more than a dollar received in the future.

Why? Because money today can be:

• Invested: It can earn interest (opportunity cost).
• Affected by Inflation: Its purchasing power decreases over time.

To use cash flows received in the future for today's decision, we must "discount" them back to their equivalent value today (called the Present Value).

3.2 The Discount Factor

The discount factor is based on the Cost of Capital (the required rate of return). It tells us how much a future dollar is worth now.

The formula for calculating the present value (PV) of a future cash flow (CF) is:
$$ PV = \frac{CF}{(1 + r)^n} $$

Where \(r\) is the discount rate (Cost of Capital) and \(n\) is the number of years.

In exams, you will usually be provided with a table of Discount Factors \(\left( \frac{1}{(1 + r)^n} \right)\) for different years and rates.

3.3 Understanding Net Present Value (NPV)

The Net Present Value (NPV) is the sum of all the Present Values of future cash flows, minus the initial capital cost.

$$ \text{NPV} = (\text{Sum of Present Values of Inflows}) - (\text{Initial Investment}) $$
If the NPV is positive, it means the project will generate more wealth (today's dollars) than the company requires.

3.4 Step-by-Step NPV Calculation

Let's use the $100,000 investment example, assuming a Cost of Capital of 10%.

1. Identify Cash Flows: List the inflow or outflow for each year.
2. Find Discount Factors (DF): Use the 10% DF table for each year.
3. Calculate Present Value (PV): Multiply the Cash Flow by the DF for that year.
4. Sum the PVs: Add up the PVs of all inflows.
5. Calculate NPV: Subtract the initial investment (Year 0 PV) from the total PV of inflows.

Example Table Layout

Year (n)	Cash Flow (\(CF\))	Discount Factor (\(10\%\))	Present Value (\(PV\))
0	($100,000)	1.000	($100,000)
1	$40,000	0.909	$36,360
2	$40,000	0.826	$33,040
3	$50,000	0.751	$37,550
Total			$7,550 (NPV)

In this example, the Total PV of Inflows ($36,360 + $33,040 + $37,550) is $106,950. Since the initial cost was $100,000, the NPV is $6,950.

3.5 The NPV Decision Rule

The Decision Rule based on the NPV calculation is simple:

• If NPV is Positive (NPV > 0): ACCEPT the project. It adds value to the company.
• If NPV is Negative (NPV < 0): REJECT the project. It destroys shareholder wealth (the returns are less than the Cost of Capital).
• If NPV is Zero (NPV = 0): The project yields exactly the required rate of return. Indifferent, but usually accepted if no better option exists.

3.6 Benefits and Limitations of Net Present Value

Benefits (Why NPV is superior)

• Time Value of Money: This is the biggest advantage. It reflects the economic reality that money decreases in value over time.
• Uses All Cash Flows: It considers the entire life of the project, including the final scrap value.
• Absolute Value: The resulting NPV figure represents the exact amount by which the project increases the firm's wealth in today's terms.

Limitations (The drawbacks)

• Complexity: It is harder to calculate and explain than PBP, requiring knowledge of discount factors.
• Relies on Cost of Capital: The result is highly sensitive to the chosen discount rate. If the rate is estimated incorrectly, the decision could be wrong.

Section 4: Evaluation and Project Selection

4.1 Using Appraisal Measures in Project Evaluation

When evaluating projects, accountants must use the quantitative results (PBP and NPV) to make informed judgements.

Decision Making Scenarios:

1. Accept/Reject: Does the project meet the company's minimum criteria (e.g., PBP must be less than 4 years, and NPV must be positive)?
2. Mutually Exclusive Projects: If only one project can be chosen (e.g., buying Machine A or Machine B), you usually choose the one with the highest positive NPV. If both are positive, the one with the highest NPV adds the most wealth.

4.2 Considering Financial Factors

Financial evaluation involves more than just the PBP and NPV figures themselves. It requires assessing the reliability of the underlying assumptions:

• Accuracy of Cash Flow Estimates: Are the estimated sales/savings realistic? Are the costs certain?
• Sensitivity Analysis: What happens to the NPV if the cost of capital increases or the sales estimates fall by 10%? (The risk assessment).
• Project Duration: Longer projects have higher risk as forecasts become less reliable.

4.3 The Importance of Non-Financial Factors

The quantitative measures (PBP and NPV) provide a solid financial baseline, but a good A-level answer must include a critical assessment of non-financial factors. These factors often determine the success or failure of a project, even if the NPV is positive.

Examples of non-financial factors to consider:

• Operational Fit: Will the new machinery be compatible with existing equipment or staff training?
• Safety and Environment: Does the new equipment meet safety standards? Does it reduce the company’s environmental impact (e.g., lower CO2 emissions)?
• Employee Morale/Impact: Will the project require redundancies (bad for morale)? Or will it improve working conditions (good for productivity)?
• Quality and Reputation: Does the project lead to a higher quality product or improve the company's public image?
• Market Conditions: Is the technology used in the project already becoming obsolete?

Encouragement: In exams, always remember to conclude your evaluation by bringing together both the financial (NPV/PBP) and non-financial arguments to justify your final decision!