## **Learning Outcomes**

After reading this article, you will be able to explain the process of analysing risk in project selection, particularly where assets require periodic replacement. You will apply discounted cash flow techniques to compare mutually exclusive projects with unequal lives using the equivalent annual cost and equivalent annual benefit methods, and identify key factors in optimal asset replacement decisions for the ACCA FM exam.

## **ACCA Financial Management (FM) Syllabus**

For ACCA Financial Management (FM), you are required to understand risk analysis as it applies to project selection, specifically:

- Evaluating asset replacement decisions using equivalent annual cost and equivalent annual benefit methods
- Appraising projects with different lifespans or replacement cycles
- Identifying and analysing risk and uncertainty in investment appraisal
- Applying discounted cash flow (DCF) techniques to asset replacement and project selection
- Recognising limitations and assumptions involved in replacement analysis

## **Test Your Knowledge**

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision._

1. What is the purpose of calculating the equivalent annual cost (EAC) when comparing two assets with different useful lives?
2. Which factor is usually ignored when using EAC for asset replacement: (a) Operating costs, (b) Tax effects, (c) Asset resale value, (d) Expected lifespan?
3. True or false? The project with the lowest EAC is always the best choice for asset replacement decisions, assuming all else equal.
4. Briefly describe the main risk or limitation of using the equivalent annual cost method in practice.

## **Introduction**

Replacement decisions are a common feature in capital investment, especially where assets such as machinery or vehicles require periodic renewal. Unlike standard investment appraisal, replacement analysis often involves projects with different useful lives, which calls for a consistent way to compare mutually exclusive options. This is where the **Equivalent Annual Cost (EAC)** and **Equivalent Annual Benefit (EAB)** come in—tools that help you select the most cost-effective or profitable option over the long term, even when project durations differ.

Making the right replacement decision ensures assets are kept efficient and total costs are minimised or benefits maximised. Understanding these methods is a key skill assessed in the ACCA Financial Management (FM) exam.

> **Key Term: replacement decision**
> The process by which a business evaluates when and how often an asset should be renewed, taking into account costs, benefits, and asset lifespans.

## **Replacement Decisions: The Challenge of Unequal Lives**

Asset replacement choices typically require managing two major challenges:

- Comparing assets or strategies with different lifetimes (e.g., replace a machine every 3 years or every 5 years)
- Assessing all costs and benefits on a consistent, like-for-like basis

Simply comparing total costs or NPVs over one cycle is not valid if the periods differ. You need to express costs (or benefits) as an annual equivalent so each option is compared over a common timeframe.

### The Approach

**Step 1:** Calculate the net present value (NPV) of cash flows for one full cycle of each option.

**Step 2:** Convert the NPV of each cycle into an equivalent annual value—either cost (EAC) for outflows or benefit (EAB) for inflows—by dividing by the relevant annuity factor.

**Step 3:** Choose the option with the lowest EAC (if minimising cost) or highest EAB (if maximising benefit).

> **Key Term: equivalent annual cost (EAC)**
> The constant annual amount, over the duration of the project, equivalent in present value terms to all the relevant costs (usually outflows) of an option or replacement strategy.
>
> **Key Term: equivalent annual benefit (EAB)**
> The constant annual amount, over the relevant period, equivalent in present value terms to all the benefits (usually inflows) of a project or strategy.

## **Worked Example 1.1**

**An asset can be replaced every 3 or every 4 years. Each time it is replaced, it costs \$16,000. Annual running costs are \$4,000 for the first year, rising by \$800 in each subsequent year. At replacement, it can be sold for \$3,000 (after 3 years) or \$1,000 (after 4 years). The required rate of return is 8%. What is the optimal replacement interval?**

> **Answer:**
>
> - For each option, discount all outflows and the final inflow (disposal) to present value.
> - For 3-year replacement:
>   - PV of costs: \$16,000 (year 0) + \$4,000 (year 1) × 0.926 + \$4,800 (year 2) × 0.857 + \$5,600 (year 3) × 0.794 − \$3,000 (year 3) × 0.794
>   - Add and calculate total NPV of costs.
>   - Divide by 3-year annuity factor (from tables).
> - Repeat for 4-year replacement.
> - The policy with the lowest EAC is the optimal cycle.

### **Exam Warning**

> When using EAC or EAB, only compare options if the replacement cycles are expected to continue for the foreseeable future (i.e., perpetual renewal). Do not compare total NPVs for different replacement periods without annualising.

## **Interpreting Results and Practical Notes**

- EAC is ideal when you aim to minimise total long-term costs (e.g., for leased vehicles, machinery).
- EAB is appropriate when project cash inflows differ in size or timing (e.g., comparing alternative investments with unequal lives).
- Maintenance, running costs, replacement cost, disposal values, and timing must be included in cash flows for EAC analysis.
- Only relevant, incremental cash flows are considered.

> **Key Term: annuity factor**
> The present value of \$1 per year for n years at a specified discount rate, used to annualise a lump sum or NPV.

## **Key Factors in Replacement Analysis**

When deciding on optimal replacement policy, consider:

- Capital cost and any future cost increases (e.g., due to inflation)
- Asset resale or scrap value at the end of each cycle
- Operating and maintenance costs (usually rising as assets age)
- The effect of tax and inflation, if significant
- The discount rate consistent with the company’s cost of capital
- The risk of technological change making newer assets more efficient or cheaper over time

Replacement analysis works best when:

- You expect the replacement to be repeated indefinitely
- The performance and costs for each cycle recur in future replacements

### **Worked Example 1.2**

**A company can invest in one of two machines: Machine X (cost \$18,000, lasts 3 years, annual running cost \$5,000, scrap \$1,000) or Machine Y (cost \$25,000, lasts 5 years, annual running cost \$3,800, scrap \$500). Discount rate is 10%. Which is better?**

> **Answer:**
>
> - Step 1: For each machine, sum PV of total costs over its lifespan (including initial cost, running costs each year, minus the scrap value discounted to present).
> - Step 2: For Machine X, divide NPV by 3-year annuity factor; for Machine Y, divide by 5-year annuity factor.
> - Compare EACs. Choose the machine with the lower EAC.

## **Limitations and Risks of EAC/EAB Methods**

While EAC/EAB allow for consistent comparison, be aware of their practical limitations:

- They assume replacement cycles will repeat indefinitely—if this isn’t true (e.g., project size, technology, or usage patterns could change), results may be misleading.
- Non-financial factors, like safety, changes in technology, or regulatory issues, may outweigh cost differences.
- Uncertainty in forecasting running costs, disposal values, or asset lives increases risk of inaccurate estimates.
- Inflation or tax should be included in cash flows if material.

### **Revision Tip**

> Practice setting out clear present value tables and using the correct annuity factors for EAC/EAB comparisons. Clearly identify the time horizon for each option.

## **Summary**

Replacement analysis using EAC and EAB helps businesses compare options with different useful lives by converting the total NPV of each option into an equivalent annual cost or benefit. This allows a valid, like-for-like decision about which option minimises long-run costs or maximises returns. Remember to account for all relevant costs and base your calculation on perpetually recurring cycles unless directed otherwise.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Understanding asset replacement decisions and challenges of unequal asset lives
- Calculating equivalent annual cost (EAC) and equivalent annual benefit (EAB)
- Applying discounted cash flow techniques for mutually exclusive projects with unequal lives
- Identifying key financial and practical factors influencing optimal replacement policy
- Recognising limitations and risks in using EAC/EAB for project selection

## **Key Terms and Concepts**

- replacement decision
- equivalent annual cost (EAC)
- equivalent annual benefit (EAB)
- annuity factor

Risk analysis and project selection - Replacement decisions and EAA