## **Learning Outcomes**

After reading this article, you will be able to calculate and interpret both the payback and discounted payback periods for investment projects. You will identify their application, explain their limitations, and assess their implications for cash flow timing and project risk—exam skills needed for ACCA Foundations in Financial Management (FFM).

## **ACCA Foundations in Financial Management (FFM) Syllabus**

For ACCA Foundations in Financial Management (FFM), you are required to understand how to appraise capital investments using payback and discounted payback methods. This includes:

- Calculating payback and discounted payback periods from a stream of projected future cash flows
- Explaining the relevance and limitations of both methods for investment decisions
- Recognising how the time value of money affects discounted payback outcomes
- Evaluating and interpreting payback results with reference to risk and liquidity
- Comparing payback approaches to alternative investment appraisal methods

## **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 does the payback period represent in capital investment decisions?
2. How does the discounted payback period improve on the basic payback calculation?
3. True or false? A project with a shorter payback is always more profitable than one with a longer payback.
4. If a project requires an initial outlay of \$30,000 and produces cash inflows of \$10,000 per year, what is its simple payback period?
5. What is a main limitation of both payback and discounted payback as investment appraisal tools?

## **Introduction**

Business investment often involves significant up-front costs, with financial benefits realised only over future years. Assessing how quickly an initial investment is returned via project-generated cash flows is a basic but important consideration for management, especially where liquidity and risk are concerns. The payback and discounted payback methods are simple tools for evaluating project acceptability, particularly in environments where quick recovery of funds is valued.

This article explores how to calculate, interpret, and evaluate the payback and discounted payback appraisal methods for ACCA exam purposes.

> **Key Term: payback period**
> The number of years it takes for an investment to recover its initial outlay from the net cash inflows generated by the project.
>
> **Key Term: discounted payback period**
> The number of years required for an investment's initial outlay to be recovered based on discounted (present value) cash inflows, i.e., after adjusting for the time value of money.

## **PAYBACK PERIOD: CALCULATION AND INTERPRETATION**

The payback period is a simple measure showing when cumulative project cash inflows will fully offset the initial investment. Cash flows after payback are ignored.

### How to Calculate the Payback Period

- List annual net cash flows.
- Cumulatively add each year's inflow to the total outlay.
- The payback period is the time until cumulative inflows first equal or exceed the investment.

If payback is reached part-way through a year, interpolate using the following:

Payback Period = Years before full recovery  
&emsp;&emsp;&emsp;&ensp;+ (Amount needed / Full year's inflow in payback year)

### **Worked Example 1.1**

**A company invests \$50,000 in a machine. Net cash inflows are \$15,000 per year. What is the payback period?**

> **Answer:**  
> End of year 3, cumulative inflows = \$45,000.  
> End of year 4, cumulative inflows = \$60,000 (> \$50,000).  
> Shortfall at end of year 3 = \$50,000 - \$45,000 = \$5,000.  
> Fraction of fourth year's inflow needed = \$5,000 / \$15,000 = 0.33 years.
> Payback = 3 + 0.33 ≈ **3.33 years**

### Strengths

- Easy to calculate and explain
- Focuses on liquidity and risk: projects recovering cash faster are seen as less risky
- Useful where cash shortages or rapid payback are prioritised (e.g., unstable economic environments)

### Limitations

- Ignores all cash flows received after payback is reached
- Does not account for the time value of money (future cash is treated as equal to present cash)
- Not a true measure of project profitability

### **Exam Warning**

> Be careful: Payback period does not rank projects by profitability. It only reflects recovery speed, not the total or present value of benefits.

## **DISCOUNTED PAYBACK PERIOD: ADJUSTING FOR TIME VALUE**

While traditional payback counts only the time pattern of cash flows, discounted payback incorporates the time value of money—essential for proper investment appraisal.

### Calculating Discounted Payback

- Apply a discount factor to each year's net cash inflow, using an appropriate cost of capital/required rate of return.
- Sum the present values (PV) year by year to see when cumulative discounted inflows equal the initial investment.
- Interpolate, if necessary, as with traditional payback.

### **Worked Example 1.2**

**A project needs an outlay of \$24,000. Cash inflows are \$10,000 per year for three years. The firm's discount rate is 10%. Calculate the discounted payback period.
(PV factors: Year 1 = 0.909, Year 2 = 0.826, Year 3 = 0.751)**

> **Answer:**  
> Discounted inflows:  
> Year 1: \$10,000 × 0.909 = \$9,090  
> Year 2: \$10,000 × 0.826 = \$8,260 (cumulative PV: \$17,350)  
> Year 3: \$10,000 × 0.751 = \$7,510 (cumulative PV: \$24,860)  
> Cumulative PV at end of year 2 = \$17,350  
> Amount left to recover: \$24,000 - \$17,350 = \$6,650  
> Fraction of third year's PV needed: \$6,650 / \$7,510 = 0.89  
> Discounted payback = 2 + 0.89 ≈ **2.89 years**

### Strengths​

- Incorporates the time value of money—cash flows in earlier years count more than later years
- Recognises both liquidity and risk

### Limitations​

- More complex—requires present value calculations
- Still ignores any benefits received after discounted payback is achieved

### **Revision Tip**

> In the exam, always show your working: present value calculations for each inflow, cumulative sums, and the fraction of year if payback occurs between years.

## **COMPARISON: PAYBACK VS DISCOUNTED PAYBACK**

| Feature             | Payback              | Discounted Payback              |
| ------------------- | -------------------- | ------------------------------- |
| Time value of money | Not considered       | Adjusted for                    |
| Simplicity          | Easier               | More involved                   |
| Looks at all cash   | Only until payback   | Only until payback              |
| Project ranking     | By speed of recovery | By speed of discounted recovery |

## **Summary**

Payback and discounted payback provide quick answers about how soon an investment will recover its cost. Their main concern is liquidity and risk—useful where rapid cash recovery is valued. However, neither reflects total profit; both methods ignore cash flows after payback. Discounted payback improves on payback by recognising the time value of money.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Calculate payback and discounted payback periods for a given set of cash flows
- Recognise the main merits and limitations of each method
- Interpret results to assess project liquidity and exposure to cash flow risk
- Identify when and why an organisation might use payback-based appraisal
- Understand the difference between traditional and discounted payback, especially regarding the time value of money

## **Key Terms and Concepts**

- payback period
- discounted payback period

Capital investment appraisal - Payback and discounted payback