## **Learning Outcomes**

After studying this article, you will be able to explain and apply the payback and discounted payback methods for project appraisal. You will be able to calculate payback (including when cash flows are uneven), calculate discounted payback using present value techniques, compare and rank projects based on these criteria, and discuss the main advantages, disadvantages, and appropriate uses of both methods in investment appraisal for ACCA FM.

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

For ACCA Financial Management (FM), you are required to understand practical investment appraisal methods and their limitations. In particular, you should focus your revision on:

- Identifying and calculating relevant cash flows for investment projects
- Calculating payback period and evaluating its role in project selection
- Determining the discounted payback period and assessing its usefulness
- Recognising the advantages, disadvantages, and practical applications of payback and discounted payback methods
- Using payback-based criteria to rank or filter investment proposals before more comprehensive appraisal

## **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 main difference between the payback and discounted payback appraisal techniques?
2. True or false? The payback period method takes account of all cash flows over the whole life of a project.
3. If a company is choosing between two projects with similar payback periods but different total returns, what are the limitations of using payback as the sole selection criterion?
4. Why might the discounted payback period be more useful than simple payback when assessing risk?

## **Introduction**

Investment appraisal is essential for managers making decisions about projects that require substantial up-front expenditure. Payback and discounted payback periods are widely used initial screening tools that focus on the speed at which invested funds are recovered. Both methods are particularly relevant where liquidity or risk is a concern, but have important limitations for longer-term value creation.

> **Key Term: payback period**
> The time required for the cumulative cash inflows from a project to equal the original investment outlay. It measures how quickly an investment can be recovered.
>
> **Key Term: discounted payback period**
> The time needed for the sum of discounted (present value) cash inflows to equal the initial investment, reflecting the time value of money.

## **PAYBACK PERIOD**

The payback period answers the question: “How long until the initial investment is recovered?” It is widely used in practice as a simple test of liquidity and early risk reduction.

- If a project has **constant annual cash flows**, payback is calculated as:

  Payback period = Initial investment / Annual cash inflow

- Where **cash flows are uneven**, cumulative cash flows are tracked year by year until the investment is repaid. If repayment occurs part-way through a year, calculate the exact payback by finding the fraction of the year needed.

### **Worked Example 1.1**

A company invests \$80,000 in new equipment. Annual net cash inflows are expected to be \$20,000 for 5 years. What is the payback period?

> **Answer:**
> Payback period = \$80,000 / \$20,000 = 4 years

### **Worked Example 1.2**

An initial investment of \$50,000 produces these projected net cash inflows:
Year 1: \$10,000  
Year 2: \$14,000  
Year 3: \$16,000  
Year 4: \$15,000

What is the payback period (in years and months)?

> **Answer:**
> Cumulative at year 3: \$10,000 + \$14,000 + \$16,000 = \$40,000  
> Remaining to recover: \$50,000 – \$40,000 = \$10,000  
> Year 4 inflow: \$15,000  
> Fraction of year: \$10,000 / \$15,000 = 0.666...  
> Payback = 3 years + (0.666 × 12) = 3 years and 8 months

### **Exam Warning**

> When calculating payback as “years and months,” multiply the decimal by 12 months and always round up to the next whole month.

## **DISCOUNTED PAYBACK PERIOD**

Payback ignores the time value of money. Discounted payback overcomes this by discounting each cash flow at the required rate of return (cost of capital), then calculating the cumulative discounted cash flows to see how long it takes to recover the investment in present value terms.

### Steps for discounted payback

1. Discount each net cash inflow using the formula:  
   Present value = Cash flow × Discount factor for the year
2. Accumulate discounted inflows each year.
3. Identify when the discounted total equals the initial investment.

### **Worked Example 1.3**

A project requires \$25,000. Cash inflows are expected as follows:
Year 1: \$7,000  
Year 2: \$8,000  
Year 3: \$9,000  
Year 4: \$8,000  
Assume a discount rate of 10%. What is the discounted payback period?

> **Answer:**
> Discount factors @10%: Year 1 = 0.909, Year 2 = 0.826, Year 3 = 0.751, Year 4 = 0.683  
> Discounted inflows:  
> Year 1: \$7,000 × 0.909 = \$6,363  
> Year 2: \$8,000 × 0.826 = \$6,608  
> Year 3: \$9,000 × 0.751 = \$6,759  
> Year 4: \$8,000 × 0.683 = \$5,464  
> Cumulative:  
> End Year 1: \$6,363  
> End Year 2: \$12,971  
> End Year 3: \$19,730  
> Year 4 needed: \$25,000 – \$19,730 = \$5,270  
> Fraction: \$5,270 / \$5,464 = 0.965  
> So, discounted payback = 3 years + (0.965 × 12 months) = 3 years and 12 months (i.e., 4 years, as payback is reached close to the end of year 4)

### **Revision Tip**

> If discounted payback never occurs—because the cumulative discounted inflows never equal the outlay—the project does not “pay back” in present value terms.

## **USING PAYBACK AND DISCOUNTED PAYBACK FOR PROJECT RANKING**

Firms often set a **maximum acceptable payback period** (e.g., 3 years). Projects that pay back within this period are considered; those that don’t are rejected. When comparing alternatives:

- Prefer projects with the shortest payback (or discounted payback) within the company’s cut-off.

However, these techniques ignore profitability and cash flows after the cut-off. Projects should only be accepted or preferred over others based on payback if the company’s primary concern is speed of recovery, not total return.

### **Worked Example 1.4**

Three projects each cost \$40,000 and have the following annual net cash inflows:

|     | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
| --- | ------ | ------ | ------ | ------ | ------ |
| A   | 20,000 | 12,000 | 8,000  | 5,000  | 0      |
| B   | 10,000 | 15,000 | 10,000 | 8,000  | 7,000  |
| C   | 14,000 | 11,000 | 9,000  | 7,000  | 4,000  |

If the maximum acceptable payback is 3 years, which projects are eligible and which pays back fastest?

> **Answer:**  
> Calculate cumulative cash flows:
>
> **A:** 20,000 → 32,000 → 40,000 (Payback at year 3)  
> **B:** 10,000 → 25,000 → 35,000 (end yr 3), needs \$5,000 more in year 4; fraction = \$5,000 / \$8,000 = 0.625; Payback = 3 years + (0.625 × 12) ≈ 3 years 8 months  
> **C:** 14,000 → 25,000 → 34,000 → 41,000 (Payback in year 4), not eligible  
> Projects A and B pay back in 3 years or just after, so A is fastest.

## **ADVANTAGES AND DISADVANTAGES OF PAYBACK AND DISCOUNTED PAYBACK**

### **Payback:**

**Advantages:**

- Simple and easy to calculate and explain.
- Emphasizes rapid capital recovery and liquidity.
- Useful when technology changes quickly or for initial screening of projects.
- Sometimes aligns with risk minimization (shorter payback means less time exposed to uncertainty).

**Disadvantages:**

- Ignores time value of money (unless using discounted payback).
- Ignores cash flows after the payback period—profitability is overlooked.
- No clear investment signal—cut-off is arbitrary.
- No direct link with shareholder wealth maximisation.

### **Discounted Payback:**

**Advantages:**

- Considers the time value of money—gives a better picture of true payback.
- Still simple to explain; focuses on early and more certain cash flows.
- Useful for risk-averse or liquidity-focused decisions where future cash flows are less predictable.

**Disadvantages:**

- Still ignores cash flows after the discounted payback period.
- Setting the maximum allowable discounted payback period remains subjective.
- More complicated than simple payback; requires discount rate and present value calculations.

## **Summary**

Payback and discounted payback are straightforward, liquidity-focused appraisal techniques. Discounted payback improves on simple payback by considering the time value of money, but both methods ignore total project profitability and overlook cash flows after the payback point. They are best used as screening tools to eliminate unsuitable projects before conducting full investment analysis using methods such as NPV.

## **Key Point Checklist**

_This article has covered the following key knowledge points:_

- Calculate payback period for both even and uneven cash flows
- Calculate discounted payback period using present value techniques
- Apply these methods to rank projects for initial screening
- Explain the main strengths and weaknesses of both techniques
- Recognise when payback and discounted payback are appropriate in investment appraisal

## **Key Terms and Concepts**

- payback period
- discounted payback period

Appraisal techniques and rankings - Payback and discounted payback