# Which One of These Statements Related to Discounted Payback is Correct? A Guide for Investors

Discounted payback is a capital budgeting technique that helps investors evaluate the profitability and feasibility of a project or investment. It measures how long it takes for the initial cost of the project to be recovered by the discounted value of future cash flows. In other words, it tells you when you will break even on your investment, taking into account the time value of money.

But how do you calculate discounted payback? And what are some of the advantages and disadvantages of using this method? In this article, we will answer these questions and more, and help you understand which one of these statements related to discounted payback is correct.

## How to Calculate Discounted Payback

To calculate discounted payback, you need to follow two steps:

1. Discount the future cash flows of the project or investment to their present value, using an appropriate discount rate. The discount rate reflects the opportunity cost of capital, or the rate of return that you could earn by investing in a different project with similar risk and duration.
2. Subtract the discounted cash flows from the initial cost of the project or investment, until the cumulative value reaches zero. The number of periods (usually years) that it takes to reach zero is the discounted payback period.

For example, suppose you invest \$10,000 in a project that generates the following cash flows over five years:

Assume that the discount rate is 10%. The discounted cash flows and the discounted payback period are shown below:

The discounted payback period is between four and five years. To find the exact value, we can use interpolation:

Discounted payback period = 4 + (651 / (651 + 1,242)) = 4.34 years

This means that it will take about four and a third years for the project to break even.

Discounted payback has some advantages and disadvantages as a capital budgeting technique. Some of the advantages are:

• It is easy to understand and calculate.
• It considers the time value of money, unlike the simple payback method.
• It favors projects that generate cash flows sooner rather than later, which reduces risk and improves liquidity.
• It can be used as a screening tool to eliminate projects that take too long to recover their initial cost.

• It does not consider the cash flows that occur after the discounted payback period, which may affect the overall profitability of the project or investment.
• It does not provide a clear criterion for accepting or rejecting a project or investment. Different projects may have different target discounted payback periods depending on their risk and duration.
• It may reject projects that have positive net present value (NPV) or internal rate of return (IRR), which are more comprehensive measures of profitability.

Now that we have learned how to calculate discounted payback and what are its pros and cons, let us look at some statements related to discounted payback and see which one is correct.

• Statement A: Discounted payback is always shorter than simple payback.
• Statement B: Discounted payback always equals simple payback when the discount rate is zero.
• Statement C: Discounted payback always equals simple payback when the cash flows are constant.
• Statement D: Discounted payback always equals simple payback when the discount rate is equal to the growth rate of cash flows.

The correct statement is B. Discounted payback always equals simple payback when the discount rate is zero. This is because when the discount rate is zero, the present value of future cash flows is equal to their nominal value, and there is no difference between discounted and simple payback.

Statement A is incorrect. Discounted payback is always longer than simple payback, unless the discount rate is zero. This is because discounting reduces the value of future cash flows, and it takes longer to recover the initial cost.

Statement C is incorrect. Discounted payback does not always equal simple payback when the cash flows are constant, unless the discount rate is zero. For example, if the initial cost is \$10,000, the cash flow is \$2,000 per year, and the discount rate is 10%, the simple payback period is five years, but the discounted payback period is 6.15 years.

Statement D is incorrect. Discounted payback does not always equal simple payback when the discount rate is equal to the growth rate of cash flows, unless both are zero. For example, if the initial cost is \$10,000, the cash flow in year one is \$2,000, and both the discount rate and the growth rate are 10%, the simple payback period is five years, but the discounted payback period is 5.65 years.

## Conclusion

Discounted payback is a useful capital budgeting technique that helps investors evaluate the profitability and feasibility of a project or investment. It measures how long it takes for the initial cost of the project to be recovered by the discounted value of future cash flows. However, it has some limitations and should not be used as the sole criterion for making investment decisions. Other metrics, such as NPV and IRR, should also be considered to get a complete picture of the project’s profitability.

We hope this article has helped you understand which one of these statements related to discounted payback is correct. If you have any questions or comments, please feel free to share them below. 