# Discounted payback method

## Definition and explanation

**Discounted payback method** of capital budgeting is a financial measure which is used to measure the profitability of a project based upon the inflows and outflows of cash for that project. Under this method, all cash flows related to the project are discounted to their present values using a certain discount rate set by the management.

The discounted payback method takes into account the time value of money and is therefore an upgraded version of the simple payback period method. Companies use this method to assess the potential benefit of undertaking a particular business project.

The discounted payback method tells companies about the time period in which the initially invested funds to start a project would be recovered by the discounted value of total cash inflow. Additionally, it indicates towards the potential profitability of a certain business venture. For example, if a project indicates that the funds or initial investment will never be recovered by the discounted value of related cash inflow, it means the project would not be profitable and the company should refrain from investing in it.

The following example illustrates how a discounted payback method differs from a traditional or simple payback method.

## Example

An opportunity arises for a company which requires an initial investment of $800,000 now. The management’s discount rate is 12%.

The amount of cash inflows expected from the new opportunity are:

- Year-1 cash Inflow: $250,000
- Year-2 cash Inflow: $400,000
- Year-3 cash Inflow: $300,000
- Year-4 cash Inflow: $450,000

**Required:** Compute the simple and discounted payback periods of the new investment opportunity. Is this investment opportunity acceptable under two methods if the maximum desired payback period of the management is 3 years?

### Solution

**1. Simple payback period**

The simple payback method dos not take into account the present value of cash flows.

Simple payback period = Years before full recovery + (Unrecovered cost at start of the year/Cash flow during the year)

= 2 + *150,000/300,000

2.5 years

*$800,000 – $650,000

We see that in year 3, the investment is not just recovered but the remaining cash inflow is surplus. The initial investment of the company would be recovered in 2.5 years. So the project is acceptable according to simple payback period method because the recovery period under this method (2.5 years) is less than the maximum desired payback period of the management (3 years).

**2. Discounted payback period**

The discounted payback method takes into account the present value of cash flows.

***Present value factor at 12%: **(1/1.12)^1 = 0.893; (1/1.12)^2 = 0.797; (1/1.12)^3 = 0.712; (1/1.12)^4 = 0.636

or

use present value of $1 table to obtain these factors.

The rest of the computations are similar to simple payback period

Discounted payback period = Years before full recovery + (Unrecovered cost at start of the year/Cash flow during the year)

3 + *44,350/286,200

3.15 years

*$800,000 – $755,650

We observe that the outcome with discounted payback method is less favorable than with the simple payback method and according to this method the initial investment would be recovered in 3.15 years.

The project is not acceptable according to discounted payback period method because the recovery period under this method (3.15 years) is more than the maximum desired payback period of the management (3 years).

## Advantages and disadvantages of discounted payback method

### Advantages/benefits:

- It takes into account the time value of money by deflating the cash flows using cost of capital of the company.
- The concept backing the method is easy to understand.

### Limitations/disadvantages:

- Both simple and discounted payback method do not take into account the full life of the project. The overall benefit and profitability of a project cannot be measured under these methods because any cash flows beyond the payback period is ignored.
- It may become a relative measure. In some situations the discounted payback period of the project may be longer than the maximum desired payback period of the management but other measures like accounting rate of return (ARR) and internal rate of return (IRR) etc. may favor the project.
- The accuracy of the output only depends upon the accuracy of the input provided, like the accuracy of figures of cash flows, the estimation of the timing of cash flows which affects their present values, and the accuracy of the discount rate to be used etc.

## 6 Comments on Discounted payback method

Very good content here. However, your computation in the example using Simple Payback period is incorrect; $800-$650=$150 (and not the $250 you have used)

please help. how can i solve this:

A municipal waste incinerator produces 20 000 tonnes of bottom ash a year, which contains ferrous metal and aluminium among the incombustible residue. Currently, this ash is disposed of in a landfill site at a cost of £110 per tonne.

Another option is to install equipment to recover the metals from the ash, which can be sold to metal reprocessors. The remaining ash will now be suitable for use as an aggregate substitute in construction projects. The construction companies are unwilling to pay for the residue, so the incinerator operator gives it away free of charge. This results in the landfill charges being avoided. The details related to this option are as follows:

Capital cost of project £8 million

Operating cost of project £300,000 per year

Equipment life 10 years

You should assume that the capital cost is paid in year 0 and processing begins in year 1.

Ferrous metal Non-ferrous metal

Percentage of ash 1% 0.5%

Separation efficiency 80% 65%

Income from sales £30 per tonne £600 per tonne

• a.Calculate the payback period for the investment.

• b.Define the term ‘internal rate of return’ and use a spreadsheet to calculate this for the project. Then investigate the rate of return as a function of landfill charges.

I love this work, thanks so much .

Hi I hope you are well.

Can you please help with the following scenario, I want to know what will be the impact on NPV and IRR:

Overspending plus construction delay i.e. overspend 20% on construction and miss the completion by 1 year.

Hi, who wrote this article. Just so I can refernce it. Thank you

Rashid Javed, December 2017.