Discounted Payback Period shows the time needed to earn enough profits to repay the original cost of the investment with taking discounting into consideration.
Why is Discounted Payback Period of a project important?
Discounted Payback Period gives the length of time required for Net Cash Flows (or Net Profits) to pay back the initial capital cost of the investment considering the time value of money as it employs the discounting concept.
It uses discounted Cash Flows. Discounted Cash Flows are present values of future Cash Flows.
Discounted Net Cash Flow = Present Value
The value of Discounted Net Cash Flow, hence Present Value, usually depends on the Discount Factor which is determined by the rate of inflation / the rate of interest and the time which is the length of investment.
How to calculate Discounted Payback Period?
STEP 1: Discount (bring to the present value) the Net Cash Flows that will occur during each year of the project. Discounted Net Cash Flow is calculated by multiplying Net Cash Flow by a Discount Factor (%). Remember that:
Net Cash Flows = Cash Inflows – Cash Outflows
STEP 2: Once you have calculated the Discounted Net Cash Flows for each period of the project, you can subtract them from Initial Cost of Investment until you arrive at zero in order to obtain Discounted Payback Period.
The Initial Cost of Investment which is the original amount invested in the project is also often referred to as the principal.
Example of calculating Discounted Payback Period
A business is thinking about purchasing a new machine at a cost of USD$5,000,000. The machine is going to be used for four years to produce products. The rate of discount to be used was set by the manager at 10% as inflation in the country was forecasted by the central bank to be around 10% in the next few years. The annual Net Cash Flows are showed below. What is the Discounted Payback Period for this investment?
In Year 1, the Net Cash Flow is USD$2,000,000.
In Year 2, the Net Cash Flow is USD$2,000,000.
In Year 3, the Net Cash Flow is USD$2,000,000.
In Year 4, the Net Cash Flow is USD$3,000,000.
| Present Value of USD$1 | |||||||||||||
| Year: | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 12% | 14% | |
| 1 | 0.990 | 0.980 | 0.971 | 0.962 | 0.952 | 0.943 | 0.935 | 0.926 | 0.917 | 0.909 | 0.893 | 0.877 | |
| 2 | 0.980 | 0.961 | 0.943 | 0.925 | 0.907 | 0.890 | 0.873 | 0.857 | 0.842 | 0.826 | 0.797 | 0.769 | |
| 3 | 0.971 | 0.942 | 0.915 | 0.889 | 0.864 | 0.840 | 0.816 | 0.794 | 0.772 | 0.751 | 0.712 | 0.675 | |
| 4 | 0.961 | 0.924 | 0.888 | 0.855 | 0.823 | 0.792 | 0.763 | 0.735 | 0.708 | 0.683 | 0.636 | 0.592 | |
| 5 | 0.951 | 0.906 | 0.863 | 0.822 | 0.784 | 0.747 | 0.713 | 0.681 | 0.650 | 0.621 | 0.567 | 0.519 | |
| 6 | 0.942 | 0.888 | 0.837 | 0.790 | 0.746 | 0.705 | 0.666 | 0.630 | 0.596 | 0.564 | 0.507 | 0.456 | |
| 7 | 0.933 | 0.871 | 0.813 | 0.760 | 0.711 | 0.665 | 0.623 | 0.583 | 0.547 | 0.513 | 0.452 | 0.400 | |
| 8 | 0.923 | 0.853 | 0.789 | 0.731 | 0.677 | 0.627 | 0.582 | 0.540 | 0.502 | 0.467 | 0.404 | 0.351 | |
| 9 | 0.914 | 0.837 | 0.766 | 0.703 | 0.645 | 0.592 | 0.544 | 0.500 | 0.460 | 0.424 | 0.361 | 0.308 | |
| 10 | 0.905 | 0.820 | 0.744 | 0.676 | 0.614 | 0.558 | 0.508 | 0.463 | 0.422 | 0.386 | 0.322 | 0.270 | |
| 11 | 0.896 | 0.804 | 0.722 | 0.650 | 0.585 | 0.527 | 0.475 | 0.429 | 0.388 | 0.350 | 0.287 | 0.237 | |
| 12 | 0.887 | 0.788 | 0.701 | 0.625 | 0.557 | 0.497 | 0.444 | 0.397 | 0.356 | 0.319 | 0.257 | 0.208 | |
| 13 | 0.879 | 0.773 | 0.681 | 0.601 | 0.530 | 0.469 | 0.415 | 0.368 | 0.326 | 0.290 | 0.229 | 0.182 | |
| 14 | 0.870 | 0.758 | 0.661 | 0.577 | 0.505 | 0.442 | 0.388 | 0.340 | 0.299 | 0.263 | 0.205 | 0.160 | |
| 15 | 0.861 | 0.743 | 0.642 | 0.555 | 0.481 | 0.417 | 0.362 | 0.315 | 0.275 | 0.239 | 0.183 | 0.140 | |
| 16 | 0.853 | 0.728 | 0.623 | 0.534 | 0.458 | 0.394 | 0.339 | 0.292 | 0.252 | 0.218 | 0.163 | 0.123 | |
| 17 | 0.844 | 0.714 | 0.605 | 0.513 | 0.436 | 0.371 | 0.317 | 0.270 | 0.231 | 0.198 | 0.146 | 0.108 | |
| 18 | 0.836 | 0.700 | 0.587 | 0.494 | 0.416 | 0.350 | 0.296 | 0.250 | 0.212 | 0.180 | 0.130 | 0.095 | |
| 19 | 0.828 | 0.686 | 0.570 | 0.475 | 0.396 | 0.331 | 0.277 | 0.232 | 0.194 | 0.164 | 0.116 | 0.083 | |
| 20 | 0.820 | 0.673 | 0.554 | 0.456 | 0.377 | 0.312 | 0.258 | 0.215 | 0.178 | 0.149 | 0.104 | 0.073 |
In Year 0, the Net Cash Flow is -USD$5,000,000, so the cumulative Discounted Net Cash Flow is -USD$5,000,000
In Year 1, the Discounted Net Cash Flow is USD$1,820,000, so the cumulative Discounted Net Cash Flow is -USD$3,180,000.
In Year 2, the Discounted Net Cash Flow is USD$1,660,000, so the cumulative Discounted Net Cash Flow is -USD$1,520,000.
In Year 3, the Discounted Net Cash Flow is USD$1,500,000, so the cumulative Discounted Net Cash Flow is -USD$20,000.
In Year 4, the Discounted Net Cash Flow is USD$2,040,000, so the cumulative Discounted Net Cash Flow is USD$2,020,000.
The running total of Net Cash Flow becomes less and less negative over time as further Discounted Net Cash Flows are received by the business.
The cumulative Discounted Net Cash Flow becomes positive in Year 4. This means that the investment has been paid back in full before the beginning of Year 4 which is in Year 3. The Discounted Payback Period would be identified as being three years plus a few days. It is because at the end of Year 3 there is still only USD$20,000 needed to pay back the remaining amount of the original investment.
Let’s figure out when exactly in Year 3 the project had been paid back. In order to find out the exact length of time needed in the latest year when the project pays back its original investment, use the following formula:
| Additional Discounted Net Cash Flow Needed | |||
| ━━━━━━━━━━━━━━━━━━━━━━━━━ | x | 365 days | |
| Discounted Net Cash Flow in the Latest Year |
A total of USD$2,040,000 is expected to be received in Year 3. So:
| USD$20,000 | |||
| ━━━━━━━━━━━ | x | 365 days = 3.57 days | |
| USD$2,040,000 |
The Discounted Payback Period for this investment is 3 years and 6 days.
How to calculate the Discount Factor manually?
If you want to manually calculate the specific Discount Factor, you should follow the steps:
STEP 1: Determine the interest rate, e.g. 11%.
STEP 2: Work out the cumulative interest rate, e.g. 11% for 3 years. It equals to (1.11)^3 which is 1.367631.
STEP 3: Place this value as the denominator, with 1 being the numerator. It equals to 1/(1.11)^3 which is 0.731.
So, the Discount Factor at the rate of discount of 11% in Year 3 is 0.731.
Comment on the result of Discounted Payback Period
Discounted Payback Period is used to calculate the value of future Net Cash Flows in terms of an equivalent value today.
Payback Period (PBP) vs. Discounted Payback Period is not the same. Payback Period (PBP) shows the time it takes for the business to pay back the investment. It does not account for inflation. On another hand, Discounted Payback Period shows the time it takes for the business to pay back the investment with Net Cash flows being adjusted for inflation. In both cases, the shorter the payback period the better. However, Payback Period (PBP) will always be shorter than Discounted Payback Period as money is losing value over time.
Time value of money is considered. Discounted Payback Period does consider time value of money while regular Payback Period (PBP) does not. Managers often compare the payback periods to alternative projects in order to rank them in priority order. Money is cash when it comes to investing. We know that Net Cash Flows received in the future tend to have less real value than Net Cash Flows received today. This is due to inflation of course. Therefore, long paybacks can reduce the value of money by inflation. The slower the money is returned to the company, the lower will be its real value. The quicker the money is returned to the company, the higher will be its real value.
Money today is preferred over money in the future. The payment today is always preferred by businesses. It is because the money received today can be saved at the current rate of interest to bring interest in one year’s time or can be spent immediately on improving or expanding the business, hence the benefits of this expenditure can be obtained immediately. There is no waiting for cash required. Also, the cash today is certain while the future cash is always uncertain. Problems may occur when forecasting the future because no one can predict what external forces will affect cash flows. This can make cash flow projections inaccurate. Therefore, managers must take this into consideration.
Choosing the right project. Business managers should choose projects with shorter Discounted Payback Periods and higher rates of return adjusted for inflation. This is because the reduction in value of money due to the effects of inflation. Firms will tend to consider investment projects that have relatively short payback periods. Payback is especially important, if future flows of money are likely to lose a large proportion of their real value due to high inflation. Also, both the size of Discounted Net Cash Flows and the timing of them must be considered.
Discounted Payback Period – Evaluation
Discounted Payback Period is a very popular method of evaluating investment projects comparing project lengths and cash-flow timings while taking into consideration the time value of money. It should be considered together with Net Present Value (NPV) which considers the numerical value of investment projects while also taking into consideration the time value of money. And, with Internal Rate of Return (IRR) which considers a percentage rate of return taking into consideration the time value of money.
Advantages of Discounted Payback Period include:
- Considers time value of money. Discounted Payback Period does consider discounting. It brings to the present value the future Net Cash Flows. The timing of the Net Cash Flows, hence present value of future money, during the payback period is taken into consideration. Therefore, Discounted Payback Period is helpful in evaluating investment projects as it compares project lengths and cash-flow timings while taking the time value of money into account.
- Useful for project comparisons in real terms. By using Discounted Payback Period companies can compare different investment projects with one another by considering today’s value of their future cash returns. It will be helpful to see which project brings the quickest payback of their investments considering the present value of future money – after adjusted for inflation.
Disadvantages of Discounted Payback Period include:
- Difficult to correctly set the discount rate. The value of Discounted Net Cash Flow, hence Present Value, is mainly determined by the discount factor which is determined by the rate of inflation / the rate of interest in a country. This may cause problems to managers as it is quite difficult to predict future inflation rates and interest rates, especially for many years ahead in longer projects.
- Difficult to accurately predict future Net Cash Flows. Yearly and Monthly Net Cash Flows are very, very unlikely to be constant. Monthly revenues, costs and profits will vary as unpredictability is the nature of business environment. For example, demand is prone to seasonal fluctuations, natural disasters happen, prices of raw materials suddenly increase due to military conflicts, etc. Hence, Discounted Payback Period might take longer and all calculations might have errors as it is extremely difficult to accurately predict future Cash Flows, especially in the long-term perspective.
In summary, remember that Investment Appraisal is evaluating the profitability or desirability of an investment project. There are two ways to do it. Quantitative Investment Appraisal is using techniques to study the financial issues of investment (think quantity in terms of percentages and money). And Qualitative Appraisal which is studying non-financial issues that may impact an investment decision (think quality and impact).
