This payback period calculator is a tool that lets you estimate the number of years required to break even from an initial investment. You can use it when analyzing different possibilities to invest your money and combine it with other tools, such as the Net Present Value or Internal Rate of Return metrics.
In this article, we will explain the difference between the regular payback period and the discounted payback period. You will also learn the payback period formula and analyze a step-by-step example of calculations.
Imagine that you are going to invest $100,000 and purchase an apartment. You are going to rent it to tenants for $24,000 a year. How many years do you need for this investment to pay back?
The period from now to the moment when your investment will be recovered is called the payback period. Intuitively, you can say that it is equal to the total investment sum divided by the annual cash inflow:
PP = I / C
In the apartment example, you could estimate the payback period with this equation:
PP = $100,000 / $24,000 = 4.17 years
The situation gets a bit more complicated if you'd like to take the time value of money into account. After all, your $100,000 will not be worth the same after ten years; in fact, they will be worth a lot less. Every year, your money will depreciate by a certain percentage, called the discount rate.
Unlike the regular payback period, the discounted payback period metric takes this depreciation of your money into consideration. The value obtained with the use of the discounted payback period calculator will be closer to reality, although undoubtedly more pessimistic.
If the cash flows are regular (each year you gain the same amount of money), it's quite easy to compute this metric. All you have to do is apply the following formula:
DPP = - ln(1 - I * R / C) / ln(1 + R)
You can check the difference between the PP and DPP of the apartment example. Let's assume a discount rate of 5%:
DPP = - ln(1 - $100,000 * 0.05 / $24,000) / ln(1 + 0.05) = 4.79 years
Now, suppose that your project will not bring you a steady cash flow. Let's analyze the example with the apartment more closely. For instance, you can say that you will not be able to find long-term tenants the first two years and will only assume $15,000 of annual income. Additionally, during the fifth year, you will have to renovate the apartment and hence decrease your total profit to $10,000. If you assume a discount rate of 5%, what will be the discounted payback period?
To answer this question, you need to follow the steps below.
PVi = Ci / (1 + R) ^ i
Again, put all of your results in a table.
|time||Cash flow||Present value|
After you're finished with the calculations, create your final table with results.
|time||Cash flow||Present value||Cumulative present value|
|initial investment||$100,000||$100,000||$ -100,000|
|year 1||$15,000||$14,286||$ -85,714|
|year 2||$15,000||$13,605||$ -72,109|
|year 3||$24,000||$20,732||$ -51,377|
|year 4||$24,000||$19,745||$ -31,632|
|year 5||$10,000||$7,835||$ -23,797|
|year 6||$24,000||$17,909||$ -5,887|
|year 7||$24,000||$17,056||$ 11,169|
|year 8||$24,000||$16,244||$ 27,413|
DPP = X + Y / Z
In our example, you have to input the following values:
DPP = 6 + $5,887 / $17,056
DPP = 6.35 years