What is the Discounted Payback Period?
Discounted payback period refers to the time period required to recover its initial cash outlay and it is calculated by discounting the cash flows that are to be generated in future and then totaling the present value of future cash flows where discounting is done by the weighted average cost of capital or internal rate of return.
Table of contents
Discounted Payback Period Formula
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For eg:
Source: Discounted Payback Period (wallstreetmojo.com)
From a capital budgeting perspective, this method is a much better method than a simple payback period.
In this formula, there are two parts.
 The first part is “a year before the period occurs.” This is important because by taking the prior year, we can get the integer.
 The next part is the division between cumulative cash flow in the year before recovery and discounted cash flowDiscounted Cash FlowDiscounted cash flow analysis is a method of analyzing the present value of a company, investment, or cash flow by adjusting future cash flows to the time value of money. This analysis assesses the present fair value of assets, projects, or companies by taking into account many factors such as inflation, risk, and cost of capital, as well as analyzing the company's future performance.read more in the year after recovery. The purpose of this part is to find out the proportion of how much is yet to be recovered.
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Explanation of Discounted Payback Period in Video
Example
Funny Inc. would like to invest $150,000 into a project as an initial investment. The firm expects to generate $70,000 in the first year, $60,000 in the second year, and $60,000 in the third year. The + [Cost of Debt * % of Debt * (1Tax Rate)]” url=”https://www.wallstreetmojo.com/weightedaveragecostcapitalwacc/”]weighted average cost of capital”Weighted”The is 10%. Find out the discounted payback period of Funny Inc.
We will go step by step.
First, we will find out the present value of the cash flow.
Let’s look at the calculations.
Please note the formula of present value – PV = FV / (1+i) ^n
 Year 0: – $150,000 / (1+0.10) ^0 = $150,000
 Year 1: $70,000 / (1+0.10) ^1 = $63,636.36
 Year 2: $60,000 / (1+0.10) ^2 = $49,586.78
 Year 3: $60,000 / (1+0.10) ^3 = $45,078.89
Now, we will calculate the cumulative discounted cash flows –
 Year 0: – $150,000
 Year 1: – 86,363.64
 Year 2: – 36,776.86
 Year 3: $8,302.03
Discounted Payback Period = Year before the discounted payback period occurs + (Cumulative cash flow in year before recovery / Discounted cash flow in year after recovery)
= 2 + ($36.776.86 / $45,078.89) = 2 + 0.82 = 2.82 years.
Example #2
A project is having a cash outflow of $ 30,000 with annual cash inflows of $ 6,000, so let us calculate the discounted payback period, in this case, assuming companies WACC is 15% and the life of the project is 10 years.
Year  Cash flow  Present value factorPresent Value FactorPresent value factor is factor which is used to indicate the present value of cash to be received in future and is based on time value of money. This PV factor is a number which is always less than one and is calculated by one divided by one plus the rate of interest to the power, i.e. number of periods over which payments are to be made.read more @ 15%  Present value of cash flows  Cumulative present value of cash flows 

1  $ 6,000  0.870  $ 5,220  $ 5,220 
2  $ 6,000  0.756  $ 4,536  $ 9,756 
3  $ 6,000  0.658  $ 3,948  $ 13,704 
4  $ 6,000  0.572  $ 3,432  $ 17,136 
5  $ 6,000  0.497  $ 2,982  $ 20,118 
6  $ 6,000  0.432  $ 2,592  $ 22,710 
7  $ 6,000  0.376  $ 2,256  $ 24,966 
8  $ 6,000  0.327  $ 1,962  $ 26,928 
9  $ 6,000  0.284  $ 1,704  $ 28,632 
10  $ 6,000  0.247  $ 1,482  $ 30,114 
In this case, the cumulative cash flows are $ 30,114 in the 10^{th} year as, so the payback period is approx. 10 years
But, if you calculate the same in simple payback, the payback period is 5 years( $30,000/$6,000)
Please note that if the discount rate increases, the distortion between the simple rate of return and discounted payback period increases. Let me explain this further. Let us take the 10% discount rate in the above example and calculate the discounted payback period.
Year  Cash flow  Present value factor @ 10%  Present value of cash flows  The cumulative present value of cash flows 

1  $6,000  0.909  $5,454  $5,454 
2  $6,000  0.826  $4,956  $10,410 
3  $6,000  0.751  $4,506  $14,916 
4  $6,000  0.683  $4,098  $19,014 
5  $6,000  0.621  $3,726  $22,740 
6  $6,000  0.564  $3,384  $26,124 
7  $6,000  0.513  $3,078  $29,202 
8  $6,000  0.466  $2,796  $31,998 
9  $6,000  0.424  $2,544  $34,542 
10  $6,000  0.385  $2,310  $36,852 
In this case, the discounting rate is 10% and the discounted payback period is around 8 years, whereas the discounted payback period is 10 years if the discount rate is 15%. But the simple payback period is 5 years in both cases. So, this means as the discount rate increases, the difference in payback periods of a discounted pay period and simple payback period increases.
Discount Rate  Simple Payback(a)  Discounted Payback(b)  The difference in payback period (b) (a) 

10%  5 Years  8 Years  3 Years 
15%  5 Years  10 Years  5 years 
I hope you guys got a reasonable understanding of what is payback period and discounted payback period. Let us take some more examples to understand the concept better.
Example #3
A company wants to replace its old semiautomatic machine with a new fully automatic machine. In the market, there are two models available in the market (Model A & Model B) at the cost of $ 5,00,000 each. The salvage valueSalvage ValueSalvage value or scrap value is the estimated value of an asset after its useful life is over. For example, if a company's machinery has a 5year life and is only valued $5000 at the end of that time, the salvage value is $5000.read more of an old machine is $ 1,00,000.The utilities of existing machinery that can be used are company purchases model A, and additional utilities to be bought are only $1,00,000. However, in case the company buys the model B, then all the existing utilities will have to be replaced, and new utilities cost$ 2,00,000, and a salvage value of old utilities is $20,000. The cash flows expected are as follows, and the discount rate is 15%
Year  A  B 

1  $ 1,00,000  $ 2,00,000 
2  $ 1,50,000  $ 2,10,000 
3  $ 1,80,000  $ 1,80,000 
4  $ 2,00,000  $ 1,70,000 
5  $ 1,70,000  $ 40,000 
Salvage value expected  $ 50,000  $ 60,000 
Expenditure at Year of investment (Year Zero)
Particulars  A  B 

Cost of machine  $ 5,00,000  $ 5,00,000 
Cost of utilities  $ 1,00,000  $ 2,00,000 
Salvage of old machine  ($ 1,00,000)  ($ 1,00,000) 
Salvage of old machine  –  ($ 20,000) 
Total Exp  $ 5,00,000  $ 5,80,000 
Year  Present value factorPresent Value FactorPresent value factor is factor which is used to indicate the present value of cash to be received in future and is based on time value of money. This PV factor is a number which is always less than one and is calculated by one divided by one plus the rate of interest to the power, i.e. number of periods over which payments are to be made.read more @ 15%  Cash inflows (Machine A)  Present value of cash flows (Machine A)  Cumulative present value of cash flows (Machine A)  Cash inflows (Machine B)  Present value of cash flows (Machine B)  Cumulative present value of cash flows (Machine B) 

0 (As calculated above)  1.00  $500,000  $500,000  $500,000  $580,000  $580,000  $580,000 
1  0.87  $100,000  $87,000  $87,000  $200,000  $174,000  $174,000 
2  0.76  $150,000  $114,000  $201,000  $210,000  $159,600  $333,600 
3  0.66  $180,000  $118,800  $319,800  $180,000  $118,800  $452,400 
4  0.57  $200,000  $114,000  $433,800  $170,000  $96,900  $549,300 
5(Including salvage value of $ 50,000 for Mach A and $ 60,000 for Mach B)  0.50  $ 170000+ $50,000  $110,000  $543,800  $100,000  $50,000  $599,300 
In this case, the discounted payback for Machine A is as follows…
Machine A is getting $ 4,33,800 at the end of year 4, and only $66,200($50000$433800) has to get in year 5. So, payback here is …
4 years+ (66,200/1,10,000) = 4.6 Years
Machine B is getting $ 5,49,300 at the end of year 4 and only $30,700 ($5,80,000 $5,49,300) has to get in year 5. So, payback here is …
4 years+ (30,700/50,000) = 4.6 Years
The discounted payback in both cases is the same.
Discounted Payback Period Calculation in Excel
Let us now do the same example above in Excel.
This is very simple. You need to provide the two inputs of Cumulative cash flow in a year before recovery and Discounted cash flow in a year after recovery. You can easily calculate the period in the template provided.
Use and Relevance
 The discounted payback period is a better option for calculating how much time a project would get back its initial investment; because, in a simple payback period, there’s no consideration for the time value of moneyTime Value Of MoneyThe Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read more.
 It can’t be called the best formula for finding out the payback period.
 But from the perspective of capital budgetingCapital BudgetingCapital budgeting is the planning process for the longterm investment that determines whether the projects are fruitful for the business and will provide the required returns in the future years or not. It is essential because capital expenditure requires a considerable amount of funds.read more and accuracy, this method is far superior to a simple payback period; because in a simple payback period, there is no consideration for the time value of money and cost of capital.
 Many managers have been shifting their focus from a simple payback period to a discounted payback period to find a more accurate estimation of tenure for recouping the initial investments of their firms.
Discounted Payback Period Calculator
You can use the following Calculator
Year before the discounted payback period occurs  
Cumulative cash flow in year before recovery  
Discounted cash flow in year after recovery  
Discounted Payback Period Formula =  
Discounted Payback Period Formula =  Year before the discounted payback period occurs + 



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