Discounted Payback Period

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.

Discounted Payback Period Formula

Discounted Payback Period = 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

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 flow in the year after recovery. The purpose of this part is to find out the proportion of how much is yet to be recovered.

Example

You can download this Discounted Payback Period Excel Template here – Discounted Payback Period Excel Template

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 weighted average cost of capital 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.

YearCash flowPresent 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 flowsCumulative present value of cash flows
1$ 6,0000.870$ 5,220$ 5,220
2$ 6,0000.756$ 4,536$ 9,756
3$ 6,0000.658$ 3,948$ 13,704
4$ 6,0000.572$ 3,432$ 17,136
5$ 6,0000.497$ 2,982$ 20,118
6$ 6,0000.432$ 2,592$ 22,710
7$ 6,0000.376$ 2,256$ 24,966
8$ 6,0000.327$ 1,962$ 26,928
9$ 6,0000.284$ 1,704$ 28,632
10$ 6,0000.247$ 1,482$ 30,114

In this case, the cumulative cash flows are $ 30,114 in the 10th 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.

YearCash flowPresent value factor @ 10%Present value of cash flowsThe cumulative present value of cash flows
1$6,0000.909$5,454$5,454
2$6,0000.826$4,956$10,410
3$6,0000.751$4,506$14,916
4$6,0000.683$4,098$19,014
5$6,0000.621$3,726$22,740
6$6,0000.564$3,384$26,124
7$6,0000.513$3,078$29,202
8$6,0000.466$2,796$31,998
9$6,0000.424$2,544$34,542
10$6,0000.385$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 RateSimple Payback(a)Discounted Payback(b)The difference in payback period (b)- (a)
10%5 Years8 Years3 Years
15%5 Years10 Years5 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 semi-automatic 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 value 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%

YearAB
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) 

ParticularsAB
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
YearPresent 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
10.87$100,000$87,000$87,000$200,000$174,000$174,000
20.76$150,000$114,000$201,000$210,000$159,600$333,600
30.66$180,000$118,800$319,800$180,000$118,800$452,400
40.57$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.

Discounted Payback Period in Excel

Use and Relevance

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          +
Cumulative cash flow in year before recovery
=
Discounted cash flow in year after recovery
0
0  += 0
0

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This has been a guide to the discounted payback period and its meaning. Here we learn how to calculate a discounted period using its formula along with practical examples. Here we also provide you with a discounted payback period calculator with a downloadable excel template.