<p>This is more finance than economics but here it is:</p>

<p>The payback period is pretty much how much time you need to recover the initial investment. </p>

<p>Each month, you are saving 10000 - 500 = 9500.  Then you simply just divide 50000 by 9500. This comes out to be around 5. </p>

<p>I made some simplifying assumptions: Discount rate is 0. This is usually not true, so you would probably have to discount the cash flows. Note: This will probably involve monthly compounding. Check out the formula for annuity. </p>

<p>Also, just FYI: payback method often results in wrong decisions. When you have a choice, always use NPV.</p>

CC BY-SA 4.0
2019-05-09T09:39:40.233Z
2019-05-09T20:24:54.703Z
2019-05-09T20:24:54.703Z
Student
<p>Your cost today is <span class="math-container">$50,000$</span> and your inflows in the future are <span class="math-container">$10,000$</span> in savings, minus <span class="math-container">$500$</span> in maintenance cost, so in total <span class="math-container">$9,500$</span> of inflow. However money today is more valuable than money tomorrow, and this is captured by the interest rate lets suppose the interest rate is <span class="math-container">$r^*$</span> (typically given annually) so let's transform it into a monthly rate <span class="math-container">$r=r^*/12$</span>, then the payback period is the amount of periods <span class="math-container">$t$</span> (here everything will be monthly, so <span class="math-container">$t$</span> months) such that the present value of the cost equal the present value of the inflows in the future:</p>

<p><span class="math-container">$$50,000=\frac{9,500}{r}\left[1-\frac{1}{(1+r)^t}\right]$$</span></p>

<p>Clearly, to solve for <span class="math-container">$t$</span> you need to know <span class="math-container">$r$</span>. The solution is probably pretty close to 5.3 months since monthly interest rates are usually very low and assuming <span class="math-container">$r=0$</span> you get that result. (of course the formula does not work for <span class="math-container">$r=0$</span>, but as mentioned before, in that case <span class="math-container">$t=50,000/9,500$</span>).</p>

CC BY-SA 4.0
2020-11-04T00:12:51.927Z
Historically higher inflation rates once made calculations like this so much more relevant, rather than within the margin of error of costs estimates.
Mox
CC BY-SA 4.0
2019-05-09T21:13:52.500Z
2019-05-09T21:13:52.500Z
Regio
<p>In order to finish a technological product, it was spent 50000 dollars (for materials, salary). 500 dollars per month is needed for support of the project (will be spend for servers). This product automated some process that required manual work for 10000 dollars per month. So, how to calculate payback period of the project? </p>

<p>My solution would be 50000:10000 = 5 month, but I don't know what to do with the cost of support per month. </p>

CC BY-SA 4.0
2019-05-09T17:09:38.180Z
Can you please accept the answer if it was helpful? Thanks
Student
<mathematical-economics><investment>
How to calculate payback period of the project?
neo
# How to calculate payback period of the project?

(Asked by: username_0 on 2019-05-09)

In order to finish a technological product, it was spent 50000 dollars (for materials, salary). 500 dollars per month is needed for support of the project (will be spend for servers). This product automated some process that required manual work for 10000 dollars per month. So, how to calculate payback period of the project?

My solution would be 50000:10000 = 5 month, but I don't know what to do with the cost of support per month.

**Tags:** mathematical-economics, investment
> **Comments:**
> **username_1**: Can you please accept the answer if it was helpful? Thanks  

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## 2 answers

### Answer by username_1 on 2019-05-09. Score: 2 | Accepted answer

This is more finance than economics but here it is:

The payback period is pretty much how much time you need to recover the initial investment.

Each month, you are saving 10000 - 500 = 9500. Then you simply just divide 50000 by 9500. This comes out to be around 5.

I made some simplifying assumptions: Discount rate is 0. This is usually not true, so you would probably have to discount the cash flows. Note: This will probably involve monthly compounding. Check out the formula for annuity.

Also, just FYI: payback method often results in wrong decisions. When you have a choice, always use NPV.


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### Answer by username_2 on 2019-05-09. Score: 1

Your cost today is $50,000$ and your inflows in the future are $10,000$ in savings, minus $500$ in maintenance cost, so in total $9,500$ of inflow. However money today is more valuable than money tomorrow, and this is captured by the interest rate lets suppose the interest rate is $r^\*$ (typically given annually) so let's transform it into a monthly rate $r=r^\*/12$, then the payback period is the amount of periods $t$ (here everything will be monthly, so $t$ months) such that the present value of the cost equal the present value of the inflows in the future:

$$50,000=\frac{9,500}{r}\left[1-\frac{1}{(1+r)^t}\right]$$

Clearly, to solve for $t$ you need to know $r$. The solution is probably pretty close to 5.3 months since monthly interest rates are usually very low and assuming $r=0$ you get that result. (of course the formula does not work for $r=0$, but as mentioned before, in that case $t=50,000/9,500$).

> **Comments:**
> **username_3**: Historically higher inflation rates once made calculations like this so much more relevant, rather than within the margin of error of costs estimates.  

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