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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.

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  • $\begingroup$ Can you please accept the answer if it was helpful? Thanks $\endgroup$ – Student May 9 at 17:09
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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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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 $t=50,000/9,500$).

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