## Places Of Interest

### How to Change the Discount Rate When Projecting at Various Time Intervals (monthly, quarterly, semi-annual)

This is one of the most common calculations you will ever do in the finance industry as an analyst or just someone who is trying to figure out the present value of future cash flows for a business. The DCF Analysis method is very common to use for valuation, but what happens if you are using non-annual periods, but want to apply an annualized discount rate to the future cash flows correctly?

Relevant Templates:

So the first thing to understand is we are dealing with compounding rates. If you have a discount rate you have come up with, that is almost always denominated as an annual rate. There are a few steps to do in order to transform that rate into a different value that represents monthly / quarterly. You can't just divide by 4 or divide by 12. The formula won't give you the proper value in that case.

When adjusting the discount rate for different time intervals, it's crucial to ensure that the time period of the discount rate matches the time period of the cash flows being discounted. To do this, you can use the following formula:

(1 + annual discount rate) ^ (1/n) - 1

If you rate is 12%, then do the following:

Monthly:
(1+0.12) ^ (1/12) - 1

Quarterly:
(1+0.12) ^ (1/4) - 1

Semi-annual:
(1+0.12) ^ (1/2) - 1

Then, once you have found the correct rate for your cash flows, you apply that with the following formula:

Future Period Cash Flow Amount  /  (1+discount rate) ^ period number

Then, simply sum up the total value of the discounted future cash flows and that is the total present value.

I end up doing a lot of these discount rate conversion formulas in real estate model templates.

Finally, be mindful of the difference between the nominal and effective rates. The above conversions give the effective rate for the period in question. If you're given a nominal rate (annual rate compounded more frequently than annually), you'd first convert that to an effective annual rate before doing these transformations.

Article found in Valuation.