> For the complete documentation index, see [llms.txt](https://vikram-bajaj.gitbook.io/introduction-to-corporate-finance-coursera/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://vikram-bajaj.gitbook.io/introduction-to-corporate-finance-coursera/time-value-of-money/discounting.md).

# Discounting

Discounting is the process of moving CFs back in time.

![](https://956443069-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0XkN7T0GfSvonH8F%2FDiscounting.JPG?generation=1586990838278959\&alt=media)Once all the CFs are moved back in time to timestamp 0, they can be aggregated (added/subtracted).

Present Value $$PV\_t(CF\_i)$$ is the present value of the cash flow $$CF\_i$$ at a previous timestamp t. The moved back CFs denote the **present values** of the cash flows today i.e. at timestamp 0.

## Simple Example

```
How much do you have to save today to withdraw $100 at the end of each year for the next 4 years,
if you can earn 5% per annum?
```

The first step is to place the CFs on the timeline:

![](https://956443069-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0XkPM8XBghdUmh1Y%2FStep1.JPG?generation=1586990835346302\&alt=media)Now, calculate their present values (at timestamp 0) by discounting:

![](https://956443069-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0XkRvSftbq85wcLK%2FStep2.JPG?generation=1586990837319924\&alt=media)Now, simply aggregate the present values:

![](https://956443069-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGr8Q9QLqT32rM-%2F-M5-0TBzyC8aF6M53_Dz%2F-M5-0XkTV_RPQMcjYEH9%2FStep3.JPG?generation=1586990836259170\&alt=media)Thus, we need to save $354.60 today to be able to withdraw $100 at the end of each of the next 4 years, earning 5% per annum.