A mid-year discount is a term used in a DCF analysis to discount future cash flows to a present value. The basic method of discounting cash flows is to use the formula:

• Cash Flow / (1 + Discount Rate)^(Year-Current Year)

The problem with the standard method is that it discounts the future value too much. It assumes that the entire value of cash flow for a given year comes in at the very end of that year, and therefore should be discounted accordingly. This is inaccurate as the cash will be flowing in over the full year. To account for this, a mid-year discount is used to assume that all the cash comes in halfway through the year to average it out. To do this, the following formula is used:

• Cash Flow / (1+Discount Rate)^((Year-Current Year)-0.5)

For example, if the current year is 2011 and we wish to work out the net present value of the cash flow in 2015 with a discount rate of 10% and an estimated cash flow of \$1000 per year, the process would be as follows:

• 2015 is the 4th year in the future
• The general formula would be 1000 / 1.1^4 = \$683
• This method assumes all the cash for 2015 comes in on the 31st December 2015 whereas in reality, it comes in throughout the year
• We use a mid-year discount to say that that cash flow will come in, on average, in 3.5 years time
• The new formula is 1000 / 1.1^3.5 = \$716

As shown, this method for how to calculate a mid-year discount makes quite a large difference, especially when summing up cash flows for multiple years into the future. 