Article: In its simplest form, the DCF formula is DCF=CFn(1+r)n{\displaystyle { ext{DCF}}={
rac {CF_{n}}{(1+r)^{n}}}}. In the formula, CFn{\displaystyle CF_{n}} refers to the future value of the cash flow for year n and r represents the discount rate. For example, using the first year of the example investment from the part "Gathering Your Variables," the present value of that cash flow for $1,000 after one year, using the discount rate of 9 percent, would be represented as: DCF=$1,000(1+0.09)1{\displaystyle { ext{DCF}}={
rac {\$1,000}{(1+0.09)^{1}}}}. The discount rate must be represent as a decimal rather than by a percentage. This is done by dividing the discount rate by 100. Therefore, the 9 percent rate from above is shown as 0.09 (9100{\displaystyle 9\div 100}) in the equation. The total value of discounted cash flows for an investment is calculated as the present values of each cash flow. So, the other cash flows must be added to the calculation in the same method as the first one. For the previous example, we would add the $2,000 and $3,000 payments at the end of the second and third years to the equation. In total, this gives: DCF=$1,000(1+0.09)1+$2,000(1+0.09)2+$3,000(1+0.09)3{\displaystyle { ext{DCF}}={
rac {\$1,000}{(1+0.09)^{1}}}+{
rac {\$2,000}{(1+0.09)^{2}}}+{
rac {\$3,000}{(1+0.09)^{3}}}} Solve your equation to get your total discounted value. The result will be the present value of your future cash flows. Start by adding the discounted rate to the 1 within parentheses: This gives DCF=$1,000(1.09)1+$2,000(1.09)2+$3,000(1.09)3{\displaystyle { ext{DCF}}={
rac {\$1,000}{(1.09)^{1}}}+{
rac {\$2,000}{(1.09)^{2}}}+{
rac {\$3,000}{(1.09)^{3}}}} From there, calculate the exponent. This is done by raising the "1.09" in parentheses to the power above it (1,2, or 3). Solve this by either typing "[lower value]^[exponent]" into Google or using the exponent button, xy{\displaystyle x^{y}} on a calculator. After solving the exponent, the equation will be: DCF=$1,0001.09+$2,0001.1881+$3,0001.295029{\displaystyle { ext{DCF}}={
rac {\$1,000}{1.09}}+{
rac {\$2,000}{1.1881}}+{
rac {\$3,000}{1.295029}}} Next, divide each cash flow by the number underneath it. This yields: DCF=$917.43+$1,683.36+$2,316.55{\displaystyle { ext{DCF}}=\$917.43+\$1,683.36+\$2,316.55} Finally, add up the present values to get the total, which is DCF=$4,917.34{\displaystyle { ext{DCF}}=\$4,917.34}. In some cases it may be necessary to change the discount rate used to account for changes to expectations, risk, or taxes. For example, businesses analyzing a project might add a risk premium on to the discount rate used to discount the cash flows from a risky project. This artificially lowers the returns to account for risk. The same might be done for a very long time window between the present and the future cash flows to account for uncertainty. Discount rates may be converted to real rates (rather than nominal rates) by removing inflation from the discount rate. A spreadsheet program, such as Excel, has functions that can help with these calculations.
What is a summary of what this article is about?
Set up your equation. Add up all discounted cash flows. Arrive at the discounted value. Adjust your discount rate.