Table 6.

Example of Discount Calculation

$\mathrm{P}=\mathrm{\sum }{\mathrm{F}}_{\mathrm{n}}{(1+\mathrm{r})}^{-\mathrm{n}}$ P = present value of a particular cost r = discount rate (use 0.03 if discount rate is 3%) n = year Fn= future cost at year n

$\ast \mathrm{P}={\mathrm{F}}_0+\frac{{\mathrm{F}}_1}{(1+\mathrm{r})}+\frac{{\mathrm{F}}_2}{{(1+\mathrm{r})}^2}+\frac{{\mathrm{F}}_3}{{(1+\mathrm{r})}^3}\cdots$ *If costs all occur at the beginning of each year, the above formula should be used. Thus, year 1 costs are not discounted and year 2 costs are discounted by one year, etc.12

If costs all occur at the end of each year, the following formula should be used: $\mathrm{P}=\frac{{\mathrm{F}}_1}{(1+\mathrm{r})}+\frac{{\mathrm{F}}_2}{{(1+\mathrm{r})}^2}+\frac{{\mathrm{F}}_3}{{(1+\mathrm{r})}^3}\cdots$

Hypothetical Cost and Discounted Cost (3% Discount) of a Cohort of 1,000 Patients Over a Four-Year Period+^:

Column 1	Column 2	Column 3	Column 4	Column 5
Year	Number Surviving	Cost per Person	Total Cost (Column 2 x Column 3)	Discounted Cost (Column 4/1.03Column 1)
1	1,000	$5,000	$5,000,000	$4,854,368
2	990	$4,500	$4,455,000	$4,199,265
3	910	$3,000	$2,730,000	$2,498,337
4	840	$6,500	$5,460,000	$4,851,139
Total			$17,645,000	$16,403,109

⁺Adapted from published example⁸

^{^}Assuming all costs occurred at the end of each year