43.13 Discounting in DES Models

With the Global Discounting option in Tree Preferences, applying discounting to a DES model is very simple. In the DES.Model.With.RepeatingEvents Model, payoff sets 9 and 10 use the same reward expression as payoff sets 1 and 2, except that global discounting is applied as shown below.

The DES time unit is set to annual because the distributions are sampling time-to-event in years. Time rewards expressions are also consistent with this time unit. Note that the ninth and tenth payoff sets have discount rates set to the variable Disc_rate, which evaluates to 0.03.

Based on the Global Discount settings above, payoff sets 1 and 2 will calculate cost and effectiveness with no discounting, while payoff sets 9 and 10 will calculate cost and effectiveness with a 3% annual discount rate. Expressions for all rewards are identical for payoff sets 1 and 9 and for payoff sets 2 and 10, but the expected values for 9 & 10 will be lower due to the impact of discounting.

Discounting Formulas

TreeAge Pro's Global Discounting function uses standard discounting formulas. Time rewards and event rewards use different formulas due to the way those rewards are accumulated. Startup rewards are unaffected by discounting because they are applied at _time 0.

Event rewards are accumulated at a specific time, so the standard discounting factor is applied.

Based on applying the discounting factor above, discounting reduces value more and more as time moves into the future. While this formula is applied to event rewards automatically via Global Discounting, you can also apply the formula manually through the Discount function.

Time rewards are accumulated over a period time, so discounting is more complicated.

The formula above calculates the discounted value of a reward that is accumulated between times a and b. Fortunately, you will not have to recreate this formula. Global Discounting takes care of it for you. There are also two discount functions - DiscountCont and DiscountContDES - which you can use to apply the continuous discounting formula yourself and find details of in the section Financial and Discounting functions.