wsfr: Calculate WSFR Aid dollars by current age
In southwick-associates/lifetime: Provide functions for lifetime pricing

Description Usage Arguments Details Functions See Also Examples

Estimated aid dollars are determined differently for the annual vs. lifetime purchasing scenarios (see functions section below). Links to a web-based reference document are included in details below.

wsfr_annual_stream(retain_all, wsfr_amount, min_amount, senior_price,
  senior_age = 65, age_cutoff = 80)

wsfr_lifetime_stream(prices, wsfr_amount, min_amount, age_cutoff = 80)

wsfr_lifetime(prices, wsfr_amount, min_amount, age_cutoff = 80)

`retain_all`	data frame of predicted years by age like that produced by `nc_retain_all`
`wsfr_amount`	numeric estimated amount for aid dollars (use SFRF for fishing, WRF for hunting)
`min_amount`	numeric the minimum expenditure that will count for a certified hunter/angler (use 2 for hunt/fish and 4 for combo)
`senior_price`	numeric price for a senior lifetime license
`senior_age`	numeric age when a participant will be expected to buy a cheap lifetime license
`age_cutoff`	numeric final age that can be counted for lifetime license-based WSFR dollars
`prices`	data frame of lifetime prices by age with at least 2 variables: current_age and price_lifetime

These calculations are based on a discussion between Tom, Dan, Eric, and Patty on 12/10/19. Primarily using https://www.law.cornell.edu/cfr/text/50/part-80 to highlight a number of points about WSFR aid predictions for lifetime license sales:

There is an age cutoff of 80 years (in lieu of a life-expectancy-based attrition estimate): section 35 bullet H
It looks like infants can be counted: section 33 bullet C
The required annual amount is $2 for hunt/fish and $4 for combo: section 34 bullet A

wsfr_annual_stream: Stream of WSFR Aid for annual license scenario

This depends largely on the estimated number of years a license buyers will participate in the future. It also assumes by default that any remaining participants will buy a lifetime license at senior_age. The stream calculation forcasts aid for relevant future years.
wsfr_lifetime_stream: Stream of WSFR Aid for lifetime license scenario
wsfr_lifetime: Total WSFR Aid for lifetime license scenario

Other estimating revenue: compound_interest, present_value_stream, wsfr_lifetime_yrs

library(dplyr)
library(ggplot2)
data(retain_all)

# annual scenario
aidA <- retain_all %>%
    wsfr_annual_stream(wsfr_amount = 16.65, min_amount = 4, senior_price = 15) %>%
    group_by(.data$current_age) %>%
    summarise(yrs = sum(pct), revenue_annual = sum(revenue_annual))

# lifetime scenario
prices <- tibble(current_age = 16:63, price_lifetime = rep(250, 48))
aidL <- wsfr_lifetime(prices, wsfr_amount = 16.65, min_amount = 4)

# there are large predicted differences in wsfr revenue outcomes
aidL$revenue_lifetime - aidA$revenue_annual