This report quantifies the net present value of the Public Service Pension Plan (PSPP), providing a monetary resolution to the contentious debates surrounding its benefits for public servants. Is PSPP as valuable as you think?
Jack, who was born on 1997-03-01, joined the public service at 23 on 2020-05-31. Suppose he plans to retire at 55 and will live until 85. How much are PSPP future payments worth in today’s dollar? Assume his highest average income over 5 consecutive years is $75,000.
We obtain the payment schedule for the above scenario using the pension calculator from the PSPC website, as follows:
| Description | Effective From Date | Effective To Date | Type | Monthly Payments | Reduction multiplier | Monthly Reduced Payments |
|---|---|---|---|---|---|---|
| Lifetime pension | 2062-03-01 | 9999-01-01 | Deferred Annuity | $2,867.68 | 1 | 2867.68 |
| Bridge benefit (Up to age 65) | 2062-03-01 | 2062-03-31 | Deferred Annuity | $1,101.43 | 1 | 1101.43 |
| Lifetime pension | 2052-03-01 | 9999-01-01 | Annual Allowance | $1,875.41 | 75% | 1406.56 |
| Bridge benefit (Up to age 65) | 2052-03-01 | 2062-03-31 | Annual Allowance | $1,101.43 | 75% | 826.07 |
Note that results from the pension calculator is saved as ‘Pension benefits options report.pdf’ in the ‘data’ folder.
We do some data joins to create a table containing PSPP’s monthly payment schedule.
suppressPackageStartupMessages(library("dplyr"))
# create a data frame with all payment dates
start_date = "2052-03-01"
end_date = "2082-03-01"
Date <- as.POSIXlt(seq(as.Date(start_date), as.Date(end_date), by="month"))
date_df = data.frame(date=Date)
# load a data frame with results from PSPC's pension calculator
payment_df = read.csv("data/payment_df.csv") %>% janitor::clean_names()
payment_df$effective_from_date = as.Date(payment_df$effective_from_date)
payment_df$effective_to_date = as.Date(payment_df$effective_to_date)
# join tables to create a table with pension payments in each month
payment_schedule_df = date_df %>% left_join(payment_df, join_by(date >= effective_from_date ,
date <= effective_to_date))
payment_schedule_df$monthly = as.numeric(payment_schedule_df$monthly)
#create a table summarizing payments by month
payment_summary_df = payment_schedule_df %>%
group_by(date) %>%
summarise(total_payment = sum(monthly))
# The result is a table that contains retirement payments from the PSPP,
## starting from 2052-03-01 (retirement date at 55) to 2082-03-01 (age 85):
payment_summary_df ## # A tibble: 361 × 2
## date total_payment
## <dttm> <dbl>
## 1 2052-03-01 00:00:00 2233.
## 2 2052-04-01 00:00:00 2233.
## 3 2052-05-01 00:00:00 2233.
## 4 2052-06-01 00:00:00 2233.
## 5 2052-07-01 00:00:00 2233.
## 6 2052-08-01 00:00:00 2233.
## 7 2052-09-01 00:00:00 2233.
## 8 2052-10-01 00:00:00 2233.
## 9 2052-11-01 00:00:00 2233.
## 10 2052-12-01 00:00:00 2233.
## # ℹ 351 more rows
Now, we want to figure out how much the pension payments are worth in today’s dollar*.
suppressPackageStartupMessages(library("FinancialMath"))
suppressPackageStartupMessages(library("scales"))
suppressPackageStartupMessages(library("lubridate"))
pension_npv = NPV(cf0=0, cf=payment_summary_df$total_payment,
times=-interval(payment_summary_df$date, mdy(03012023)) %/% months(1), i=0)
cat(paste0("The PSPP's NPV is:",dollar(pension_npv)," (",mdy(03012023)," dollar)"))## The PSPP's NPV is:$1,299,935 (2023-03-01 dollar)
rate_vector = seq(0,0.15,0.01) #a vector of annual discount rate
pension_value_vector = c()
for (rate in rate_vector){
curr_value = NPV(cf0=0, cf=payment_summary_df$total_payment,
times=-interval(payment_summary_df$date, mdy(03012023)) %/% months(1), i=rate/12)
pension_value_vector = c(pension_value_vector,curr_value)
}
return_df = data.frame(annual_discount_rate = rate_vector, pension_npv=pension_value_vector)
return_df$pension_npv = dollar(return_df$pension_npv )
return_df$monthly_discount_rate = percent(return_df$annual_discount_rate/12)
return_df$annual_discount_rate = percent(return_df$annual_discount_rate)
names(return_df) = c("ROI (Annual)","Cash required for investment (2023 dollar)","ROI (Monthly)")
kable(return_df)| ROI (Annual) | Cash required for investment (2023 dollar) | ROI (Monthly) |
|---|---|---|
| 0.0% | $1,299,935 | 0.000% |
| 1.0% | $824,441 | 0.083% |
| 2.0% | $526,561 | 0.167% |
| 3.0% | $338,698 | 0.250% |
| 4.0% | $219,411 | 0.333% |
| 5.0% | $143,143 | 0.417% |
| 6.0% | $94,040 | 0.500% |
| 7.0% | $62,206 | 0.583% |
| 8.0% | $41,425 | 0.667% |
| 9.0% | $27,766 | 0.750% |
| 10.0% | $18,728 | 0.833% |
| 11.0% | $12,709 | 0.917% |
| 12.0% | $8,674 | 1.000% |
| 13.0% | $5,952 | 1.083% |
| 14.0% | $4,106 | 1.167% |
| 15.0% | $2,846 | 1.250% |
Valued in 2023 dollar, the Net Present Value (NPV) of cash inflows generated by PSPP payments in Scenario 1 equates to $526,561 for 31.75 years of service, considering a 2% discount factor (representing the inflation rate). This translates to $16,585 when distributed over Jack’s entire tenure of service.
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