Here's my thinking:I need some help conceptually with how funding ratio works with PV, NPV, inflation, income & expenses (read a LOT about them including viewtopic.php?t=407798&start=50)
Let's take some very simplified models for the conversation:
Inflation: 3.0%
Income: $65K/yr from Non-COLA adjusted pension
Expenses: $50K/yr
Analysis from today (2024) thru 2053, 30 periods
Funding Ratio = (PV of Incomes) / (PV of Expenses)
Let's get PV of Income:
FPV = (3%,$65K,$65K,...,$65K) = $1,274K
Let's get PV of Expenses:
FPV = (3%,$50K,$50K,...,$50K) = $980K
This implies a FR = $1,274K/$980K = 130%
Now, where I'm confused is I think this is wrong! When I look at the last year in real dollars....
In the year 2053:
Income = $65K (in 2024 $) = $26K (in 2053 $)
Expenses = $50K (in 2024 $) = $125K (in 2053 $)
Tell me if you think that statement is wrong. If you agree with that statement, it implies that while my income is DIVIDED by (1+r)^n, my expenses are MULTIPLIED by (1+r)^n. If my expenses are multiplied, I would have to use -3% for my PV calculation, which would make my FR = $1,274K / $2,490K = 51%
I'm sure I'm confused about something, and I know it is likely my assumption on how to treat PV of expenses. I just can't wrap my head around using traditional PV of expenses which would discount them year after year when, in fact, they are rising???
No negative sign is needed for the interest rate because that would imply current dollars are worth less than future dollars (negative inflation).
I think the problem is you are calculating the present worth value of a series of 50k expenses--you are holding the expenses constant just as you are the income (I'm understanding your intent is to not let your income rise with inflation, but hold constant).
If your intent is to let the expenses rise with inflation, then each year's expense value should rise by 3%. It doesn't stay 50k. By the final one 30 years down the road, your expense will be $121,363. But, the present worth value of that last year's expense is still $50,000. In fact, because each year's expense is keeping up with inflation, each year's expense adds exactly 50k to the present worth value. Hence, the present worth value of your expenses is 50k x 30 =$1.5 million. So the funding ratio would be 1.274k/1.5k = 85%
Effectively that means you have 85% of your expenses funded by your income at a 3% inflation rate.
Statistics: Posted by HairyReasoner — Mon Sep 09, 2024 9:10 pm