The time value of money is a core principle in the world of finance. It is also an important factor in actuarial calculations.
In general the time value of money is the idea that money is money available to you today is more valuable than that same amount paid at a later date. The reason is the fact that the money in your hand today could be invested and therefore be worth more than the same sum a year from now.
Since we deal primarily with LOSAP and payments that will be made in the future, I’m going to concentrate on the present value of a future payment. The present value, or PV of a payment owed in the future (Future Value, or FV) can be determined using the formula PV = FV ÷ (1 + i) ^ t. In this equation, i is the interest rate we assume will be earned and t is the number of years until the payment in the future is owed.
So let’s pretend we owe a $100,000 payment in five years. The 10-year treasury rate is roughly 2.5%, so we’ll use that for our interest rate assumption. Therefore, the present value of that $100,000 payment owed in five years is $88,385 today. Just to say it another way, $88,385 on 1/1/2020 is worth the same as $100,000 on 1/1/2025, assuming a 2.5% interest rate. If you were given the choice between being given $88,385 today or $100,000 in five years, how would you make that decision? There are many variables to consider. Some may think they can earn 10% in their investment portfolio and would gladly take the $88,385 because they believe they’ll have the opportunity to have more than $100,000 in five years (about $142,345 if 10% is earned each year). Others may look at their savings account earning 1% and think a 2.5% rate is more than double their savings, and would rather take the $100,000 in five years.
One important takeaway is how the interest rate assumption significantly changes the present value. If we double the interest rate to 5.0%, the present value becomes $78,353, or about $10,000 less. This means present value is relative, depending on the interest rate used.
Another important takeaway is that as time advances, the present value increases. This gives the impression that the sum is “growing” like an investment would. Here is the present value of that $88,385 at each year:
t=0, PV = $88,385
t=1, PV = $90,595
t=2, PV = $92,860
t=3, PV = $95,182
t=4, PV = $97,562
t=5, PV = $100,000
The idea of Present Value is an important concept that will be a building block to understand how contributions and lump-sum benefits are determined for LOSAP.
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