Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $645 million that must be paid in 25 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.5 percent, what is the present value of this liability?
The correct answer and explanation is :
To calculate the present value (PV) of an unfunded pension liability, we use the formula for the present value of a single future payment:
[
PV = \frac{FV}{(1 + r)^t}
]
Where:
- ( PV ) is the present value,
- ( FV ) is the future value (in this case, the unfunded pension liability),
- ( r ) is the discount rate (annual rate of return or interest rate),
- ( t ) is the number of years into the future.
In this case:
- The future value ((FV)) is $645 million,
- The discount rate ((r)) is 5.5%, or 0.055 as a decimal,
- The number of years ((t)) is 25 years.
Now, let’s plug the values into the formula:
[
PV = \frac{645,000,000}{(1 + 0.055)^{25}}
]
Let’s compute the denominator:
[
1 + 0.055 = 1.055
]
Now, raise 1.055 to the power of 25:
[
1.055^{25} \approx 3.669
]
So, the formula becomes:
[
PV = \frac{645,000,000}{3.669}
]
Now, divide the future value by this number:
[
PV \approx 175,953,679.30
]
Thus, the present value of the unfunded pension liability is approximately $175.95 million.
Explanation:
This calculation is based on the principle of time value of money, which suggests that a dollar today is worth more than a dollar in the future due to its earning potential. By discounting the future pension liability, we assess how much the liability is worth in today’s terms, given a specified discount rate. A 5.5% annual discount rate reduces the future value of the liability over time, reflecting the opportunity to invest that amount today and earn returns over the next 25 years. Therefore, the present value of the liability is much lower than its face value due to the passage of time and the earning potential of money invested at 5.5%.