You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die). If you will receive $30,000 per year at the end of each year starting 25 years from now, what is the present value of your retirement plan if the discount rate is 5.5%?
To calculate the present value of your retirement plan, we need to determine the current worth of future cash flows discounted at the given rate. In this case, the cash flows you will receive are $30,000 per year starting 25 years from now and continuing indefinitely, even after your death.
To compute the present value, we will use the formula for the present value of a perpetuity:
Present Value = Cash Flow / Discount Rate
However, since there is a delay of 25 years before the payments begin, we need to discount the cash flows for those 25 years as well.
Step 1: Calculate the present value of the first 25 years' worth of cash flows:
PV of cash flows in the first 25 years = $30,000 / (1 + 0.055)^25
Step 2: Calculate the present value of the perpetuity:
PV of perpetuity = $30,000 / 0.055
Step 3: Add the present value of the first 25 years' cash flows to the present value of the perpetuity to get the total present value:
Present Value = PV of cash flows in the first 25 years + PV of perpetuity
Calculating each step:
PV of cash flows in the first 25 years = $30,000 / (1 + 0.055)^25 = $30,000 / (1.055)^25 = $30,000 / 1.879675 = $15,955.87
PV of perpetuity = $30,000 / 0.055 = $545,454.55
Present Value = PV of cash flows in the first 25 years + PV of perpetuity = $15,955.87 + $545,454.55 = $561,410.42
Therefore, the present value of your retirement plan is approximately $561,410.42.