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Lincoln Memorial hospital has just been informed that private donor is willing to contribute $5 million per year at the beginning of each year for fifteen years. What is the current dollar value of this contribution if the discount rate is 9 percent?
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The standard present value of an annuity formula assumes that the payment is made at the end of a period, yours is made at the beginning, so
PV = 5million + 5million( 1 - 1.09)^-14)/.09
= $ 43,930,751.94
notice the first term is 5 million, plus I added the other 14 payments.
To calculate the current dollar value of a future contribution, you need to use the concept of present value. Present value accounts for the time value of money, meaning that a dollar received in the future is worth less than a dollar received today.
To calculate the present value of the contribution, you can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment per period
r = Discount rate
n = Number of periods
In this case, the payment per period (PMT) is $5 million per year, the discount rate (r) is 9 percent (which you need to convert to a decimal by dividing it by 100), and the number of periods (n) is 15 (as the contribution will last for 15 years).
Now, let's calculate the present value (PV) of the contribution:
PV = $5,000,000 * [(1 - (1 + 0.09)^(-15)) / 0.09]
PV ≈ $44,268,304.30
Therefore, the current dollar value of the contribution, considering a discount rate of 9 percent, is approximately $44,268,304.30.