Boulder City Hospital has just been informed that a private donor is willing to contribute $10 million per year at the beginning of each year for fifteen years. What current dollar value of this contribution if the discount rate is 14 percent?
To calculate the current dollar value of the contribution, we need to calculate the present value of the $10 million per year for fifteen years. The present value is the current value of a future cash flow, considering the time value of money.
To find the present value, we can use the formula:
PV = CF / (1 + r)^n
Where:
PV = Present value
CF = Cash flow per year
r = Discount rate
n = Number of years
In this case, CF = $10 million, r = 14%, and n = 15 years.
Let's plug in the values and calculate:
PV = $10,000,000 / (1 + 0.14)^15
Using a calculator or spreadsheet, we can solve this equation:
PV ≈ $10,000,000 / (1.14)^15
PV ≈ $10,000,000 / 4.074
PV ≈ $2,451,250
Therefore, the current dollar value of the contribution is approximately $2,451,250 when the discount rate is 14 percent.