If a hospital received $5,000 in payments per year at the end of each year for the next tweleve years from an uninsured patient who underwent an expensive operation, what would be the current value of these commection payments:
at 3% rate of return?
at a 13% percent rate of return?
If the funds were received at the beginning of the year, what would be the current value of these collection payment?
To calculate the present value of future cash flows, we can use the formula for the present value of an annuity. The formula is given as:
PV = P * (1 - (1+r)^(-n))/r
Where:
PV = Present Value
P = Payment per period
r = Interest rate per period
n = Number of periods
Given that the hospital received $5,000 per year for the next twelve years, we can calculate the present value of these collection payments at different rates of return.
At a 3% rate of return:
P = $5,000, r = 3%, n = 12
Using the formula:
PV = 5000 * (1 - (1+0.03)^(-12))/0.03
= $48,685.96
Therefore, the present value of these collection payments at a 3% rate of return is approximately $48,685.96.
At a 13% rate of return:
P = $5,000, r = 13%, n = 12
Using the formula:
PV = 5000 * (1 - (1+0.13)^(-12))/0.13
= $31,148.41
Therefore, the present value of these collection payments at a 13% rate of return is approximately $31,148.41.
Now, if the funds were received at the beginning of the year instead of the end, we need to adjust the formula slightly. Instead of using the regular present value of an annuity formula, we use the formula for the present value of an annuity due, which includes an additional factor of (1+r) in the numerator.
At a 3% rate of return:
PV = 5000 * ((1 - (1+0.03)^(-12))/0.03) * (1+0.03)
= $49,913.64
Therefore, the present value of these collection payments received at the beginning of the year at a 3% rate of return is approximately $49,913.64.
At a 13% rate of return:
PV = 5000 * ((1 - (1+0.13)^(-12))/0.13) * (1+0.13)
= $35,259.25
Therefore, the present value of these collection payments received at the beginning of the year at a 13% rate of return is approximately $35,259.25.