The chief financial officer of a home health agency needs to determine the present value of a $10,000 investment received at the end of year 10. What is the present value if the discount rate is: a. 6 percent? b. 9 percent? c. 12 percent? d. 15 percent?
8796.99
To determine the present value of a future investment, you need to use the formula for present value, which is:
PV = FV / (1 + r)^n
where:
PV = Present Value
FV = Future Value
r = Discount Rate
n = Number of periods
In this case, the future value is $10,000, and the number of periods is 10. We need to calculate the present value for four different discount rates: 6%, 9%, 12%, and 15%.
a. For a discount rate of 6%:
PV = $10,000 / (1 + 0.06)^10
Using a calculator:
PV = $10,000 / (1.06)^10
PV ≈ $5,861.83
b. For a discount rate of 9%:
PV = $10,000 / (1 + 0.09)^10
Using a calculator:
PV = $10,000 / (1.09)^10
PV ≈ $4,258.35
c. For a discount rate of 12%:
PV = $10,000 / (1 + 0.12)^10
Using a calculator:
PV = $10,000 / (1.12)^10
PV ≈ $3,172.29
d. For a discount rate of 15%:
PV = $10,000 / (1 + 0.15)^10
Using a calculator:
PV = $10,000 / (1.15)^10
PV ≈ $2,438.67
The present values for the different discount rates are approximately:
a. $5,861.83
b. $4,258.35
c. $3,172.29
d. $2,438.67
Therefore, the present value of a $10,000 investment received at the end of year 10 is different for each discount rate specified.