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?
I saw your post earlier, but was not sure of your use of the phrase "discount rate" as it is used in the US (I am in Canada), so I am taking a guess that all we have is a standard compound interest problem
I will do the first one, if you think the solution is correct, do the others the same way
a) PV = 10000(1.06)^-10 = $ 5583.95
check:
if I invest 5583.95 at 6% per annum compouded annually for 10 years, I will have
5583.95(1.06)^10 = 5583.95(1.790847697) = 10000.00
To determine the present value of the $10,000 investment, we can use the formula for calculating the present value of a future amount:
Present Value = Future Value / (1 + Discount Rate)^Number of Periods
a. Discount rate: 6 percent
Number of periods: 10 years
Present Value = $10,000 / (1 + 0.06)^10
Present Value = $10,000 / (1.06)^10
Present Value ≈ $5,993.84
b. Discount rate: 9 percent
Number of periods: 10 years
Present Value = $10,000 / (1 + 0.09)^10
Present Value = $10,000 / (1.09)^10
Present Value ≈ $4,550.50
c. Discount rate: 12 percent
Number of periods: 10 years
Present Value = $10,000 / (1 + 0.12)^10
Present Value = $10,000 / (1.12)^10
Present Value ≈ $3,604.78
d. Discount rate: 15 percent
Number of periods: 10 years
Present Value = $10,000 / (1 + 0.15)^10
Present Value = $10,000 / (1.15)^10
Present Value ≈ $2,758.42
Therefore, the present value of the $10,000 investment received at the end of year 10 is approximately:
a. $5,993.84 at a 6 percent discount rate
b. $4,550.50 at a 9 percent discount rate
c. $3,604.78 at a 12 percent discount rate
d. $2,758.42 at a 15 percent discount rate.
To determine the present value of a future cash flow, you need to use the formula for calculating the present value of a single amount. The formula is:
PV = FV ÷ (1 + r)^n
Where:
PV = Present value
FV = Future value
r = Discount rate
n = Number of periods
Let's calculate the present value for each of the given discount rates:
a. Discount rate of 6 percent:
PV = 10,000 ÷ (1 + 0.06)^10
PV = 10,000 ÷ 1.79084797
PV ≈ $5,583.04
b. Discount rate of 9 percent:
PV = 10,000 ÷ (1 + 0.09)^10
PV = 10,000 ÷ 2.36736913
PV ≈ $4,218.38
c. Discount rate of 12 percent:
PV = 10,000 ÷ (1 + 0.12)^10
PV = 10,000 ÷ 3.10585397
PV ≈ $3,223.24
d. Discount rate of 15 percent:
PV = 10,000 ÷ (1 + 0.15)^10
PV = 10,000 ÷ 3.88969262
PV ≈ $2,572.57
Therefore, the present value for each discount rate is approximately:
a. $5,583.04
b. $4,218.38
c. $3,223.24
d. $2,572.57