Compute the present value of a $100 cash flow for the following combinations of discount rates and times:
a. r = 8 percent. t = 10 years.
b. r = 8 percent. t = 20 years.
c. r = 4 percent. t = 10 years.
d. r = 4 percent. t = 20 years
To compute the present value of a cash flow, you need to use the present value formula. The formula is:
PV = CF / (1 + r)^t
Where:
PV = Present Value
CF = Cash Flow
r = Discount Rate
t = Time
Let's calculate the present value for each combination of discount rates and times:
a. r = 8 percent, t = 10 years
PV = 100 / (1 + 0.08)^10
b. r = 8 percent, t = 20 years
PV = 100 / (1 + 0.08)^20
c. r = 4 percent, t = 10 years
PV = 100 / (1 + 0.04)^10
d. r = 4 percent, t = 20 years
PV = 100 / (1 + 0.04)^20
Now, let's calculate the values:
a. r = 0.08 (8 percent), t = 10
PV = 100 / (1 + 0.08)^10
PV = 100 / (1.08)^10
PV ≈ $46.92
b. r = 0.08 (8 percent), t = 20
PV = 100 / (1 + 0.08)^20
PV ≈ $23.17
c. r = 0.04 (4 percent), t = 10
PV = 100 / (1 + 0.04)^10
PV ≈ $67.56
d. r = 0.04 (4 percent), t = 20
PV = 100 / (1 + 0.04)^20
PV ≈ $55.73
So, the present value for each combination of discount rates and times are as follows:
a. PV ≈ $46.92
b. PV ≈ $23.17
c. PV ≈ $67.56
d. PV ≈ $55.73