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
an EXCEL spreadsheet is very useful for these types of calculations.
PV = sum[ 100./((1.+r)^i) ]
where i goes from 1 to t.
take it from here.
dghew
To compute the present value of a cash flow, you can use the formula:
Present Value = Cash Flow / (1 + Discount Rate) ^ Time
Let's calculate the present value for each combination of discount rates and times:
a. r = 8 percent, t = 10 years
Present Value = $100 / (1 + 0.08) ^ 10
Present Value = $46.65 approximately
b. r = 8 percent, t = 20 years
Present Value = $100 / (1 + 0.08) ^ 20
Present Value = $30.17 approximately
c. r = 4 percent, t = 10 years
Present Value = $100 / (1 + 0.04) ^ 10
Present Value = $67.56 approximately
d. r = 4 percent, t = 20 years
Present Value = $100 / (1 + 0.04) ^ 20
Present Value = $54.29 approximately
Therefore, the present value of a $100 cash flow for the given combinations of discount rates and times are approximately:
a. $46.65
b. $30.17
c. $67.56
d. $54.29
To compute the present value of a cash flow, you need to use the formula for present value. The formula for present value is:
PV = CF / (1 + r)^t
where PV is the present value, CF is the cash flow, r is the discount rate, and t is the time in years.
Now, let's calculate the present value for each combination:
a. For r = 8 percent and t = 10 years:
PV = 100 / (1 + 0.08)^10
= 100 / (1 + 0.08)^10
= 100 / (1.08)^10
≈ 46.26
So, the present value of a $100 cash flow, with a discount rate of 8 percent and a time of 10 years, is approximately $46.26.
b. For r = 8 percent and t = 20 years:
PV = 100 / (1 + 0.08)^20
= 100 / (1 + 0.08)^20
= 100 / (1.08)^20
≈ 21.73
So, the present value of a $100 cash flow, with a discount rate of 8 percent and a time of 20 years, is approximately $21.73.
c. For r = 4 percent and t = 10 years:
PV = 100 / (1 + 0.04)^10
= 100 / (1 + 0.04)^10
= 100 / (1.04)^10
≈ 67.56
So, the present value of a $100 cash flow, with a discount rate of 4 percent and a time of 10 years, is approximately $67.56.
d. For r = 4 percent and t = 20 years:
PV = 100 / (1 + 0.04)^20
= 100 / (1 + 0.04)^20
= 100 / (1.04)^20
≈ 45.26
So, the present value of a $100 cash flow, with a discount rate of 4 percent and a time of 20 years, is approximately $45.26.