Calculate the total present value today (to 2 decimal places) of the following cash flows:
$300 due in 2 years from today
$1,000 due in 5 years from today
$200 due in 15 years from today
Use an interest rate of 12% per annum.
i=0.12
use
P=F*(P/F,i,n)=F/((1+i)^n)
P1=-300/(1.12^3)=213.53
P2=-1000/(1.12^5)=567.43
P3=-200/(1.12^15)=36.54
(negative because money is due in the future)
P=P1+P2+P3 [present value]
P1=-300/(1.12^3)=-213.53
P2=-1000/(1.12^5)=-567.43
P3=-200/(1.12^15)=-36.54
(negative because money is due in the future)
To calculate the total present value, we need to discount each cash flow to its present value. The present value is the value of a future cash flow in terms of today's dollars, taking into account the time value of money.
In this case, we will use an interest rate of 12% per annum to discount the cash flows.
To calculate the present value of each cash flow:
1. $300 due in 2 years from today:
PV1 = $300 / (1 + 0.12)^2
2. $1,000 due in 5 years from today:
PV2 = $1,000 / (1 + 0.12)^5
3. $200 due in 15 years from today:
PV3 = $200 / (1 + 0.12)^15
Now, let's calculate the present value of each cash flow:
PV1 = $300 / (1 + 0.12)^2
= $300 / (1.12)^2
= $300 / 1.2544
≈ $239.04
PV2 = $1,000 / (1 + 0.12)^5
= $1,000 / (1.12)^5
= $1,000 / 1.7623
≈ $567.85
PV3 = $200 / (1 + 0.12)^15
= $200 / (1.12)^15
= $200 / 4.1384
≈ $48.32
Finally, to calculate the total present value, we sum up the present values of each cash flow:
Total Present Value = PV1 + PV2 + PV3
≈ $239.04 + $567.85 + $48.32
≈ $855.21
Therefore, the total present value of the cash flows is approximately $855.21.
To calculate the total present value of future cash flows, we need to discount each cash flow back to today's value using the given interest rate. The formula to calculate the present value of a future cash flow is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the future cash flow, r is the interest rate, and n is the number of years in the future.
Let's calculate the present value for each cash flow and then sum them up to find the total present value:
1. $300 due in 2 years from today:
PV1 = $300 / (1 + 0.12)^2
= $300 / (1.12)^2
= $300 / 1.2544
≈ $239.09
2. $1,000 due in 5 years from today:
PV2 = $1,000 / (1 + 0.12)^5
= $1,000 / (1.12)^5
= $1,000 / 1.7623
≈ $567.43
3. $200 due in 15 years from today:
PV3 = $200 / (1 + 0.12)^15
= $200 / (1.12)^15
= $200 / 5.2137
≈ $38.34
Now, let's sum up the present values to find the total present value:
Total PV = PV1 + PV2 + PV3
= $239.09 + $567.43 + $38.34
≈ $844.86
Therefore, the total present value of the given cash flows, to 2 decimal places, is approximately $844.86.