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]
$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.
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]
P2=-1000/(1.12^5)=-567.43
P3=-200/(1.12^15)=-36.54
(negative because money is due in the future)
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
β $239.04
PV2 = $1,000 / (1 + 0.12)^5
= $1,000 / (1.12)^5
= $1,000 / 1.7623
β $567.85
PV3 = $200 / (1 + 0.12)^15
= $200 / (1.12)^15
= $200 / 4.1384
β $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
β $239.04 + $567.85 + $48.32
β $855.21
Therefore, the total present value of the cash flows is approximately $855.21.
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
β $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
β $567.43
3. $200 due in 15 years from today:
PV3 = $200 / (1 + 0.12)^15
= $200 / (1.12)^15
= $200 / 5.2137
β $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
β $844.86
Therefore, the total present value of the given cash flows, to 2 decimal places, is approximately $844.86.