6. You are scheduled to pay a $350 cash flow in one year, and receive a $1,000 cash flow in years 3 and 4. If interest rates are 10 percent per year, what is the combined present value of these cash flows?
PV = 350(1.1)^-1 + 1000(1.1)^-3 + 1000(1.1)^-4
=
Ah, the art of cash flows and interest rates! You want to know the combined present value of these cash flows? Well, buckle up, my friend, because here's the deal:
To find the present value, we need to discount each cash flow back to the present using the interest rate of 10 percent per year. So let's crunch some funny numbers!
The present value of the $350 cash flow in one year, when discounted at 10 percent, is approximately $318.18. (I'm not a math genius, just a hilarious bot!)
Now, the $1,000 cash flow in years 3 and 4 needs a bit more work. We have to bring those future cash flows back to the present. The present value of $1,000 in year 3, discounted at 10 percent, is around $751.31. For year 4, it's approximately $683.01.
Now, to find the combined present value, simply add up all those present values:
$318.18 + $751.31 + $683.01 = $1,752.50
Ta-da! The combined present value of these cash flows is approximately $1,752.50. Remember, humor and financial calculations make a great pair!
To calculate the combined present value of these cash flows, we need to discount each cash flow at the given interest rate. Here are the steps:
1. Let's start by finding the present value of the $350 cash flow in year 1. Since it is due in one year, the discount rate will be applied once:
PV1 = CF1 / (1 + r)n
PV1 = $350 / (1 + 0.10)^1
PV1 = $350 / 1.10
PV1 = $318.18
2. Next, let's find the present value of the $1,000 cash flow in year 3. Since it is due in three years, the discount rate will be applied three times:
PV3 = CF3 / (1 + r)n
PV3 = $1,000 / (1 + 0.10)^3
PV3 = $1,000 / (1.10)^3
PV3 = $751.31
3. Similarly, let's find the present value of the $1,000 cash flow in year 4. Since it is due in four years, the discount rate will be applied four times:
PV4 = CF4 / (1 + r)n
PV4 = $1,000 / (1 + 0.10)^4
PV4 = $1,000 / (1.10)^4
PV4 = $683.01
4. Finally, to find the combined present value, we sum up the present values of each cash flow:
Combined PV = PV1 + PV3 + PV4
Combined PV = $318.18 + $751.31 + $683.01
Combined PV = $1,752.50
Therefore, the combined present value of these cash flows is $1,752.50.
To calculate the present value of each cash flow, we need to discount them back to their present value using the interest rate. The present value formula is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of years.
For the first cash flow of $350 in one year, the present value would be calculated as follows:
PV1 = $350 / (1 + 0.10)^1 = $350 / (1.10) = $318.18
For the second and third cash flows of $1,000 in years 3 and 4, the present value would be calculated as follows:
PV2 = $1,000 / (1 + 0.10)^3 = $1,000 / (1.10^3) = $751.31
PV3 = $1,000 / (1 + 0.10)^4 = $1,000 / (1.10^4) = $683.01
To find the combined present value, we sum up the individual present values:
Combined PV = PV1 + PV2 + PV3 = $318.18 + $751.31 + $683.01 = $1,752.50
Therefore, the combined present value of these cash flows is $1,752.50.