ABC corp. expects to receive $2000 per year for years and $3500 per year for the next 10 years. what is the percentage value of this 20 years cash flow? use an 7% discount rate

To calculate the present value of the cash flows, we need to discount each future cash flow back to its present value using the given discount rate of 7%.

Let's calculate the present value of the first set of cash flows, which is $2000 per year for 10 years.

Step 1: Calculate the present value factor (PVF) for each year using the formula:

PVF = 1 / (1 + r)^n

where:
- r is the discount rate (7% or 0.07 in decimal form), and
- n is the year.

For example, the PVF for year 1 would be:

PVF1 = 1 / (1 + 0.07)^1 = 0.9346 (rounded to four decimal places)

Similarly, the PVF for year 2 would be:

PVF2 = 1 / (1 + 0.07)^2 = 0.8734 (rounded to four decimal places)

We repeat this process for each year.

Step 2: Multiply each cash flow by its corresponding present value factor and sum them up to get the total present value:

PV1 = $2000 * PVF1
PV2 = $2000 * PVF2
...
PV10 = $2000 * PVF10

Total present value of the first set of cash flows = PV1 + PV2 + ... + PV10

Once we have the total present value for the first set of cash flows, we can move on to calculating the present value of the second set of cash flows, which is $3500 per year for 10 years.

Step 3: Repeat the steps above to calculate the present value of the second set of cash flows:

PV11 = $3500 * PVF11
PV12 = $3500 * PVF12
...
PV20 = $3500 * PVF20

Total present value of the second set of cash flows = PV11 + PV12 + ... + PV20

Finally, to calculate the percentage value of the cash flows over 20 years, we need to divide the total present value by the initial cash flows and multiply by 100:

Percentage value = (Total present value / (10 * $2000 + 10 * $3500)) * 100

Note: This calculation assumes that the cash flows occur at the end of each year.

To calculate the percentage value of the cash flow, we will use the concept of present value.

First, we need to find the present value of each cash flow at a discount rate of 7%.

For the first cash flow of $2000 per year for 10 years, we can use the formula for the present value of an ordinary annuity:

PV = P * [(1 - (1 + r)^-n) / r]

Where:
PV = Present Value
P = Payment per period
r = Discount rate
n = Number of periods

Using the values:
P = $2000
r = 7% or 0.07 (decimal)
n = 10

PV = $2000 * [(1 - (1 + 0.07)^-10) / 0.07]
PV = $2000 * [(1 - 0.5084) / 0.07]
PV = $2000 * (0.4916 / 0.07)
PV = $2000 * 7.0233
PV = $14,046.60 (rounded to 2 decimal places)

For the second cash flow of $3500 per year for 10 years, we can use the same formula:

P = $3500
r = 7% or 0.07 (decimal)
n = 10

PV = $3500 * [(1 - (1 + 0.07)^-10) / 0.07]
PV = $3500 * [(1 - 0.5084) / 0.07]
PV = $3500 * (0.4916 / 0.07)
PV = $3500 * 7.0233
PV = $24,576.55 (rounded to 2 decimal places)

Next, we need to sum the present values of both cash flows:

Total PV = $14,046.60 + $24,576.55
Total PV = $38,623.15

Finally, to calculate the percentage value of the cash flow, we divide the total present value by the sum of the original cash flows and multiply by 100:

Percentage Value = (Total PV / (Cash Flow 1 + Cash Flow 2)) * 100
Percentage Value = ($38,623.15 / ($2000 * 10 + $3500 * 10)) * 100
Percentage Value = ($38,623.15 / ($20,000 + $35,000)) * 100
Percentage Value = ($38,623.15 / $55,000) * 100
Percentage Value = 70.22% (rounded to 2 decimal places)

Therefore, the percentage value of the 20 years cash flow is approximately 70.22%.