suppose your firm is planning to invest in a project that will generate the following income stream:a negative flow $250000 per year for 5 years, a positive floww of $550000 in year 6, and a positive flow of $600000 per year in the year 7 through9. What is the present value of this income if the appropriate discount rate is 11% for the first 3 years and 12% threrafter?

To find the present value of the income stream, we need to discount each cash flow to its present value and then sum them up. The present value (PV) of a cash flow is calculated using the following formula:

PV = CF / (1 + r)^n

Where:
PV is the present value
CF is the cash flow
r is the discount rate
n is the number of periods

Let's calculate the present value of each cash flow step by step:

Step 1: Calculate the present value of the negative cash flow in year 1 to year 5:
The cash flow for the first 5 years is -$250,000. Since the discount rate is 11% for the first 3 years, we'll use that rate for years 1 to 3. For years 4 and 5, we'll use the rate of 12%. The formula becomes:

PV1 = -$250,000 / (1 + 0.11)^1 (Year 1)
PV2 = -$250,000 / (1 + 0.11)^2 (Year 2)
PV3 = -$250,000 / (1 + 0.11)^3 (Year 3)
PV4 = -$250,000 / (1 + 0.12)^4 (Year 4)
PV5 = -$250,000 / (1 + 0.12)^5 (Year 5)

Step 2: Calculate the present value of the positive cash flow in year 6:
The cash flow in year 6 is $550,000. We'll use the rate of 12% for this year.
PV6 = $550,000 / (1 + 0.12)^6

Step 3: Calculate the present value of the positive cash flows in year 7 to year 9:
The cash flow for years 7 to 9 is $600,000 each year. We'll also use the rate of 12% for these years.
PV7 = $600,000 / (1 + 0.12)^7
PV8 = $600,000 / (1 + 0.12)^8
PV9 = $600,000 / (1 + 0.12)^9

Step 4: Sum up all the present values to find the total present value:
Total PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9
= PV1 + PV2 + PV3 + PV4 + PV5 + PV6 + PV7 + PV8 + PV9

Now, let's substitute the values into the formulas and calculate the present value.