To find the Internal Rate of Return (IRR) of Project B using discount rates of 17% and 18%, we'll proceed step by step. The IRR is the discount rate that makes the Net Present Value (NPV) of a project equal to zero. Here's how the calculation works:

Step 1: Formula for Net Present Value (NPV)

The NPV formula is:

$\text{NPV} = \sum \left( \frac{C_t}{(1 + r)^t} \right) - \text{Initial Investment}$

Where:

• $C_t$ is the cash flow at time $t$,
• $r$ is the discount rate (either 17% or 18%),
• $t$ is the time period (typically in years).

Step 2: Calculate the NPV at 17%

Let's denote the project's cash flows as follows (assuming they're provided):

• Initial investment (Year 0): $-C_0$,
• Year 1 cash flow: $C_1$,
• Year 2 cash flow: $C_2$,
• Year 3 cash flow: $C_3$, etc.

We'll calculate the NPV at a discount rate of 17% using these cash flows.

Step 3: Calculate the NPV at 18%

We repeat the same process but with a discount rate of 18%. The NPV will likely be different.

Step 4: Use Linear Interpolation to Estimate the IRR

Once we have the two NPVs (one at 17% and one at 18%), we can interpolate between these two values to estimate the IRR using the following formula:

$\text{IRR} = r_1 + \left( \frac{\text{NPV}_1}{\text{NPV}_1 - \text{NPV}_2} \right) \times (r_2 - r_1)$

Where:

• $r_1 = 17\%$,
• $r_2 = 18\%$,
• $\text{NPV}_1$ is the NPV at 17%,
• $\text{NPV}_2$ is the NPV at 18%.

To continue:

Please provide the specific cash flows for Project B so that I can complete the NPV calculations and determine the IRR precisely.

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Would you like to provide the cash flows for further analysis?

Related Questions:

1. What does a positive NPV indicate about a project's profitability?
2. How is the IRR different from the NPV method in project evaluation?
3. Why is linear interpolation used for estimating IRR?
4. What are the limitations of using only two discount rates in IRR calculation?
5. How do changes in cash flow patterns affect the calculation of IRR?

Tip: A higher discount rate reduces the present value of future cash flows, impacting NPV calculations.