A firm evaluates all of its projects by applying the IRR rule.

Year	Cash Flow
0	–$ 157,000
1	59,000
2	80,000
3	64,000
What is the project's IRR?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

If the required return is 15 percent, should the firm accept the project?

To calculate the project's Internal Rate of Return (IRR), we need to solve for the discount rate (r) that makes the Net Present Value (NPV) of the project's cash flows equal to zero. The formula for NPV is:

\[
\text{NPV} = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}
\]
where:
- $CF_t$ is the cash flow at time $t$,
- $r$ is the IRR we are trying to find,
- $t$ is the time period.

### Cash flows:
- $CF_0 = -157,000$
- $CF_1 = 59,000$
- $CF_2 = 80,000$
- $CF_3 = 64,000$

We need to solve the following equation for $r$ (IRR):

\[
0 = -157,000 + \frac{59,000}{(1+r)^1} + \frac{80,000}{(1+r)^2} + \frac{64,000}{(1+r)^3}
\]

This is a nonlinear equation and typically requires either trial-and-error or a financial calculator to solve. I'll calculate the IRR using numerical methods.

Let me compute that for you.The project's Internal Rate of Return (IRR) is approximately **13.82%**.

### Decision:
If the required return (also called the hurdle rate) is 15%, the project should **not** be accepted because the IRR (13.82%) is lower than the required return of 15%. 

Would you like more details or have any questions?

Here are 5 follow-up questions you might consider:
1. What are the implications of IRR being lower than the required return?
2. How does IRR compare with other investment evaluation metrics like NPV?
3. What happens if IRR equals the required return?
4. How would changing the required return affect the decision?
5. What is the relationship between IRR and risk?

**Tip:** IRR assumes all cash flows are reinvested at the same rate, which might not always be realistic. Consider the reinvestment rate assumption when using IRR for decision-making.

A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow 0 –$ 157,000 1 59,000 2 80,000 3 64,000 What is the project's IRR? If the required return is 15 percent, should the firm accept the project?

Learn how to calculate the Internal Rate of Return (IRR) for a project with an initial investment of $157,000 and cash flows over 3 years: $59,000, $80,000, and $64,000. This step-by-step solution demonstrates how to apply the IRR rule and whether the project should be accepted with a required return of 15%.

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