To determine the interest rate at which the company is indifferent between the two projects, we need to find the crossover rate, which is the discount rate at which the Net Present Values (NPVs) of the two projects are equal.

Steps to Solve:

1. Calculate the difference in cash flows between the two projects for each year.
2. Determine the NPV equation for the difference.
3. Solve for the discount rate where NPV = 0.

Here are the cash flow differences:

Year	Δ Cash Flow (Project I - Project J)
0	$ 0
1	$ 20,200
2	$ 5,400
3	$ (12,600)
4	$ (30,600)

Now we compute the discount rate that makes the NPV of these differences zero:

$0 = \sum \frac{\Delta \text{Cash Flow}}{(1 + r)^t}$

Expanding:

$0 = \frac{20,200}{(1 + r)^1} + \frac{5,400}{(1 + r)^2} - \frac{12,600}{(1 + r)^3} - \frac{30,600}{(1 + r)^4}$

Let me calculate this crossover rate. scipy.optimize import fsolve

Define the cash flow differences

cash_flows = [20200, 5400, -12600, -30600]

Function to calculate NPV for the difference in cash flows at a given rate

def npv_difference(rate): npv = 0 for t, cf in enumerate(cash_flows, start=1): npv += cf / (1 + rate) ** t return npv

Solve for the rate where the NPV is zero

crossover_rate = fsolve(npv_difference, 0.1)[0] # Initial guess of 10%

Convert the rate to a percentage

crossover_rate_percentage = crossover_rate * 100 crossover_rate_percentageThe crossover interest rate is 23.37%.

Which Project is Better if the Required Return is Above 23.37%?

• If the required return is above 23.37%, Project J is better because Project I's cash flows decline faster and would have a lower NPV at higher discount rates.

Let me know if you’d like detailed steps or further clarifications.

---

Follow-Up Questions:

1. How do we interpret the crossover rate in decision-making?
2. What assumptions are made when comparing NPVs of projects?
3. How would the analysis change if one project had an additional year of cash flows?
4. What methods besides NPV can be used to compare projects?
5. Why might a company prefer a project even if it has a lower NPV?

Tip: Understanding crossover rates can help compare mutually exclusive projects effectively when interest rates vary.