Question

Irving owns a chain of movie theaters. He is considering whether he should build a new theater downtown. The expected rate of return is 15 percent per year. IIe can borrow moncy at a 12 percent interest rate to finance the project. Should Irving proceed with this project? a. Yes. b. No.

Short answer

a. Yes.

Step-by-step solution

Understanding Key Terms

First, identify the key elements. The expected rate of return is 15% and the interest rate for borrowing money is 12%.

Comparing Rates

Compare the expected rate of return (15%) against the borrowing interest rate (12%).

Decision Criterion

If the expected rate of return (15%) is greater than the borrowing rate (12%), the project is generally considered profitable.

Conclusion

Since 15% (expected rate of return) is greater than 12% (interest rate), it is financially beneficial for Irving to proceed with building the new theater.

Key concepts

Expected Rate of Return

The expected rate of return is a prediction of the profitability anticipated from an investment. In simpler terms, it tells investors how much profit they can expect over a period compared to the amount invested. For Irving, the theater's expected rate of return is 15%. This percentage indicates he can expect an annual profit that is 15% of the initial investment in his new theater.

Understanding the expected rate of return helps potential investors to make informed decisions about where to allocate their resources. If the rate aligns with or exceeds their goals or the costs of financing an investment, it's considered favorable. A realistic estimation based on market analysis and past data ensures that the expected rate of return is both achievable and sustainable.

Calculate the expected return using this formula: \[ \text{Expected Rate of Return} = \frac{\text{Expected Profit}}{\text{Initial Investment}} \times 100 \]
This calculation allows Irving to clearly see the relationship between the profit he expects and the amount of money he invests.

Interest Rate Comparison

Interest rate comparison evaluates whether the costs associated with financing an investment are justified by its expected return. For Irving, this means comparing the 15% expected rate of return with the 12% interest rate on borrowed funds.

When deciding whether to push forward with a project, comparing these rates is crucial. If the expected rate of return exceeds the interest rate on loans, it usually signifies that the investment will produce enough profits to cover loan costs and generate additional income.

Here’s the simple comparison method:

• Expected Rate of Return: 15%
• Interest Rate on Loan: 12%

Since the expected rate of return is higher than the borrowing rate, Irving’s decision to build the theater can be justified. The higher return rate implies that the theater will likely bring in more revenue than the cost of financing.

Profitability Analysis

Profitability analysis helps in assessing whether an investment will be successful in generating financial gain. By analyzing profitability, Irving can determine if building the new theater is a good business move.

Irving's analysis involves looking at the difference between the expected rate of return and the interest rate. With a 15% expected rate of return and a 12% loan interest rate, the project holds a 3% profit margin.

Profitability can be analyzed using the formula:\[ \text{Profitability Margin} = \text{Expected Rate of Return} - \text{Interest Rate} \]In this case, \[ \text{Profitability Margin} = 15\% - 12\% = 3\% \]
This margin means that Irving should expect a 3% gain after covering the loan interest. For investors, a positive profitability margin like this signifies a feasible and worthwhile investment. Factors such as market conditions, economic trends, and operational costs must also be considered to get a comprehensive view of profitability. However, as it stands, Irving's decision to construct the new theater is justified by positive profitability analysis.