Question

The owner of a coffee shop has $1000 in debt, anthe current value of the coffee shop's assets is s900. thecurrent risk free interest rate is 10%. the owner 's oljective is to maximize the value of her equity in the shop, andshe is contemplating two different business strategis. let us label these strategies a and b.

under strategy a, sheplans to offer free coffee with any purchase of desert. her market research team informed her that this strategy will0 or $800 next year.

under strategy b, she would sell food alongincrease the value of the coffee shop either to $12with coffee. most restaurants fail and her market research team predicts that this strategy will increase the value ofthe coffee shop to either $4000 or $200.

which straiegy results in a higher equity value today?

Answer 1

To determine which strategy results in a higher equity value today, the owner needs to calculate the expected value of equity for each strategy. Equity is the value of assets minus the debt. Strategy B has a high-risk, high-reward scenario, but without specific probabilities or details about Strategy A, a definitive comparison cannot be made.

Step-by-step explanation:

The owner of the coffee shop is evaluating two different business strategies to maximize her equity in the coffee shop. With a debt of $1000 and assets currently valued at $900, the aim is to choose a strategy that provides the highest equity value today.

Equity is calculated as the value of the assets minus any debt owed. Assuming the risk-free rate is 10%, under Strategy A, no details are given, but under Strategy B, the coffee shop would start selling food and the outcomes are either a value increase to $4000 or a decrease to $200.

With Strategy B, we can calculate the expected value of the equity by considering the probabilities of success and failure provided by her market research team. If the probabilities are not given, we would need that information to proceed, or we would simply take the average of the two potential outcomes. However, because the potential for loss ($200 in assets against $1000 in debt) could lead to negative equity, this strategy is riskier.

To compare both strategies, the owner would typically prefer the strategy that offers the higher expected value of equity, after considering the associated risks and factoring in the current risk-free interest rate.