91Ó°ÊÓ

You are considering the purchase of an old fire station, which you plan to convert to an indoor playground. The fire station can be purchased for \(\$ 200,000\), and the playground will generate lifetime profits (excluding the cost of the building) of \(\$ 700,000\). (Assume that those profits are all realized one year after opening.) However, there is a \(20 \%\) chance that the city council will rezone the district to exclude establishments such as yours; a hearing is scheduled for the coming year, and if your building is rezoned, your profit will be zero. Assume that there is no other building currently under consideration. a. Assume an interest rate of \(10 \% .\) Calculate the net present value of opening the playground today. Note that the cost of purchasing the building today is certain, but the benefits are uncertain. b. Calculate the net present value today of opening the playground in one year, after the zoning issues have been decided. Note that the benefits of opening the playground are uncertain today, but will be certain in one year. c. Based on your answers to (a) and (b), should you open the playground today, or should you wait until the zoning commission reaches its decision?

Step by step solution

01

Calculate Probability-Weighted Future Profits

The potential profits from the playground are \(700,000, with a 20% chance of rezoning which would result in \)0. Therefore, expected future profits can be calculated as \( 0.8 \times 700,000 + 0.2 \times 0 = 560,000 \).

02

Calculate NPV of Profits from Opening Today

The relevant amount to discount to present value is the expected future profit of $560,000. Using the formula \( NPV = \frac{C}{(1 + r)^n} \), where \( C = 560,000 \), \( r = 0.1 \), \( n = 1 \), the NPV is \( \frac{560,000}{1.1} = 509,091 \).

03

Calculate NPV of Initial Investment Today

The immediate cost to purchase the building is $200,000, so the net present value today by opening the playground today is \( 509,091 - 200,000 = 309,091 \).

04

NPV Calculation if Opening in One Year

If rezoning decisions are postponed by one year, the decision to open then will be based on certainty. If allowed, profits are $700,000. The NPV then is \( \frac{700,000}{1.1} = 636,364 \) with a certainty of realizing these profits since rezoning outcomes become clear prior to opening.

05

Conclusion Based on NPV

Comparing current opportunities, the NPV today ($309,091) is less than the NPV in one year ($636,364). Therefore, it is financially more beneficial to wait until the rezoning decision is made.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Expected Future Profits

Expected future profits are a crucial concept when evaluating potential investments. They provide an estimate of the earnings a business or project is likely to generate over time. This estimation is often adjusted for the probability of different outcomes. In our example, the playground has potential profits of \(700,000, with a 20% risk of earning nothing due to rezoning changes. To calculate this, we use probability-weighted averages:

• 80% chance of making \)700,000 if the area isn't rezoned.
• 20% chance of earning $0 if rezoning occurs.

By multiplying each profit figure by its probability and summing the results, we find the expected future profit: \[ 0.8 \times 700,000 + 0.2 \times 0 = 560,000. \] This calculation aids investors in estimating what can realistically be expected from the project given the risks involved.

Interest Rate's Role in Evaluating Investments

Interest rates are a key element in financial decision-making. They help determine the present value of future cash flows, which allows investors to make apples-to-apples comparisons between financial decisions made today and potential benefits realized later. Lower interest rates typically increase present values, making future cash flows more attractive, whereas higher rates do the opposite.Using the Net Present Value (NPV) formula, we calculate the worth of future profits today:\[ NPV = \frac{C}{(1 + r)^n}. \] Here, \(C\) represents the expected future profit, \(r\) is the interest rate, and \(n\) is the number of years into the future the profit is realized. With a 10% interest rate and a one-year period, expected profits of $560,000 yield a present value:\[ \frac{560,000}{1.1} = 509,091. \] Using interest rates in this way helps investors understand how much future earnings are worth today and make informed decisions accordingly.

Managing Uncertainty in Investments

Uncertainty is an inherent part of investment, and managing it effectively is crucial for success. In any investment scenario like our indoor playground, uncertainties such as zoning changes pose significant financial risk. To manage this uncertainty, scenario analysis and probability-weighted calculations are essential. In our case, there's a 20% chance of rezoning leading to zero profit—a substantial uncertainty that needs to be factored into financial evaluations. By accounting for possible outcomes and their probabilities, investors can more accurately determine expected profits and mitigate the impacts of uncertainty. Having reliable data and a clear understanding of potential risks can greatly aid in dealing with uncertainties and making better investment decisions.

Impact of Financial Decision-Making

Financial decision-making involves determining the best course of action to maximize profitability while minimizing risks. With the fire station example, the decision hinges on whether to invest immediately or wait. NPV calculations become key: by comparing the present value of profits if invested today ($309,091) versus waiting a year for rezoning outcomes ($636,364), a decision can be made. In this case, waiting for rezoning decisions, which guarantees certainty, presents a much higher NPV. Effective financial decision-making considers not only the numbers but also broader factors like market conditions and risk appetite. This comprehensive view helps investors choose the best path forward while aligning with their financial goals and risk tolerance.