91Ó°ÊÓ

Ricardo is considering purchasing an ostrich, which he can graze for free in his backyard. Once the ostrich reaches maturity (in exactly three years), Ricardo will be able to sell it for \(\$ 2,000\). The ostrich \(\operatorname{costs} \$ 1,500\) a. Suppose that interest rates are \(8 \% .\) Calculate the net present value of the ostrich investment. Does the NPV indicate that Ricardo should buy the ostrich? b. Suppose that Ricardo passes on the ostrich deal and invests \(\$ 1,500\) in his next-best opportunity: a safe government bond yielding \(8 \% .\) How much money will he have at the end of three years? Is this outcome better or worse than buying the ostrich? c. Calculate the net present value of the ostrich if interest rates are \(11 \% .\) Does the NPV method indicate that Ricardo should buy the ostrich? d. If Ricardo passes on the ostrich deal and invests in a government bond yielding \(11 \%,\) how much money will he have at the end of three years? Is this outcome better or worse than buying the ostrich? e. Based on your answers to (b) and (d), how well does the NPV method capture the concept of opportunityc ost?

Step by step solution

01

Calculate Future Ostrich Value Given

The future value of the ostrich once it reaches maturity and is sold is given as \( \$2000 \). This is the expected cash inflow that Ricardo will receive in 3 years.

02

Calculate Net Present Value with 8% Interest Rate

To calculate the Net Present Value (NPV) of the ostrich investment at an 8% interest rate, we use the NPV formula: \[ \text{NPV} = \frac{\text{Future Cash Flow}}{(1 + r)^n} - \text{Initial Investment} \] where \( r = 0.08 \) and \( n = 3 \). \[ \text{NPV} = \frac{2000}{(1 + 0.08)^3} - 1500 \] \[ \text{NPV} = \frac{2000}{1.2597} - 1500 \approx \frac{2000}{1.2597} - 1500\] \[ \approx 1587.65 - 1500 = 87.65 \] The NPV is \( \$87.65 \), which indicates Ricardo should buy the ostrich, as it's positive.

03

Calculate Future Value of Government Bond at 8% Yield

To find the future value of an investment in a government bond with an 8% yield, we use the future value formula: \[ \text{Future Value} = P \times (1 + r)^n \] where \( P = 1500 \), \( r = 0.08 \), and \( n = 3 \). \[ \text{Future Value} = 1500 \times (1+0.08)^3 \] \[ = 1500 \times 1.2597 = 1889.55 \] Ricardo will have \( \\(1889.55 \) from the bond, which is less than the \( \\)2000 \) from selling the ostrich, meaning the ostrich is a better option.

04

Calculate Net Present Value with 11% Interest Rate

Using the same NPV formula with an 11% interest rate, \( r = 0.11 \): \[ \text{NPV} = \frac{2000}{(1 + 0.11)^3} - 1500 \] \[ \text{NPV} = \frac{2000}{1.3676} - 1500 \] \[ \approx 1462.36 - 1500 = -37.64 \] The NPV is \( -\$37.64 \), which suggests Ricardo should not buy the ostrich, as it's negative.

05

Calculate Future Value of Government Bond at 11% Yield

Calculate the future value of the government bond with an 11% yield: \[ \text{Future Value} = 1500 \times (1 + 0.11)^3 \] \[ = 1500 \times 1.3676 = 2051.40 \] Ricardo will have \( \\(2051.40 \) from the bond, which is more than the \( \\)2000 \) from selling the ostrich. The bond is a better option.

06

Compare Outcomes and Opportunity Cost

Comparing the results: - At an 8% interest rate, the NPV indicates buying the ostrich is better because the future value of the bond is lower than the ostrich sale. - At an 11% interest rate, the NPV method correctly suggests not buying the ostrich since the bond offers a higher return. The NPV method effectively captures opportunity cost by comparing expected returns from alternative investments.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Opportunity Cost

Opportunity cost is a fundamental concept in economics and investment decision-making. It represents the value of the next best alternative forgone when choosing a particular action. In Ricardo's case, opportunity cost comes into play when he considers buying the ostrich or investing in a government bond.
- If Ricardo buys the ostrich, the opportunity cost is the potential return from the government bond he decides not to invest in. - At an 8% interest rate, the ostrich has a higher NPV, meaning the opportunity cost is worth it. - Conversely, at an 11% interest rate, the bond yields a better return compared to buying the ostrich.
Therefore, the NPV method serves as a useful tool in evaluating whether the benefits of an investment exceed its opportunity cost.

Interest Rate

Interest rates play a crucial role in determining the viability of investment options. They affect how we calculate the present value of future returns, an essential part of the Net Present Value (NPV) formula.
- Interest rates reflect the time value of money, indicating how much a sum of money is worth today versus in the future. - Higher interest rates generally decrease the NPV of future cash flows, making them less attractive.
For Ricardo, evaluating the ostrich investment at both 8% and 11% interest rates showed differing outcomes:
- At 8%, the ostrich was a good investment given the positive NPV. - At 11%, the NPV was negative, which made the bond a more appealing alternative.
Through this comparison, Ricardo can understand how varying interest rates impact his investment decisions.

Investment Decision

Investing successfully requires making informed decisions, often by comparing potential investment options using tools like Net Present Value (NPV).
- NPV helps determine whether an investment's future returns justify the initial expenditure. - Positive NPV means the investment should ideally be pursued, as it is expected to generate more value than its cost.
In the exercise, Ricardo faces an investment decision between an ostrich and a government bond:
- At 8% interest, the ostrich deal looks appealing with a positive NPV of $87.65, suggesting a profitable decision. - At 11% interest, the NPV becomes negative at -$37.64, signaling a bad investment choice.
Ultimately, investment decisions like Ricardo's rely on assessing these financial metrics to make effective choices.

Future Value

The concept of future value is essential for understanding how current investments grow over time. Future value helps indicate what a sum of money today will be worth in the future, considering growth factors like interest rates.
- Future Value Formula: \[ \text{Future Value} = P \times (1 + r)^n \] where \(P\) is the principal, \(r\) is the interest rate, and \(n\) is the number of periods.
In Ricardo's case, the future value of both the ostrich sale and bond investment reveals:
- Selling the ostrich in three years yields \\(2000. - Investing \\)1500 in a bond at an 8% rate provides \\(1889.55, less than the ostrich. - With an 11% rate, the bond's future value increases to \\)2051.40, exceeding the ostrich return.
Understanding these future value differences plays a critical role in helping Ricardo, and indeed all investors, make informed decisions.