Question

A firm is considering three possible one-year investments, which we will name \(X, Y,\) and \(Z\) .Investment X would cost \(\$ 10\) million now and would return \(\$ 11\) million next year, for a net gain of \(\$ 1\) million. .Investment Y would cost \(\$ 100\) million now and would return \(\$ 105\) million next year, for a net gain of \(\$ 5\) million. Investment Z would cost \(\$ 1\) million now and would return \(\$ 1.2\) million next year, for a net gain of \(\$ 200,000\) The firm currently has \(\$ 150\) million of cash on hand that it can loan out at 15 percent interest. Which of the three possible investments should it undertake? a. X only. b. Y only. c. Z only. d. X and Y. e. X and Z. f. X, Y, and Z.

Short answer

The firm should choose Investment Z only (answer c).

Step-by-step solution

Calculate Opportunities Lost by Not Loaning Money

If the firm loans out the money at a 15% interest rate, it will earn a return of 15% on any amount. Calculate the interest earned if the \\( 150\\) million is loaned out:\[150,000,000 \times 0.15 = 22,500,000\]This means if the firm loans out the entire \\( 150\\) million, they earn \\( 22.5\\) million in interest for the year.

Evaluate the Return for Each Investment

Now, calculate the return rates for investments X, Y, and Z,- **Investment X:** Net gain of \\( 1\\) million on \\( 10\\) million. Percentage Gain = \( \frac{1,000,000}{10,000,000} \times 100 = 10\% \)- **Investment Y:** Net gain of \\( 5\\) million on \\( 100\\) million. Percentage Gain = \( \frac{5,000,000}{100,000,000} \times 100 = 5\% \)- **Investment Z:** Net gain of \\( 200,000\\) on \\( 1\\) million. Percentage Gain = \( \frac{200,000}{1,000,000} \times 100 = 20\% \)

Compare Investment Returns with Loaning Money

Compare each investment's percentage gain with the 15% interest from loaning out the money: - **Investment X** has a return of 10%, which is less than 15%. - **Investment Y** has a return of 5%, which is less than 15%. - **Investment Z** has a return of 20%, which is greater than 15%.

Determine the Optimal Investment Decision

Since Investment Z offers the highest return (20%), which is greater than the 15% interest from loaning out the money, they should select Investment Z over loaning. However, Investments X and Y both have lower returns than the loan option. Choosing X and Y would be less optimal compared to loaning out that portion of money.

Key concepts

Opportunity Cost

Opportunity cost is an essential concept in decision-making, especially when it involves investments. Think of opportunity cost as the benefits you miss out on when choosing one option over another. In the given scenario, the firm must decide whether to invest in projects X, Y, or Z, or simply lend out the money at a 15% interest rate. The opportunity cost of choosing an investment over lending out money is the interest they would have earned.
By understanding opportunity cost, firms can make informed choices. They compare the potential gains from an investment against the guaranteed returns from alternative options, like lending the money. This helps in maximizing profits and minimizing wasted resources.

Interest Rates

Interest rates play a crucial role in investment decision-making. They represent the cost of borrowing money or the gain from lending it. In this case, the firm has an option to lend its capital at an interest rate of 15%.
This means that by not investing in any of the projects and instead fully lending its $150 million, the firm would earn $22.5 million over one year.

• If an investment yields a lower return than the interest rate, it's generally less attractive.
• Interest rates serve as a benchmark for evaluating alternative investments.

Lending can be seen as a risk-free alternative when compared to other potential investments, which might not offer similar resilience against market fluctuations.

Percentage Gain

Percentage gain is a simple yet profound metric used to evaluate the potential profitability of an investment. It is the ratio of the net gain on the investment to the initial cost, expressed as a percentage. This metric provides a direct comparison between the efficiency and effectiveness of various investments.

• For Investment X: - Net gain is $1 million on an initial $10 million, - It results in a 10% percentage gain.
• For Investment Y: - Net gain is $5 million on an initial $100 million, - This gives a 5% percentage gain.
• For Investment Z: - Net gain is $200,000 on an initial $1 million, - Resulting in a 20% percentage gain.

Using percentage gain, firms can determine which investments yield the highest profit relative to their cost, optimizing their overall capital efficiency.

Capital Allocation

Capital allocation refers to how a firm decides to deploy its available financial resources across various opportunities to maximize its returns. For the firm in question, determining the best capital allocation involves selecting from among the investments X, Y, Z, or opting to lend at 15% interest.
Effective capital allocation ensures that funds are utilized in a manner that generates the highest possible returns with acceptable levels of risk.

• Investment Z, with a 20% return, surpasses the loan's 15% return, making it a favorable choice.
• Investments X and Y, which are below the 15% threshold, might prove to be less optimal compared to lending.

Thus, the firm should allocate capital towards options offering the highest net benefit while adjusting for risk and opportunity cost.