Question

Paolo currently has $\mathrm{\$}100,000$ invested in bonds that earn him 4 percent interest per year. He wants to open a pizza restaurant and is considering either selling the bonds and using the $\mathrm{\$}100,000$ to start his restaurant or borrowing $\mathrm{\$}100,000$ from a bank, which would charge him an annual interest rate of 6 percent. He finally decides to sell the bonds and not take out the bank loan. He reasons: "Because I already have the $\mathrm{\$}100,000$ invested in the bonds, I don't have to pay anything to use the money. If I take out the bank loan, I have to pay interest, so my costs of producing pizza will be higher if I take out the loan than if I sell the bonds." Evaluate Paolo's reasoning.

Short answer

Paolo's reasoning is incorrect as it ignores the concept of opportunity cost. Even though he doesn't pay interest when he sells his bonds, he forgoes the interest he could have earned, which amounts to an opportunity cost. Hence, using the $\$100,000$ from bonds is not free. The cost of selling his bonds is the lost interest, $\$4,000$, which he would not be receiving.

Step-by-step solution

Concept of Opportunity Cost

The opportunity cost is the cost of forgoing the next best alternative when a decision is made. In this case, $\$100,000$ invested in bonds provides an opportunity cost. The opportunity cost of using $\$100,000$ from the invested bonds to start the pizza restaurant is the foregone 4% interest per year.

Calculate Yearly Returns from Bonds

If Paolo does not sell the bonds, he will earn an interest of 4% per annum. Therefore, interest earned per year from the bond would be $4\mathrm{\%}\times \$100,000=\$4,000$.

Calculate Yearly Interest for the Bank Loan

If Paolo decides to borrow $\$100,000$ from the bank, he would be charged an annual interest rate of 6%. The yearly interest would amount to $6\mathrm{\%}\times \$100,000=\$6,000$.

Compare the costs

If Paolo starts the restaurant by selling his bonds, he misses out on earning the annual interest of $\$4,000$. If he starts the restaurant with the bank loan, he has to pay $\$6,000$ in interest. Although he doesn't pay anything explicitly when he sells the bonds, his actual cost due to lost interest is $\$4,000$. He would pay $\$6,000$ if he took out the bank loan. While the cost of taking the bank loan seems higher, the opportunity cost of using his own money is not zero, as Paolo initially thought.

Key concepts

Interest Rates

Interest rates are a fundamental economic factor influencing individual and business decisions on savings and investments. Concerning Paolo’s situation, interest rates affect his choice between utilizing the funds he has in bonds or taking out a loan for his restaurant venture.

Interest earned from bonds is a type of passive income that accrues over time without active involvement. Paolo’s bonds yield a 4% return, causing a conflict when compared to the 6% he would owe on a bank loan. This variance in rates is pivotal; it illustrates a cost consideration that impacts his net earnings and the feasibility of his business plan.

Through understanding the weight of interest rates, we can see how they incentivize or discourage debt and savings. In Paolo’s case, because the interest on the loan is higher than the earnings from the bond, it constitutes a significant factor in determining the lower-cost option for financing his restaurant.

Investment Decision-Making

When Paolo decides to sell his bonds and use the liquidity to finance his venture, he's making a crucial investment decision. Investment decision-making involves comparing potential returns and associated risks of different options.

The certainty of a 4% return competes with the uncertain profit margin of a new restaurant business. For a calculated investor, a risk assessment of the new business’s potential profitability versus the guaranteed bond yield is critical.

An aspect of investment decision-making that Paolo seems to overlook is the concept of leveraging. Taking on debt, such as a bank loan, can potentially amplify the returns of an investment if the business generates profit higher than the cost of borrowing. Nevertheless, this comes with increased risk, which must be thoroughly weighed against the potential rewards.

Economic Reasoning

Economic reasoning involves making decisions based on cost-benefit analysis, marginal analysis, and the evaluation of opportunity costs. Paolo initially fails to apply sound economic reasoning, disregarding the 4% interest from his bonds as a cost.

In economic terms, every choice made has an opportunity cost—the benefit you miss out on when choosing an alternative. Paolo’s oversight is in not recognizing that by using his own money, he forgoes the 4% interest he would otherwise earn. This represents the opportunity cost of his investment into the restaurant.

Applying solid economic reasoning would require Paolo to assess not just the out-of-pocket costs but also the implicit costs, such as the opportunity cost of his bonds. While the loan appears more expensive due to the higher interest rate, it's imperative to consider all variables—including foregone income—to make an informed decision that accurately weighs the true cost against potential benefits.