Question

Suppose that Apple and the investors buying the firm's bonds both expect a 2 percent inflation rate for the year. Given this expectation, suppose the nominal interest rate on the bonds is 6 percent and the real interest rateis 4 percent. Suppose that a year after the investors purchase the bonds, the inflation rate turns out to be 6 percent, rather than the 2 percent that had been expected. Who gains and who loses from the unexpectedly high inflation rate?

Short answer

The investors lose because of the reduced purchasing power of the money returned on their investment. Apple gains as they repay their debt with money that is worth less due to the increased inflation.

Step-by-step solution

Understand the concept

Understand the relationship between nominal interest rate, real interest rate and inflation rate. The nominal interest rate is sum of expected inflation rate and the real interest rate. It's given by the Fisher Equation: \(i = r + π\), where \(i\) is the nominal interest rate, \(r\) is the real interest rate, and \(π\) is inflation rate.

Find the expected nominal return

The expected nominal return on the bond is the nominal interest rate which is 6 percent according to the problem.

Calculate the actual inflation and real return

The actual inflation turned out to be 6 percent which is higher than the expected 2 percent. That means, the investors expected 4 percent as their real return, \(i - π = 6% - 2% = 4%\). But due to unexpected inflation, their real return ended up being less, \(i - π = 6% - 6% = 0%\). In essence, the real money returned has lower purchasing power than expected.

Determine who gains or loses

Higher than expected inflation leads to a reduction in the purchasing power of money returned on investment. The investors who purchased the company's bonds have therefore lost from the unexpectedly high inflation rate. Conversely, Apple who owes money to the investors in the form of bonds is now able to pay back the borrowed amount with money that is 'worth less', so Apple stands to gain from the unexpectedly high inflation.

Key concepts

Nominal Interest Rate

The nominal interest rate is the advertised or stated interest rate on a financial instrument, such as a bond or a loan. It is the percentage at which money invested or borrowed grows, regardless of any changes in the purchasing power of that money. Nominal interest rate doesn't account for inflation, which is crucial when assessing the actual earnings or cost.

In the exercise scenario, the nominal interest rate is given as 6%. This means that investors were promised this rate of return on the bonds they purchased from Apple. However, this rate is based on expectations about future inflation. If inflation turns out to be different from expected, the actual value of the returns can vary significantly.

• Represents the money growth rate.
• Not adjusted for inflation.
• Simple calculation: no consideration of purchasing power changes.

This makes it essential for investors to also consider the potential impact of inflation when evaluating investment opportunities, as it helps determine real economic returns.

Real Interest Rate

Real interest rate reflects the true, inflation-adjusted return on an investment or cost of a loan. It's an important concept because it provides a clearer picture of the actual gain or loss of purchasing power over time. Calculating the real interest rate helps in understanding the true cost of borrowing or the true yield on an investment.

The formula to find the real interest rate is given by subtracting the inflation rate from the nominal interest rate. However, in practice, it may be adjusted for other factors, but its primary purpose is to show how much more we get after considering inflation.

• Real interest rate = Nominal interest rate - Inflation rate.
• Takes into account the erosion of purchasing power.
• Offers a more accurate measure of financial health.

In the provided exercise, the expected real interest rate was 4%, calculated by subtracting the anticipated inflation (2%) from the nominal interest rate (6%). However, actual inflation at 6% resulted in a real return of 0%, showing the devastating impact unexpected inflation can have on real returns.

Fisher Equation

The Fisher Equation is a fundamental equation in finance that connects nominal interest rates, real interest rates, and inflation expectations. This equation is named after economist Irving Fisher, who introduced the relationship as a way to understand the effects of inflation on interest rates.

The equation is expressed as:\[i = r + \pi\]Where:

• \(i\) is the nominal interest rate,
• \(r\) is the real interest rate, and
• \(\pi\) is the inflation rate.

The Fisher Equation helps in re-evaluating investments whenever there is a shift in inflation expectations or actual inflation outcomes, ensuring a deeper understanding of real returns and borrowing costs.

In the context of the exercise, the Fisher Equation was used to illustrate the scenario when expected inflation was 2%. With a nominal rate of 6%, the investors expected a real return of 4%. When inflation unexpectedly rose to 6%, the equation demonstrated why the real return dropped to 0%, showing Apple gaining and bond investors losing due to increased inflation.