Book cover for The Economics of Money, Banking, and Financial Markets

The Economics of Money, Banking, and Financial Markets

Frederic S. Mishkin

ISBN #9780132770248

10th Edition

610 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section provides a comprehensive overview of how interest rates affect the valuation of various debt instruments through the concept of present value. It details methods for calculating yield to maturity for different types of loans and bonds, explains the inverse relationship between interest rates and bond prices, and distinguishes between nominal and real interest rates using the Fisher equation. The material equips investors and borrowers with the tools to evaluate the true cost of borrowing and the real return on investments.

Learning Objectives

1

Explain the concept of present value and its importance in discounting future cash flows.

2

Calculate yield to maturity for various debt instruments including simple loans, fixed-payment loans, coupon bonds, discount bonds, and perpetuities.

3

Analyze the inverse relationship between bond prices and interest rates and evaluate the impact of interest rate risk on long-term bonds.

4

Differentiate between nominal and real interest rates using the Fisher equation to assess the true cost of borrowing and return on investments.

Key Concepts

CONCEPT

DEFINITION

Present Value

The current worth of a future sum of money or stream of cash flows given a specific rate of return, used to discount future values to the present.

Yield to Maturity (YTM)

The total return anticipated on a bond if the bond is held until it matures, incorporating all coupon payments and the difference between the purchase price and par value.

Coupon Bond

A bond that pays periodic interest payments (coupons) and returns the principal at maturity.

Discount Bond

A bond sold for less than its face value and does not pay periodic coupon payments; instead, the return is the difference between the purchase price and maturity value.

Perpetuity

A type of bond or cash flow that pays a constant stream of interest payments indefinitely.

Nominal Interest Rate

The interest rate before adjustments for inflation; it does not reflect the real purchasing power of money.

Real Interest Rate

The interest rate after taking inflation into account, representing the true cost of funds.

Fisher Equation

An equation that describes the relationship between nominal interest rates, real interest rates, and inflation, typically expressed as 1 + nominal rate = (1 + real rate) × (1 + inflation rate).

Interest-Rate Risk

The risk that changes in interest rates will negatively affect the value of an investment, particularly for long-term bonds.

Example Problems

Example 1

Would a dollar tomorrow be worth more to you today when the interest rate is $20 \%$, or when it is $10 \% ?$

Example 2

Write down the formula that is used to calculate the yield to maturity on a twenty-year $10 \%$ coupon bond with $\$ 1,000$ face value that sells for $\$ 2,000$.

Example 3

To pay for college, you have just taken out a $\$ 1,000$ government loan that makes you pay $\$ 126$ per year for 25 years. However, you dont have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than $12 \%$ (this is the yield to maturity on a normal $\$ 1,000$ fixed-payment loan in which you pay $\$ 126$ per year for $25 \text { years }) ?$

Example 4

Is it better for bondholders when the yield to maturity increases or decreases?

Example 5

A financial adviser has just given you the following advice: "Long-term bonds are a great investment because their interest rate is over $20 \%$. " Is the financial adviser necessarily right?
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Step-by-Step Explanations

QUESTION

How do you calculate the present value of a future cash flow?

STEP-BY-STEP ANSWER:

Step 1: Identify the future cash flow amount (F) that will be received.
Step 2: Determine the discount rate (r) that reflects the opportunity cost or required rate of return.
Step 3: Identify the number of periods (n) until the cash flow is received.
Step 4: Use the present value formula: PV = F / (1 + r)^n.
Step 5: Calculate the result to find the present value.
Final Answer:

Present Value Calculation

QUESTION

How can you determine the yield to maturity (YTM) of a coupon bond?

STEP-BY-STEP ANSWER:

Step 1: Identify the bond's current market price, its coupon payment, face value, and time to maturity.
Step 2: Set up the equation where the present value of all future coupon payments and the face value repaid at maturity equals the current bond price.
Step 3: Use the formula: Price = Σ (Coupon / (1 + YTM)^t) + (Face Value / (1 + YTM)^n), where t ranges over each period.
Step 4: Solve for YTM, often using iterative methods or a financial calculator, as the equation does not usually have an algebraic solution.
Step 5: Interpret the YTM as the effective annual return if the bond is held until maturity.
Final Answer:

Calculating Yield to Maturity for a Coupon Bond

QUESTION

Why does an increase in interest rates lead to a decrease in bond prices?

STEP-BY-STEP ANSWER:

Step 1: Recognize that bonds pay fixed future cash flows (coupons and principal).
Step 2: Understand that when market interest rates rise, new bonds are issued with higher yields.
Step 3: To remain competitive, existing bonds with lower rates must be sold at lower prices.
Step 4: The present value of the fixed interest payments and principal decreases with higher discount rates, reducing the bond’s price.
Step 5: Conclude that there is an inverse relationship between interest rates and bond prices.
Final Answer:

Understanding the Relationship Between Bond Prices and Interest Rates

QUESTION

How does the Fisher equation help in distinguishing between nominal and real interest rates?

STEP-BY-STEP ANSWER:

Step 1: Identify the nominal interest rate provided in the market.
Step 2: Determine the expected inflation rate during the period.
Step 3: Apply the Fisher equation: 1 + nominal rate = (1 + real rate) × (1 + inflation rate).
Step 4: Rearrange the equation to solve for the real interest rate.
Step 5: Interpret the real interest rate as the true return after adjusting for inflation.
Final Answer:

Using the Fisher Equation

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Common Mistakes

  • Assuming that the nominal interest rate reflects the true cost or return without considering inflation.
  • Failing to account for the inverse relationship between bond prices and interest rates, leading to miscalculations in bond valuation.
  • Overlooking interest-rate risk, particularly for long-term bonds, by not adjusting discount rates appropriately.
  • Confusing the effective yield (YTM) with the coupon rate, without considering market price variations.