Understanding Interest Rates

Front 1

True or False: A dollar paid to you tomorrow is worth more than a dollar paid to you today if the interest rate is high rather than low.

Back 1

FALSE

When the interest rate is high, you forgo more interest in waiting to receive the dollar. Therefore, the present value of this dollar is less when the interest rate is high. From the present value relationship:

Present Value = (Future Value) / (1 + i)

where i is the interest rate, or yield to maturity. When i increases, the present value of the future value falls. Conversely,

Future Value = (Present Value) x (1 + i)

When i increases, the future value increases for a given present value.

Front 2

A Treasury bill (T-bill) is a government discount bond that matures in one year or less. Suppose that you purchase a T-bill that matures in one year. This T-bill has a face value of $1,000 and a current price of $960. To the nearest tenth of a percent, the yield to maturity for this T-bill is:

Back 2

4.2%

The yield to maturity is the interest rate that equates the one-year T-bill's price to its present value. Therefore, the T-bill's price (P) is:

P = F / (1 + i)

where i denotes the yield to maturity and F denotes the face value. Solving for the yield to maturity gives:

i = (F - P) / P

In this example, the yield to maturity is therefore calculated as follows:

i = ($1,000 - $960) / $960
i = 0.0416666
i = 4.2%

Front 3

Which of the following statements regarding bond prices and yields is correct?

I. When the yield to maturity rises, the present value of coupon payments decreases.

II. When the current yield rises, the bond price falls and the yield to maturity rises.

III. The current yield and the yield to maturity always move in opposite directions.

IV. The yield on a discount basis understates the yield to maturity.

V. The current yield better estimates the yield to maturity for long-term bonds as compared to short-term bonds.

Back 3

I, II, IV, and V

An increase in the yield to maturity implies that future coupon payments are worth less in present-value terms because the bond owner forgoes more interest. An increase in the current yield implies that the bond price falls, so the yield to maturity must also increase. For this reason, the current yield and the yield to maturity always move in the same direction.

The discount yield understates the yield to maturity because it measures the percentage gain based on face value rather than current price and because the formula uses 360 days in a year rather than 365. Although the discount yield provides reasonable estimates of the yield to maturity for short-term bonds, the current yield better measures the yield to maturity for longer-term bonds. For a perpetuity, the current yield equals the yield to maturity. Therefore, the current yield better estimates the yield to maturity for bonds with a longer term to maturity; such bonds behave more like perpetuities than li

Front 4

True or False: In general, the expected rate of return on a bond equals its yield to maturity.

Back 4

FALSE

The yield to maturity measures the interest that a bond owner receives each year if the bond is held until maturity. In practice, most investors do not hold coupon bonds until they mature, so they focus on the expected rate of return.

The expected rate of return from owning a bond after one year equals the coupon payment plus any expected capital gain from a change in the price over the year. The expected rate of return equals the yield to maturity only when the bond owner holds the bond until maturity, or no capital gain or loss exists over any holding period less than the time to maturity.

Front 5

True or False: Discount bonds and simple loans possess no interest-rate risk.

Back 5

TRUE

Because both discount bonds and simple loans possess a single fixed payment after one year, there is no capital gain or loss earned on these debt instruments. That is, the yield to maturity equals the expected rate of return.

The price of the discount bond equals its face value upon maturity and, unlike coupon bonds, discount bonds make no interest payments before maturity.

Front 6

When people take out a loan, they pay a nominal interest rate. Likewise, bond yields are quoted in nominal terms. The nominal interest rate times the loan amount equals the dollar amount the borrower must pay in interest. The expected real interest rate times the loan amount measures the expected purchasing power of these dollars. Unexpected changes in the inflation rate affect borrowers and lenders.

Suppose that a bank offers a loan with a nominal interest rate of 10% and the expected inflation rate in the economy equals 3%. The terms of the loan are not renegotiated, so the borrower has a guaranteed nominal interest rate of 10%.

What is the expected real interest rate for this loan?

Back 6

7%

If you pay a 10% nominal interest rate and prices are expected to grow at a rate of 3% each year, then the expected real interest rate is as follows:

Expected Real Interest Rate = Nominal Interest Rate - Expected Inflation Rate
Expected Real Interest Rate = 10% - 3%
Expected Real Interest Rate = 7%

Front 7

When people take out a loan, they pay a nominal interest rate. Likewise, bond yields are quoted in nominal terms. The nominal interest rate times the loan amount equals the dollar amount the borrower must pay in interest. The expected real interest rate times the loan amount measures the expected purchasing power of these dollars. Unexpected changes in the inflation rate affect borrowers and lenders.

Suppose that a bank offers a loan with a nominal interest rate of 10% and the expected inflation rate in the economy equals 3%. The terms of the loan are not renegotiated, so the borrower has a guaranteed nominal interest rate of 10%.

Suppose that the inflation rate unexpectedly falls from 3% to 2%. Which of the following will occur?

The borrower benefits from a lower nominal interest rate:The lender and borrower are not affected because the nominal interest rate is fixed:The lender benefits from a lower nominal interest rate:The borrower benefits from higher real interest rate.

Back 7

The lender benefits from a higher real interest rate.

The loan contract fixes the nominal rate at 10% based on the expected 3% inflation rate, implying a real interest rate of 7%. When inflation unexpectedly falls to 2%, the actual real interest rate rises to 8%. Because the borrower pays more interest in real terms, the borrower is worse off than before, while the lender collects more in real interest, so the lender is better off than before.