Question 1

The Windjammer Co. bonds are currently selling for $1,003.17. These bonds mature in three years, pay interest annually, and have a yield-to-maturity of 6.63%. What is the coupon rate?

Accepted Answer

The coupon rate can be found by setting up the bond pricing formula, where the price of the bond equals the present value of the coupon payments plus the present value of the face value. Given the bond's price ($1,003.17), yield-to-maturity (6.63%), and maturity (3 years), we can solve for the coupon payment. The correct coupon rate results in a bond price closest to $1,003.17 when plugged into the formula. Without doing the exact math here, understanding the relationship between bond price, yield, and coupon rate is key. A bond priced above par (face value) indicates its coupon rate is higher than the yield-to-maturity. Among the given options, 6.75% is the only rate higher than the yield-to-maturity of 6.63%, making it the correct choice.

Question 2

Gabriel Corporation has outstanding $1,000, 8% semi-annual coupon bonds. The bonds have fourteen years remaining to maturity. If the current price for these bonds is $1,118.74, what is the annualized yield to maturity?

Accepted Answer

The yield to maturity (YTM) can be calculated using the bond price formula, considering the semi-annual interest payments and the time to maturity. Given the bond's price of $1,118.74, a face value of $1,000, a coupon rate of 8% (which translates to $40 semi-annually since 8% of $1,000 is $80 per year), and 14 years to maturity (or 28 periods semi-annually), the YTM reflects the interest rate that equates the present value of all future cash flows from the bond (coupon payments and the repayment of the principal) to the bond's current price. The correct YTM, considering semi-annual compounding, is approximately 6.68% annually when solving for the rate that matches the given price. This involves a financial calculator or an iterative process using a bond pricing formula, where the calculated YTM that aligns with the given price is option A) 6.68%.

Question 3

Today Katerina purchased a bond at a quoted price of 98.7. The bond matures in five years, pays semi-annual interest, and has a 6.5% coupon rate. If Katerina holds the bond to maturity, what real rate of return will she earn if inflation remains constant at 2%?

Accepted Answer

The nominal yield to maturity is approximately 6.81%. Adjusting for 2% inflation, the real rate of return is approximately 4.72%.

Question 4

High Noon Sun, Inc. has a 5%, semi-annual coupon bond with a current market price of $988.52. The bond has a par value of $1,000 and a yield to maturity of 5.29%. How many years is it until this bond matures?

Accepted Answer

The answer of High Noon Sun, Inc. has a 5%,...

Question 5

The Langley Company has 6% annual coupon bonds that are currently selling for $989.53 and have eleven years left to maturity. What is the yield to maturity?

Accepted Answer

The answer of The Langley Company has 6% annual coupon...

Question 6

A corporate bond is quoted at a price of 96.48 and carries a 5.75% coupon. The bond pays interest semiannually. What is the current yield on one of these bonds?

Accepted Answer

The current yield is calculated by dividing the annual interest payment by the bond's current price. The annual interest payment is 5.75% of the bond's par value, which is typically $1000, so the annual interest is $57.50. Since the bond is quoted at 96.48, the price is $964.80. The current yield is then $57.50 / $964.80 = 0.0596, or 5.96%.

Question 7

A Treasury bond is quoted at a price of 100:07 with a current yield of 6.4858%. What is the coupon rate?

Accepted Answer

The coupon rate can be found by multiplying the quoted price by the current yield. The quoted price of 100:07 means $100.21875 (since 07/32 = 0.21875). The current yield is given as 6.4858%. Therefore, the annual interest payment is $100.21875 * 6.4858% ≈ $6.50. Hence, the coupon rate is 6.50%.

Question 8

The market price of a bond is $1,236.94, it has 14 years to maturity, a $1,000 face value, and pays an annual coupon of $100. What is the yield to maturity?

Accepted Answer

The answer of The market price of a bond is...

Question 9

A Treasury bond is quoted at a price of 104:18 with a 4.75% coupon. The bond pays interest semiannually. What is the current yield on one of these bonds?

Accepted Answer

The current yield is calculated by dividing the annual coupon payment by the bond's price. The annual coupon payment is 4.75% of the bond's par value (assumed to be $1000 unless stated otherwise), which equals $47.50. The bond's price is quoted as 104:18, which translates to 104.5625% of par (since 18/32 = 0.5625), or $1045.625. Therefore, the current yield = ($47.50 / $1045.625) * 100 = 4.54%.

Question 10

Barkstone Candies bonds have a face value of $1,000 and a current market price of $1,047.20. The bonds have a 6% coupon rate. What is the current yield on these bonds?

Accepted Answer

The current yield is calculated by dividing the annual coupon payment by the current market price of the bond. The annual coupon payment is 6% of the $1,000 face value, which is $60. The current market price is $1,047.20. Therefore, the current yield is $60 / $1,047.20 = 0.0573 or 5.73%.

Question 11

You purchased a bond one year ago for $839.67 and just received the annual coupon of $81. You sell the bond today for $829.31. What is your real return if inflation was 5%?

Accepted Answer

The nominal return is calculated as: [(829.31 - 839.67 + 81) / 839.67] = 8.80%. The real return is then: [(1 + 0.0880) / (1 + 0.05)] - 1 = 3.41%.

Question 12

Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 96.5% of their face value, calculate the yield to maturity at the end of year 10.

Accepted Answer

The answer of Ajax Corporation issued 10,000 units of $1,000...

Question 13

The High Noon Corporation offers a 12% bond with a current market price of $923.60. The yield to maturity is 14.2%. The face value is $1,000. Interest is paid semi-annually. How many years is it until this bond matures?

Accepted Answer

The answer of The High Noon Corporation offers a 12%...

Question 14

The 5.25% semi-annual coupon bonds for Martha's Cupboards, Inc. are currently quoted in the newspaper at a price of 101.25. The bonds mature in seven years. What is the yield to maturity on these bonds?

Accepted Answer

The yield to maturity (YTM) is calculated based on the bond's current price, coupon rate, and time to maturity. Given the bond's price is above par (101.25), the YTM will be slightly lower than the coupon rate of 5.25%. The closest option is 5.04%.

Question 15

The outstanding bonds of RTF, Inc., provide a real rate of return of 3.3%. The current rate of inflation is 2.85%. What is the nominal rate of return on these bonds?

Accepted Answer

The nominal rate of return can be calculated using the Fisher equation, which is (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Plugging in the given values: (1 + nominal rate) = (1 + 0.033) * (1 + 0.0285) = 1.062455, which gives a nominal rate of approximately 6.24%.

Question 16

Steubenville Liquidators wants to raise $6.2 million to expand their business. To accomplish this, they plan to sell 20-year, $1,000 face value, zero-coupon bonds. The bonds will be priced to yield 9.5%. What is the minimum number of bonds they must sell to raise the $6.2 million they need (Use values in dollar)?

Accepted Answer

To find the minimum number of bonds, calculate the present value of one bond using the formula: PV = FV / (1 + r)^n, where FV = $1,000, r = 9.5% or 0.095, and n = 20. Then, divide $6.2 million by the present value of one bond to find the number of bonds needed. The correct calculation results in approximately 38,078 bonds.

Question 17

Elise's Crafts needs $225,000 today to purchase some new equipment. The firm is a planning on issuing 10-year zero-coupon bonds. The current market rate of interest is 6.5%. How many bonds must Elise's Crafts sell to raise the money they need?

Accepted Answer

To find the number of bonds needed, calculate the present value of a zero-coupon bond using the formula: PV = F / (1 + r)^n, where F is the face value (assumed $1,000), r is the interest rate (6.5%), and n is the number of years (10). Solve for the number of bonds by dividing the total amount needed ($225,000) by the present value of one bond. This calculation results in approximately 423 bonds.

Question 18

Curtis bought an 8.5% annual coupon bond at par. One year later, he sold the bond at a quoted price of 98. During the year, market interest rates rose and inflation was 3%. What real rate of return did Curtis earn on this investment?

Accepted Answer

The real rate of return can be calculated using the formula: $$ \text{Real Rate of Return} = \frac{\text{Nominal Rate of Return} - \text{Inflation Rate}}{1 + \text{Inflation Rate}} $$ Curtis bought the bond at par (100) and sold it at 98, which means he had a loss of 2% on the principal. However, he also received an 8.5% coupon payment. So, the nominal rate of return is $8.5\% - 2\% = 6.5\%$. Given an inflation rate of 3%, the real rate of return is: $$ \text{Real Rate of Return} = \frac{6.5\% - 3\%}{1 + 3\%} = \frac{3.5\%}{1.03} \approx 3.40\% $$

Question 19

What is the yield to maturity on a 15-year, zero-coupon bond selling for 37.5% of par value?

Accepted Answer

The yield to maturity (YTM) for a zero-coupon bond can be calculated using the formula: YTM = [(Face Value / Present Value)^(1/n)] - 1, where n is the number of years to maturity. Plugging in the values: YTM = [(100 / 37.5)^(1/15)] - 1, which results in approximately 6.76%.

Question 20

The bonds of Frank's Welding, Inc. pay an 8% coupon, have a 7.98% yield to maturity and have a face value of $1,000. The current rate of inflation is 2.5%. What is the real rate of return on these bonds?

Accepted Answer

The real rate of return can be calculated using the Fisher equation, which is approximately: real rate = nominal rate - inflation rate. Here, the nominal rate is the yield to maturity, which is 7.98%. Subtracting the inflation rate of 2.5% from 7.98% gives a real rate of return of approximately 5.48%. However, due to a calculation oversight, the correct interpretation of the Fisher equation in this context should lead to a recalculated answer that aligns with the options provided. Given the options and the typical approach to such calculations, the correct answer intended seems to be a misinterpretation of the calculation process. Re-evaluating with the correct application of the Fisher equation or considering the approximation for small percentages (real rate ≈ nominal rate - inflation rate), the answer provided does not match the correct calculation based on the given data. The correct calculation should directly apply the given numbers: 7.98% - 2.5% = 5.48%, which suggests a mistake in the initial response. The correct choice should reflect the accurate calculation based on the Fisher equation, which appears to have been misunderstood in the initial response.

Quiz 7: Interest Rates and Bond Valuation