Question 1

The outstanding bonds of Jacksen Global Freight carry an 8% coupon and have a current market price of $1,054. The bonds have a face value of $1,000. 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 8% of the face value, which is $80. The current yield is $80 / $1,054 = 0.0759 or 7.59%.

Question 2

If investors require a 7% nominal return and the expected inflation rate is 3%, what is the expected real return?

Accepted Answer

The expected real return can be calculated using the Fisher equation: (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Solving for the real rate gives: (1 + 0.07) / (1 + 0.03) - 1 = 0.0388 or 3.88%.

Question 3

If the nominal rate is 4.5% and the inflation rate is 1.8%, determine the real rate.

Accepted Answer

The answer of If the nominal rate is 4.5% and...

Question 4

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 103.5% of their face value, calculate the yield to maturity on the date of the issue.

Accepted Answer

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

Question 5

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 4.

Accepted Answer

The yield to maturity (YTM) can be calculated using a financial calculator or spreadsheet software by inputting the present value (PV) as -$965 (since the bonds were sold at 96.5% of their face value), the future value (FV) as $1,000 (the face value of the bond), the payment (PMT) as $20 (since the coupon rate is 4% of the $1,000 face value, paid semi-annually, which equals $40 annually or $20 per period), the number of periods (N) as 32 (since there are 16 years left until maturity and payments are semi-annual, so 16*2), and then solving for the interest rate per period and doubling it for an annual rate. This calculation yields a YTM close to 4.30%, making choice B the correct answer.

Question 6

This morning, Marty bought a 4% coupon bond at par value. The bond pays semi-annual interest and has twenty years to maturity. By what percentage will the price of Marty's bond change if market interest rates rise by 1.5% tonight?

Accepted Answer

The price of a bond moves inversely to changes in interest rates. If interest rates rise, the price of existing bonds falls because new bonds are issued at the higher rate, making the older, lower-yielding bonds less attractive. The percentage change in a bond's price for a given change in yields is measured by its duration. For a 20-year bond with semi-annual payments and a 4% coupon, the duration will be less than 20 years but still significant, indicating a substantial sensitivity to interest rate changes. A 1.5% increase in market interest rates would significantly decrease the bond's price, and given the options, a decrease of -18.06% is plausible for a long-duration bond like the one described.

Question 7

Micalah's Crafts needs $225,000 today to purchase some new equipment. They are planning on issuing 10-year bonds with a 6% coupon rate and semi-annual interest payments. The current market rate of interest is 6.5%. How many bonds must Micalah's Crafts sell to raise the money they need?

Accepted Answer

The bonds will sell at a discount because the coupon rate (6%) is less than the market rate (6.5%). The present value of each bond's cash flows (interest payments and principal) must be calculated using the market rate. The number of bonds needed is determined by dividing the total amount needed ($225,000) by the price of one bond calculated using the present value formula. This results in needing to sell approximately 234 bonds.

Question 8

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 103.5% of their face value, calculate the yield to maturity at the end of year 8.

Accepted Answer

The yield to maturity (YTM) calculation involves solving for the interest rate in the present value of a bond formula. Given the bond's price (103.5% of face value), coupon rate (4% annually, 2% semi-annually), and time to maturity (12 years remaining after 8 years), the YTM is approximately 3.64% when calculated using a financial calculator or spreadsheet.

Question 9

Which one of the following bonds has the greatest interest rate risk?

Accepted Answer

Zero-coupon bonds have higher interest rate risk compared to coupon bonds of the same maturity because they do not pay interest until maturity. Among the options, the 20-year, zero-coupon bond (C) has the longest duration, making it the most sensitive to changes in interest rates.

Question 10

A bond that pays interest annually yields an 8.5% rate of return. The inflation rate for the same period is 4.6%. What is the actual real rate of return on this bond?

Accepted Answer

The real rate of return can be calculated using the formula: [(1 + nominal rate) / (1 + inflation rate)] - 1. Plugging in the given values: [(1 + 0.085) / (1 + 0.046)] - 1 = 0.0373 or 3.73%.

Question 11

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 103.5% of their face value, calculate the yield to maturity at the end of year 4.

Accepted Answer

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

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 on the date of the issue.

Accepted Answer

The yield to maturity is the annual rate of return an investor can expect to receive if they hold the bond until maturity. It is calculated using the following formula:YTM = (C + (FV - PV) / N) / ((FV + PV) / 2)where:C = the annual coupon paymentFV = the face value of the bondPV = the present value of the bondN = the number of years to maturityIn this case, the annual coupon payment is $40 (4% of $1,000), the face value of the bond is $1,000, the present value of the bond is $965 (96.5% of $1,000), and the number of years to maturity is 20. Plugging these values into the formula, we get:YTM = (40 + (1000 - 965) / 20) / ((1000 + 965) / 2)= (40 + 35 / 20) / ((1000 + 965) / 2)= (40 + 1.75) / ((1965) / 2)= 41.75 / 982.5= 0.0425= 4.25%Therefore, the yield to maturity on the date of the issue is 4.25%.

Question 13

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 8.

Accepted Answer

The yield to maturity (YTM) can be calculated using the bond's current price, face value, coupon rate, and time to maturity. Given the bonds were sold at 96.5% of face value, the price is $965. The semi-annual coupon payment is $20 (4% of $1,000 divided by 2). With 24 periods remaining (12 years), the YTM calculation using these inputs results in approximately 4.38%.

Question 14

The yield to maturity on a bond is currently 6.48%. The real rate of return is 2.87%. What is the rate of inflation?

Accepted Answer

The answer of The yield to maturity on a bond...

Question 15

Baker's Men's Wear has a 5.5%, semiannual coupon bond outstanding with a current market price of $978.90. The bond has a par value of $1,000 and a yield to maturity of 5.76%. How many years is it until this bond matures?

Accepted Answer

The bond has a yield to maturity of 5.76%, which is greater than its coupon rate of 5.5%. This means that the bond is selling at a discount. The number of years until the bond matures can be calculated using the following formula:Number of years to maturity = (Par value - Market price) / (Coupon payment * (1 + Yield to maturity / 2)^(-2 * Number of years to maturity))Plugging in the given values, we get:Number of years to maturity = (1000 - 978.90) / (55 * (1 + 0.0576 / 2)^(-2 * Number of years to maturity))Solving for the number of years to maturity, we get:Number of years to maturity = 11.10 years

Question 16

Calculate the duration of an 8% coupon bond that makes annual coupon payments that is currently priced at $950 and has three years left to maturity.

Accepted Answer

The duration of a bond is calculated using the weighted average time to receive the bond's cash flows. Given the bond's price, coupon rate, and time to maturity, the duration is approximately 2.8 years.

Question 17

If the nominal rate is 5.5%, and the real rate is 1.5%, determine the inflation rate.

Accepted Answer

The inflation rate can be calculated using the Fisher equation, which is approximately given by the formula: inflation rate ≈ nominal rate - real rate. Therefore, the inflation rate ≈ 5.5% - 1.5% = 4%. The closest option to this calculation is 3.94%.

Question 18

ABC Corporation has 3-year, 7% annual coupon bonds outstanding. Given an 8.5% yield to maturity, determine the duration of these bonds.

Accepted Answer

The correct answer is A because the duration of a bond is a measure of its price sensitivity to changes in interest rates. The higher the duration, the more sensitive the bond's price is to changes in interest rates. In this case, the bond has a duration of 2.70, which means that a 1% increase in interest rates would cause the bond's price to decrease by 2.70%.

Question 19

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 103.5% of their face value, calculate the yield to maturity at the end of year 10.

Accepted Answer

The yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until it matures. The YTM calculation takes into account the bond's current market price, its face value, its coupon interest rate, and the time to its maturity. It also assumes that all coupon payments are reinvested at the same rate as the bond's current yield. Given that the bonds were sold at 103.5% of their face value, this implies a premium over the face value. However, without the specific formula or financial calculator inputs used to directly calculate YTM, which involves solving for the interest rate in the present value of a bond formula, it's not possible to accurately determine the YTM from the information provided alone. The correct answer would typically require the use of a financial calculator or a spreadsheet to solve for the yield to maturity, considering the bond's selling price, face value, coupon rate, and time to maturity. The choice provided as correct (B) is based on the assumption that a calculation was made considering these factors.

Question 20

ABC Corporation has 4-year, 5% annual coupon bonds outstanding. Given a 6.5% yield to maturity, determine the duration of these bonds.

Accepted Answer

Duration measures the sensitivity of a bond's price to changes in interest rates, typically calculated as the weighted average time to receive the bond's cash flows. For a bond with a 4-year maturity, a 5% annual coupon, and a yield to maturity of 6.5%, the duration will be less than its maturity because the bond pays coupons before maturity, which means the investor receives some of the investment before the bond's final maturity. The correct duration of 3.52 years (option C) suggests that on average, the bond's cash flows are received in 3.52 years, taking into account the time value of money and the bond's coupon payments and final principal repayment. Calculating the exact duration involves a present value calculation of each cash flow, weighted by the time until the cash flow occurs, and then summing these values.

Quiz 7: Interest Rates and Bond Valuation