Fin Ch. 6

What is the coupon payment of a 15-year $10,000 bond with a 9% coupon rate with semiannual payments?

$10,000 × 0.09/2 = $450

An investor holds a Ford bond with a face value of $5000 , a coupon rate of 8.5%, and semiannual payments that matures on January 15, 2029. How much will the investor receive on January 15, 2029?

$5000 + ($5000*0.085/2)= $5212.5

A corporate bond makes payments of $9.67 every month for ten years with a final payment of $2009.67. Which of the following best describes this bond?

$9.67 × 12 / (2,009.67 - 9.67) = 5.802%

A bond certificate includes ________.

) the terms of the bond

A company releases a five-year bond with a face value of $1000 and coupons paid semiannually. If market interest rates imply a YTM of 8%, which of the following coupon rates will cause the bond to be issued at a premium?

10%

A ten-year, zero-coupon bond with a yield to maturity of 4% has a face value of $1000 . An investor purchases the bond when it is initially traded, and then sells it four years later. What is the rate of return of this investment, assuming the yield to maturity does not change?

4%

A company releases a five-year bond with a face value of $1000 and coupons paid semiannually. If market interest rates imply a YTM of 6%, what should be the coupon rate offered if the bond is to trade at par?

6%

An investor purchases a 30-year, zero-coupon bond with a face value of $5000 and a yield to maturity of 8.4%. He sells this bond ten years later. What is the rate of return on his investment, assuming yield to maturity does not change?

8.4%

How are the cash flows of a coupon bond different from an amortizing loan?

A coupon bond pays interest over the life of the bond and returns the principal at the end of the term. Thus the cash flows are smaller over the life of the bond with a lump -sum payment at the end. In contrast, an amortizing loan has identical cash flows over its life with a part of the cash flow going toward interest and the balance as return of principal

What care, if any, should be taken regarding the sign of the cash flows while drawing the timeline and associated cash flows of a coupon bond?

A typical coupon bond will have the first cash flow in the opposite direction as compared to all the rest of the cash flows over its life. The first cash corresponds to the issuer borrowing the money, while all the rest of the cash flows are payments by the issuer to the bondholder either in the form of interest or principal.

How are the cash flows of a zero-coupon bond different from those of a coupon bond?

A zero-coupon bond has only two cash flows over its life. The first one is associated with the issues borrowing the money and the second when the issuer returns the principal. A coupon bond, on the other hand, has several cash flows over its life. The first cash flow of both these types of bonds, zero-coupon and coupon are similar as they denote the issuer borrowing the money. However, for a coupon bond the subsequent cash flows over its life correspond to the interest payment promised by the issuer with a final payment equal to the return of principal.

Which of the following risk-free, zero-coupon bonds could be bought for the lowest price? A) one with a face value of $1,000, a YTM of 4.8%, and 5 years to maturity B) one with a face value of $1,000, a YTM of 3.2%, and 8 years to maturity C) one with a face value of $1,000, a YTM of 6.8%, and 10 years to maturity D) one with a face value of $1,000, a YTM of 5.9%, and 20 years to maturity

A) Price = $1,000 / (1 + 4.8%)5 = $791 B) Price = $1,000 / (1 + 3.2%)8 = $777 C) Price = $1,000 / (1 + 6.8%)10 = $518 D) Price = $1,000 / (1 + 5.9%)20 = $318 (lowest price)

13) Which of the following is true about the face value of a bond?

All of the above are true.

What is the coupon payment of a 25-year $1000 bond with a 4.5% coupon rate with quarterly payments?

B) $1000 × 0.045 / 4 = $11.25

Which of the following statements regarding bonds and their terms is FALSE?

By convention, the coupon rate is expressed as an effective annual rate.

Which of the following bonds is trading at par? A) a bond with a $2,000 face value trading at $1,987 B) a bond with a $1,000 face value trading at $999 C) a bond with a $1,000 face value trading at $1,000 D) a bond with a $2,000 face value trading at $2,012

C

Which of the following statements is true of bond prices? A) A fall in bond prices causes interest rates to fall. B) A fall in interest rates causes a fall in bond prices. C) A rise in interest rates causes bond prices to fall. D) Bond prices and interest rates are not connected.

C

A university issues a bond with a face value of $5000 and a coupon rate of 4.41% that matures on July 15, 2018. The holder of such a bond receives coupon payments of $110.25 . How frequently are coupon payments made in this case?

C) semiannually

A bond is currently trading below par. Which of the following must be true about that bond? A) The bondʹs yield to maturity is less than its coupon rate. B) The bond is a zero-coupon bond. C) The bondʹs yield to maturity is greater than its coupon rate. D) B or C above

D

Which of the following best describes a bond rated by Standard & Poorʹs and Moody as B? A) judged to be high quality by all standards B) considered to be medium grade obligations C) neither highly protected nor poorly secured D) generally lacks the characteristics of a desirable investment

D

A 20-year bond with a $1,000 face value was issued with a yield to maturity of 4.3% and pays coupons semi-annually. After ten years, the yield to maturity is still 4.3% and the clean price of the bond is $959.71 . After three more months go by, what would you expect the dirty price to be?

FV = $1,000, PV = -959.71 , n = 20, i = 2.15%, solve for PMT. PMT = $19.00 , so coupon rate per 6 month period = 1.90 %. Accrued interest for three months = $19.00 /2= $9.50 , so dirty price = $959.71 + $9.50 = $969.21 .

The coupon value of a bond is the face value of the bond.

False

What issues should one be careful of when calculating the bond price from its yield to maturity using the time value of money (TVM) keys of a financial calculator?

It is quite simple to transfer the bond cash flow timeline to a financial calculator. Care has to be taken when using the TVM keys in understanding that the last cash flow, i.e., the return of principal by the issuer, is automatically augmented by the last coupon payment and no special steps are needed for that.

How can the financial calculator be used to calculate the price of a coupon bond from its yield to maturity?

Most popular financial calculators can help compute the price of a coupon bond in several ways. Two such ways may be using ʹtime value of money (TVM) keys and cash flow (CF) keys.

A risk-free, zero-coupon bond with a face value of $10,000 has 15 years to maturity. If the YTM is 6.1%, which of the following would be closest to the price this bond will trade at?

Price = (Face value) / (1 + YTM)N. Price = ($10,000 ) / (1 + 6.1%)15 = $4114

Why is the yield to maturity of a zero-coupon, risk-free bond that matures at the end of a given period the risk-free interest rate for that period?

Since such a bond provides a risk-free return over that period, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity.

How are investors in zero-coupon bonds compensated for making such an investment?

Such bonds are purchased at a discount, below their face value.

A bond is said to mature on the date when the issuer repays its notional value.

True

A bond will trade at a discount if its coupon rate is less than its yield to maturity.

True

Bonds with a high risk of default generally offer high yields.

True

17) Which of the following statements regarding bonds and their terms is FALSE?

When prices are quoted in the bond market, they are conventionally quoted in increments of $1,000.

A risk-free, zero-coupon bond with a $5000 face value has 15 years to maturity. The bond currently trades at $3750 . What is the yield to maturity of this bond?

YTM = (Face Value / Price) 1/n - 1; YTM = ($5000 / $3750 )1/15 - 1 = 1.936 %

If the yield to maturity of all of the following bonds is 6%, which will trade at the greatest premium per $100 face value? A) a bond with a $10,000 face value, four years to maturity and 6.2% semiannual coupon payments B) a bond with a $500 face value, seven years to maturity and 5.2% annual coupon payments C) a bond with a $5,000 face value, seven years to maturity and 5.5% annual coupon payments D) a bond with a $1,000 face value, five years to maturity and 6.3% annual coupon payments

a bond with a $1,000 face value, five years to maturity and 6.3% annual coupon payments

A corporate bond which receives a BBB rating from Standard & Poorʹs is considered ________.

an investment grade bond

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 5 years. The bond certificate indicates that the stated coupon rate for this bond is 8.1% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 10.6%, then this bond will trade at ________.

discount bc coupon less than YTM

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 5 years. The bond certificate indicates that the stated coupon rate for this bond is 10.0% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 7.5%, then this bond will trade at ________.

premium bc coupon greater than YTM

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 8.2% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 7.3%, then the price that this bond trades for will be closest to ________.

FV = $1000 I = 3.65 (7.3/2) PMT = $41 N = 20 (10 × 2) Compute PV = 1063.10

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in five years. The bond certificate indicates that the stated coupon rate for this bond is 8.5% and that the coupon payments are to be made semiannually. Assuming that this bond trades for $1081.73 , then the YTM for this bond is closest to ________.

FV = $1000 PMT = $42.50 ($85 / 2) N = 10 (5 × 2) PV = -$1081.73 Compute I = 3.2783 × 2 = 6.5565 %.

The Sisyphean Company has a bond outstanding with a face value of $5000 that reaches maturity in 8 years. The bond certificate indicates that the stated coupon rate for this bond is 8.2% and that the coupon payments are to be made semiannually. Assuming that this bond trades for $4541.53 , then the YTM for this bond is closest to ________.

FV = $5000 PMT = $205 ($410 /2) N = 16 (8 × 2) PV = -$4541.53 Compute I = 4.9426 × 2 = 9.8852 %.

The Sisyphean Company has a bond outstanding with a face value of $1000 that reaches maturity in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 8.0% and that the coupon payments are to be made semiannually. Assuming the appropriate YTM on the Sisyphean bond is 11.1%, then the price that this bond trades for will be closest to ________.

FV = 1000 I = 5.55 (11.1/2) PMT = $40 ($80/2) N = 20 (10 × 2) Compute PV = 815.54

Before it matures, the price of any bond is always less than its face value.

False

Bond traders generally quote bond yields rather than bond prices, since yield to maturity depends on the face value of the bond.

False

Prior to its maturity date, the price of a zero-coupon bond is its face value.

False

The credit spread of a bond shrinks if it is perceived that the probability of the issuer defaulting increases.

False

Treasury bonds have original maturities from one to ten years, while Treasury notes have original maturities of more than ten years.

False

What is the dirty price of a bond?

the bondʹs actual cash price

A firm issues 5-year bonds with a coupon rate of 4.7%, paid semiannually. The credit spread for this firmʹs 5-year debt is 1.2%. New 5-year Treasury notes are being issued at par with a coupon rate of 5.1%. What should the price of the firmʹs outstanding 5-year bonds be if their face value is $1,000?

Calculate the PV of the bond with FV = $1,000, YTM = 3.150 %, PMT = 23.50 , and N = 10, which = $932.28 .

A firm issues two -year bonds with a coupon rate of 6.7%, paid semiannually. The credit spread for this firmʹs two -year debt is 0.8%. New two -year Treasury notes are being issued at par with a coupon rate of 3.1%. What should the price of the firmʹs outstanding two -year bonds be per $100 of face value?

Calculate the PV of the bond with FV = $100, YTM = 1.95 %, PMT = 3.35 , and N = 4 which = $105.34 .

A five-year bond with a $1,000 face value has a yield to maturity is 5.0% and itʹs coupon rate is 6.0% paid annually. The dirty price of this bond exactly 6 months after its second coupon payment is closest to ________.

Calculate the clean price right after second coupon payment using FV = $1,000. YTM = 5.0%, PMT = 60, and N = 3; clean price = $1027.23 ; accrued interest six months after last coupon is $30 ; dirty price = $1027.23 + $30 = $1057.23 .

What is the yield to maturity of a one-year, risk-free, zero-coupon bond with a $10,000 face value and a price of $9400 when released?

Calculate the discount rate that equates $10,000 to $9400 in one year. 1 + YTMn = (Face value / price)1/n. YTMn = 6.383%

The Sisyphean Company has a bond outstanding with a face value of $5000 that matures in 10 years. The bond certificate indicates that the stated coupon rate for this bond is 8.9% and that the coupon payments are to be made semiannually. How much will each semiannual coupon payment be?

Coupon payment = (coupon rate × face value)/number of coupons per year = (0.089 × 5000) / 2 = $222.5

Which of the following statements regarding bonds and their terms is FALSE?

The yield to maturity of a bond is the discount rate that sets the future value (FV) of the promised bond payments equal to the current market price of the bond.

A risk-free, zero-coupon bond has 15 years to maturity. Which of the following is closest to the price per $1000 of face value that the bond will trade at if the YTM is 6.1%?

Price = (Face value) / (1 + YTM)N. Price = ($1000 ) / (1 + 6.1%)10 = $553.15

Which of the following statements regarding bonds and their terms is FALSE?

Prior to its maturity date, the price of a zero-coupon bond is always greater than its face value.

A bond has a $10,000 face value, ten years to maturity, and 8% semiannual coupon payments. What would be the expected difference in this bondʹs price immediately before and immediately after the next coupon payment?

The expected difference in this bondʹs price will be $400 since the bond pays semiannual coupon of $400 .

A company issues a ten-year $1,000 face value bond at par with a coupon rate of 6.7% paid semiannually. The YTM at the beginning of the third year of the bond (8 years left to maturity) is 8.1%. What was the percentage change in the price of the bond over the past two years?

The new price would be $918.73 . ($918.73 - $1000)/1000 = -8.13%

13) Which of the following statements regarding bonds and their terms is FALSE?

The only cash payments the investor will receive from a zero-coupon bond are the interest payments that are paid up until the maturity date.

28) What issues should one be careful of when calculating the bond price from its yield to maturity using the cash flow (CF) keys of a financial calculator?

There are two issues that one has to be careful about when using the CF keys in computing the price of coupon bonds from its yield to maturity. Since the coupon payments are generally identical over the life of the bond, it might be prudent to use the frequency key while entering this cash flow. That is the first pitfall to be aware of as the frequency to be entered into the calculator has to be reduced by one to account for the last coupon payment that gets added to the return of principal. Similarly, the last cash flow has to be the sum of principal and the last coupon payment.

25) What care, if any, should be taken regarding the timing of the cash flows while drawing the timeline and associated cash flows of a coupon bond?

There are two issues that one has to be careful of in marking the timing of cash flows associated with a coupon bond. The first is to be cognizant of the periodicity of the coupon payment, as most coupons are not paid annually. The second is to make sure that the return of principal at the end of the life also has a last coupon payment associated with it.

The only cash payment an investor in a zero-coupon bond receives is the face value of the bond on its maturity date.

True

Under what situation should the clean price, dirty price, and the price calculated by the basic annuity and present value (PV) equations for a bond be equal?

Typically, while drawing the timeline for bond cash flows, the price calculated is the price on the date of coupon payment. Even on this date there would be a pre-coupon payment price and a post-coupon payment price. The clean price, dirty price and the price calculated by the annuity and present value (PV) equations converge to a single price right after the coupon has detached from the bond and paid to the holder.

Why are the interest rates of U.S. Treasury securities less than the interest rates of equivalent corporate bonds?

U.S. Treasury securities are widely regarded to be risk-free.

Under what situation can a zero-coupon bond be selling at par to its face value?

Unlike a coupon bond, a zero-coupon bond does not have a periodic cash flow with one lump-sum payment of the face value at its maturity. Consequently, a zero-coupon bond will be always selling at a price less than its face value and can never sell at par with its face value. If it does then the time value of money concepts will be violated, which never happens.

Under what situation can a zero-coupon bond be selling at a premium?

Unlike a coupon bond, a zero-coupon bond does not have a periodic cash flow with one lump-sum payment of the face value at its maturity. Consequently, a zero-coupon bond will be always selling at a price less than its face value. If it does then the time value of money concepts will be violated, which never happens.

Which of the following statements regarding bonds and their terms is FALSE?

Unlike the case of bonds that pay coupons, for zero-coupon bonds, there is no formula to solve for the yield to maturity.

What must be the price of a $10,000 bond with a 6.1% coupon rate, semiannual coupons, and five years to maturity if it has a yield to maturity of 10% APR?

Using FV = $10,000 , periods to maturity = 10 , PMT = 305.00 , and periodic discount rate = 5.0% per period, calculate PV = $8494.26 .

What is the yield to maturity of a ten-year, $10,000 bond with a 5.4% coupon rate and semiannual coupons if this bond is currently trading for a price of $9207.93 ?

Using FV = $10,000 , periods to maturity = 20 , PMT = 270.00 , and PV = $9207.93 , calculate discount rate = 3.2445 % per period; 3.2445 × 2 = 6.489 %.

What must be the price of a $1000 bond with a 5.8% coupon rate, annual coupons, and 20 years to maturity if YTM is 7.8% APR?

Using FV = $1000 , periods to maturity = 20 , PMT = $58.00 , and discount rate = 7.8% per period, calculate PV = $800.68

A bond has five years to maturity, a $1000 face value, and a 5.5% coupon rate with annual coupons. What is its yield to maturity if it is currently trading at $846.11 ?

Using FV = $1000 , periods to maturity = 5, PMT = 55.00 , and PV = $846.11 , calculate discount rate = 9.5089 % per period.

What is the yield to maturity of a(n) eight-year, $5000 bond with a 4.4% coupon rate and semiannual coupons if this bond is currently trading for a price of $4723.70 ?

Using FV = $5000 , periods to maturity = 16 , PMT = 110.00 , and PV = $4724 , calculate discount rate = 2.6275 % per period; 2.6275 × 2 = 5.255 %.

Which of the following best illustrates why a bond is a type of loan?

When an investor buys a bond from an issuer, the investor is giving money to the issuer, with the assurance that it will be repaid at a date in the future.