FIN 3716 chapter 6

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

$11.25 $1000 × 0.045 / 4 = $11.25

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?

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

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

$450 $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?

$5212.50 $5000 + $5000 × 0.085 /2 = $5212.5

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%?

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

Which of the following best shows the timeline for cash flows from a five-year bond with a face value of $2,000, a coupon rate of 5.0%, and semiannual payments?

0 1 2 10 +-----+-----+-----+--- . . . -----+ $50 $50 $50 $50 $2050

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?

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

Maturity (years) 1 2 3 4 5 Price $97.25 $94.53 $91.83 $89.23 $87.53 The above table shows the price per $100-face value bond of several risk-free, zero-coupon bonds. What is the yield to maturity of the two year, zero-coupon, risk-free bond shown?

2.85% Calculate the discount rate that equates $100 to $94.53 in two years. 1 + YTMn = (Face value / price)1/n. YTMn = 2.85%

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?

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

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.

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.

) 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 ________.

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

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?

A) 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 coupon rate of an eight-year, $10,000 bond with semiannual coupons and a price of $9006.6568 , if it has a yield to maturity of 6.5%?

A) Using FV = $10,000 , periods to maturity = 16, and discount rate = 3.25%, calculate PMT = $244.4000 ; annual coupon payment = $244.4000 × 2 = $488.8000 ; coupon rate = 4.888%.

1 2 59 60 +-----+---- ...-----+-----+ $57.5 $57.5 $57.5 $5057.5 A corporation issues a bond that generates the above cash flows. If the periods are of 3 -month intervals, which of the following best describes that bond? A) a 15-year bond with a notional value of $5000 and a coupon rate of 4.6% paid quarterly B) a 15-year bond with a notional value of $5000 and a coupon rate of 1.2% paid annually C) a 30-year bond with a notional value of $5000 and a coupon rate of 3.5% paid semiannually D) a 60-year bond with a notional value of $5000 and a coupon rate of 4.6% paid quarterly

A) a 15-year bond with a notional value of $5000 and a coupon rate of 4.6% paid quarterly

A bond certificate includes ________. A) the terms of the bond B) the individual to whom payments will be made C) the yield to maturity of the bond D) the price of the bond

A) the terms of the 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 ________.

B) As the coupon rate of 8.1% is less than the YTM of 10.6% on the bonds, so they will trade at a discount.

Which of the following statements regarding bonds and their terms is FALSE? A) Bonds are securities sold by governments and corporations to raise money from investors today in exchange for a promised future payment. B) By convention, the coupon rate is expressed as an effective annual rate. C) Bonds typically make two types of payments to their holders. D) The time remaining until the repayment date is known as the term of the bond.

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

Consider a zero-coupon bond with $100 face value and 15 years to maturity. If the YTM is 7.4%, this bond will trade at a price closest to ________.

B) FV = 100 I = YTM PMT = 0 N = 15 Compute PV = FV/ (1 + i)^N = 100/ (1 + 0.074 )^15 = 34.27

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 ________.

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

A $1000 bond with a coupon rate of 6.2% paid semiannually has eight years to maturity and a yield to maturity of 8.3%. If interest rates rise and the yield to maturity increases to 8.6%, what will happen to the price of the bond?

B) The price of the bond will fall by $15.78

Which of the following statements regarding bonds and their terms is FALSE? A) One advantage of quoting the yield to maturity rather than the price is that the yield is independent of the face value of the bond. B) Unlike the case of bonds that pay coupons, for zero-coupon bonds, there is no formula to solve for the yield to maturity. C) Because we can convert any bond price into a yield, and vice versa, bond prices and yields are often used interchangeably. D) The internal rate of return (IRR) of a bond is given a special name, the yield to maturity (YTM).

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

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 ?

B) 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%.

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 ________.

C) As the coupon rate of 10.0% is more than the YTM of 7.5% on the bonds, so the bonds will trade at a premium.

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 ________.

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

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?

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

Consider a zero-coupon bond with a $1000 face value and 10 years left until maturity. If the YTM of this bond is 10.2%, then the price of this bond is closest to ________. A) $1000 B) $454.32 C) $530.04 D) $379

D) $379

Consider a zero-coupon bond with a $1000 face value and 15 years left until maturity. If the bond is currently trading for $431 , then the yield to maturity on this bond is closest to ________.

D) 5.77%

Which of the following is true about the face value of a bond? A) It is the notional amount we use to compute coupon payments. B) It is the amount that is repaid at maturity. C) It is usually denominated in standard increments, such as $1,000. D) All of the above are true.

D) All of the above are true

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 ________.

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

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 ?

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

Which of the following best illustrates why a bond is a type of loan? A) The issuers of bonds make regular payments to bondholders. B) When a company issues a bond, the buyer of that bond becomes an owner of the issuing company. C) Funds raised are used to finance long-term projects. D) 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.

D) 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.

Which of the following statements regarding bonds and their terms is FALSE? A) Zero-coupon bonds are also called pure discount bonds. B) The internal rate of return (IRR) of an investment opportunity is the discount rate at which the net present value (NPV) of the investment opportunity is equal to zero. C) The yield to maturity for a zero-coupon bond is the return you will earn as an investor from holding the bond to maturity and receiving the promised face value payment. D) When prices are quoted in the bond market, they are conventionally quoted in increments of $1,000

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

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

D) one with a face value of $1,000, a YTM of 5.9%, and 20 years to maturity D) Price = $1,000 / (1 + 5.9%)20 = $318 (lowest price)

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

FALSE

The coupon value of a bond is the face value of the bond. T/F

False

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

False

Which of the following statements regarding bonds and their terms is FALSE? A) The amount of each coupon payment is determined by the coupon rate of the bond. B) Prior to its maturity date, the price of a zero-coupon bond is always greater than its face value. C) The zero-coupon bond has no periodic interest payments. D) Treasury bills are U.S. government bonds with a maturity of up to one year

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

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 $5000 bond with a coupon rate of 5.7% paid semiannually has ten years to maturity and a yield to maturity of 6.4%. If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?

The price of the bond will rise by $293.50 .

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

True

Zero-Coupon Bonds 1) The only cash payment an investor in a zero-coupon bond receives is the face value of the bond on its maturity date T/F

True

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.

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?

a 10-year bond with a face value of $2,000 and a coupon rate of 5.8% with monthly payments $9.67 × 12 / (2,009.67 - 9.67) = 5.802%

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 ?

c) 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%

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

false

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?

semiannually