Question 1

You are considering investing in a security that matures in 10 years with a par value of $1,000. During the first five years, the security has an 8 percent coupon with quarterly payments (i.e., you receive $20 a quarter for the first 20 quarters)Another 10-year bond has an 8 percent semiannual coupon (i.e., the coupon payment is $40 every six months). This bond is selling at its par value, $1,000. This bond has the same risk as the security you are thinking of purchasing. Given this information, what should be the price of the security you are considering purchasing?

Accepted Answer

The answer of You are considering investing in a security...

Question 2

A company is issuing $1,000 bonds at par value. The coupon rate (and yield to maturity) on the bonds is 8 percent (with annual payments) and the bonds will mature in 10 years. The bonds can be called at a call premium of 5 percent above face value after 3 years. What is the after-tax yield to call for an investor with a 31 percent tax rate?

Accepted Answer

To solve this problem, we need to calculate the yield to call after 3 years, taking into account the call premium and the investor's tax rate.

1. Calculate the price of the bond after 3 years:
The bond will have 7 years left until maturity after 3 years.
Using the formula for the present value of a bond:
PV = C x [(1 - (1 + r)-n) / r] + FV / (1 + r)n
Where PV is the present value of the bond, C is the annual coupon payment, r is the semi-annual yield to maturity, n is the number of semi-annual periods remaining until maturity, and FV is the face value of the bond.
PV = 40 x [(1 - (1 + 0.04)-14) / 0.04] + 1,000 / (1 + 0.04)14
PV = $1,061.69

2. Calculate the after-tax yield to call:
The call price is 1.05 x $1,000 = $1,050.
Since the investor will receive $1,050 in 3 years, we can calculate the semi-annual yield to call using the following formula:
Yield to call = [(Call price - Purchase price) / (Purchase price x Number of periods)] x (1 - Tax rate)
Yield to call = [(1,050 - 1,061.69) / (1,061.69 x 6)] x (1 - 0.31)
Yield to call = -0.005
Yield to call (annualized) = -0.01 or -1%
(Note: A negative yield to call means that the bond is not callable at a profit for the investor)

3. Calculate the after-tax yield to maturity:
Using the same formula as step 1:
PV = 40 x [(1 - (1 + r)-20) / r] + 1,000 / (1 + r)20
Solving for r with a financial calculator or Excel, we get r = 3.3% (semi-annual yield to maturity).
The annual yield to maturity is 2 x 3.3% = 6.6%

4. Compare the after-tax yield to maturity with the yield to call:
Since the yield to call is negative, the investor should hold the bond to maturity to achieve the after-tax yield of 6.6%.

Therefore, the best choice is C.

Question 3

McGriff Motors has bonds outstanding which will mature in 12 years. The bonds pay a 12 percent semiannual coupon and have a face value of $1,000 (i.e., the bonds pay a $60 coupon every six months). The bonds currently have a yield to maturity of 10 percent. The bonds are callable in 8 years and have a call price of $1,050. What are the bonds' yield to call?

Accepted Answer

The answer of McGriff Motors has bonds outstanding which will...

Question 4

A corporate bond with an 11 percent semiannual coupon has a yield to maturity of 9 percent. The bond matures in 20 years but is callable in ten years. The maturity value is $1,000. The call price is $1,055. What is the bond's yield to call?

Accepted Answer

To calculate the yield to call, we need to find the rate at which the present value of the remaining cash flows (coupon payments and call price) equals the current price of the bond. Here's the calculation:

Step 1: Find the present value of the remaining cash flows if the bond is held to maturity in 20 years:

PMT = 55 (11% of $1,000 / 2 semiannual payments per year)
N = 20 * 2 = 40 (total number of semiannual periods)
I/Y = 4.5% (half of the annual yield of 9%)
FV = 1,000 (maturity value)
CPT PV = $887.89

Step 2: Find the present value of the remaining cash flows if the bond is called in 10 years:

PMT = 55 (11% of $1,000 / 2 semiannual payments per year)
N = 10 * 2 = 20 (remaining number of semiannual periods until call date)
I/Y = ? (what we're solving for)
FV = 1,055 (call price)
CPT PV = -$1,000 (the cash flows are negative because we're assuming the bond will be called and the investor will receive the call price, which is higher than the face value)

Using trial and error or a financial calculator, we can find that the yield to call is 8.58%. This is the rate at which the present value of the remaining cash flows equals the current price of the bond, which is the call price of $1,055.

Question 5

Meade Corporation bonds mature in 6 years and have a yield to maturity of 8.5 percent. The par value of the bonds is $1,000. The bonds have a 10 percent coupon rate and pay interest on a semiannual basis. What are the current yield and capital gains yield on the bonds for this year? (Assume that interest rates do not change over the course of the year).

Accepted Answer

The answer of Meade Corporation bonds mature in 6 years...

Question 6

A 15-year bond with a 10 percent semiannual coupon has a par value of $1,000. The bond may be called after 10 years at a call price of $1,050. The bond has a nominal yield to call of 6.5 percent. What is the bond's yield to maturity, stated on a nominal, or annual basis?

Accepted Answer

The yield to maturity (YTM) is calculated based on the bond's current price, coupon payments, and time to maturity. Given the bond's nominal yield to call is 6.5%, and considering the bond's coupon rate and call price, the YTM is slightly higher, calculated to be approximately 6.95% on an annual basis.

Question 7

Semiannual payment bonds with the same risk (Aaa) and maturity (20 years) as your company's bonds have a nominal (not EAR) yield of 9 percent. Your company's treasurer is thinking of issuing at par some $1,000 par value, 20-year, quarterly payment bonds. She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20-year, semiannual payment bonds. What would the quarterly interest payment be, in dollars?

Accepted Answer

To find the quarterly interest payment, first calculate the EAR for the semiannual bond: EAR = (1 + 0.09/2)^2 - 1 = 9.2025%. Then, find the quarterly rate that gives the same EAR: (1 + r)^4 = 1.092025, solving gives r = 0.02225. The quarterly interest payment is 0.02225 * $1,000 = $22.25.

Question 8

Fish & Chips Inc. has two bond issues outstand¬ing, and both sell for $701.22. The first issue has an annual coupon rate of 8 percent and 20 years to maturity. The second has an identical yield to maturity as the first bond, but only 5 years until maturity. Both issues pay interest annually. What is the annual interest payment on the second issue?

Accepted Answer

The answer of Fish & Chips Inc. has two bond...

Question 9

Assume that McDonald's and Burger King have similar $1,000 par value bond issues outstanding. The bonds are equally risky. The Burger King bond has an annual coupon rate of 8 percent and matures 20 years from today. The McDonald's bond has a coupon rate of 8 percent, with interest paid semiannually, and it also matures in 20 years. If the nominal required rate of return, rd, is 12 percent, semiannual basis, for both bonds, what is the difference in current market prices of the two bonds?

Accepted Answer

The McDonald's bond pays interest semiannually, so it will have more frequent compounding compared to the Burger King bond, which pays annually. This results in a slightly higher present value for the McDonald's bond, leading to a difference in their market prices.

Question 10

A 6-year bond which pays 8 percent interest semiannually sells at par ($1,000). Another 6-year bond of equal risk pays 8 percent interest annually. Both bonds are non-callable and have a face value of $1,000. What is the price of the bond which pays annual interest?

Accepted Answer

The bond paying annual interest will also sell at par ($1,000) because both bonds have the same coupon rate and yield, and the market conditions are the same.

Question 11

A 12-year bond with a 10 percent semiannual coupon and a $1,000 par value has a nominal yield to maturity of 9 percent. The bond can be called in five years at a call price of $1,050. What is the bond's nominal yield to call?

Accepted Answer

The bond's nominal yield to call is the annualized rate of return an investor would earn if they bought the bond at its current price and held it until it was called in five years. The bond's current price can be calculated using the following formula:Bond Price = (Coupon Payment / (1 + Yield to Maturity / 2)^1) + (Coupon Payment / (1 + Yield to Maturity / 2)^2) + ... + (Coupon Payment + Par Value / (1 + Yield to Maturity / 2)^n)where:Coupon Payment = $1,000 * 10% / 2 = $50Yield to Maturity = 9% / 2 = 4.5%n = 12 * 2 = 24Plugging these values into the formula, we get:Bond Price = $50 / (1 + 0.045)^1 + $50 / (1 + 0.045)^2 + ... + ($50 + $1,000) / (1 + 0.045)^24Bond Price = $1,050.25The bond's nominal yield to call can then be calculated using the following formula:Nominal Yield to Call = (Call Price - Bond Price) / (Bond Price * Number of Years to Call)Nominal Yield to Call = ($1,050 - $1,050.25) / ($1,050.25 * 5)Nominal Yield to Call = 8.98%

Question 12

Hood Corporation recently issued 20-year bonds. The bonds have a coupon rate of 8 percent and pay interest semiannually. Also, the bonds are callable in 6 years at a call price equal to 115 percent of par value. The par value of the bonds is $1,000. If the yield to maturity is 7 percent, what is the yield to call?

Accepted Answer

To calculate the yield to call, we need to find the present value of cash flows till the call date, assume that after the call date the bond will be redeemed at par value.

The annual coupon payment is $80 (=$1,000 × 8%). Since the bond pays semiannual interest, the semiannual coupon payment is $40. The bond has 40 semiannual periods (20 years × 2 semiannual periods per year).

Using the formula for the present value of a bond, we can find the price today of $1 of face value received in 6 years: 
PV = $1,000 × 1.15⁶ = $1,781.56

The present value of the interest payments is: 
PV = $40 × [1− 1 / (1 + (7% / 2))⁴⁰] / (7% / 2) = $702.24

The present value of the face value received in 20 years is: 
PV = $1,000 / (1 + 7%)²⁰ = $214.55

Therefore, the price of the bond today is: 
Price = $702.24 + $214.55 = $916.79

The yield to call is the interest rate that makes the present value of cash flows equal to the current market price ($916.79), assuming the bond is called in 6 years:

$916.79 = $40 × [1− 1 / (1 + (YTC / 2))¹²] / (YTC / 2) + $1,781.56 / (1 + YTC / 2)¹²

Using trial and error or a financial calculator, we find that the yield to call is approximately 7.75%. Therefore, the answer is B) 7.75%.

Quiz 4: Bond Valuation

A corporate bond with an 11 percent semiannual coupon has a yield to maturity of 9 percent. The bond matures in 20 years but is callable in ten years. The maturity value is $1,000. The call price is $1,055. What is the bond's yield to call?

A 15-year bond with a 10 percent semiannual coupon has a par value of $1,000. The bond may be called after 10 years at a call price of $1,050. The bond has a nominal yield to call of 6.5 percent. What is the bond's yield to maturity, stated on a nominal, or annual basis?

A 6-year bond which pays 8 percent interest semiannually sells at par ($1,000) . Another 6-year bond of equal risk pays 8 percent interest annually. Both bonds are non-callable and have a face value of $1,000. What is the price of the bond which pays annual interest?

A 12-year bond with a 10 percent semiannual coupon and a $1,000 par value has a nominal yield to maturity of 9 percent. The bond can be called in five years at a call price of $1,050. What is the bond's nominal yield to call?