Question 1

Recently, Ohio Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required annual return is 20 percent, what should the bonds sell for in the market today?

Accepted Answer

The answer of Recently, Ohio Hospitals Inc. filed for bankruptcy....

Question 2

The current price of a 10-year, $1,000 par value bond is $1,158.91. Interest on this bond is paid every six months, and the nominal annual yield is 14 percent. Given these facts, what is the annual coupon rate on this bond?

Accepted Answer

The bond's price is higher than its par value, indicating it is selling at a premium. The nominal yield of 14% suggests the coupon rate must be higher than 14% to justify the premium price, making 17% the most plausible rate.

Question 3

A corporate bond which matures in 12 years, pays a 9 percent annual coupon, has a face value of $1,000, and a yield to maturity of 7.5 percent. The bond can first be called four years from now. The call price is $1,050. What is the bond's yield to call?

Accepted Answer

The yield to call (YTC) is calculated by determining the interest rate that equates the present value of the bond's cash flows (coupons and call price) to its current price, assuming it is called at the earliest opportunity. Given the bond's annual coupon of 9% ($90), call price of $1,050, and callable in 4 years, the YTC is approximately 6.73%.

Question 4

A bond that matures in 11 years has an annual coupon rate of 8 percent with interest paid annually. The bond's face value is $1,000 and its yield to maturity is 7.5 percent. The bond can be called 3 years from now at a price of $1,060. What is the bond's nominal yield to call?

Accepted Answer

The answer of A bond that matures in 11 years...

Question 5

A corporate bond has a face value of $1,000, and pays a $50 coupon every six months (i.e., the bond has a 10 percent semiannual coupon). The bond matures in 12 years and sells at a price of $1,080. What is the bond's nominal yield to maturity?

Accepted Answer

The answer of A corporate bond has a face value...

Question 6

An 8 percent annual coupon, noncallable bond has ten years until it matures and a yield to maturity of 9.1 percent. What should be the price of a 10-year noncallable bond of equal risk which pays an 8 percent semiannual coupon? Assume both bonds have a par value of $1,000.

Accepted Answer

The answer of An 8 percent annual coupon, noncallable bond...

Question 7

Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months and has 10 years to go before it matures. If you buy this bond, you expect to hold it for 5 years and then to sell it in the market. You (and other investors) currently require a nominal annual rate of 16 percent, but you expect the market to require a nominal rate of only 12 percent when you sell the bond due to a general decline in interest rates. How much should you be willing to pay for this bond?

Accepted Answer

The answer of Assume that you are considering the purchase...

Question 8

Your client has been offered a 5-year, $1,000 par value bond with a 10 percent coupon. Interest on this bond is paid quarterly. If your client is to earn a nominal rate of return of 12 percent, compounded quarterly, how much should she pay for the bond?

Accepted Answer

To determine the price your client should pay for the bond, we need to use the present value formula:

PV = C * [1 - 1 / (1 + r/n)^nt] / (r/n) + F / (1 + r/n)^nt

Where: 
PV = Present Value
C = Coupon payment
r = Nominal rate of return
n = Number of compounding periods per year
t = Number of years
F = Par value

Plugging in the given information, we get:

PV = 25 * [1 - 1 / (1 + 0.03)^20] / (0.03) + 1000 / (1 + 0.03)^20
PV = $926.37

Therefore, your client should pay $926.37 for the bond in order to earn a nominal rate of return of 12 percent, compounded quarterly. The best choice is B.

Question 9

Assume that a 15-year, $1,000 face value bond pays interest of $37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)

Accepted Answer

The bond pays $37.50 every quarter, and the required quarterly rate is 3% (12% annual rate divided by 4). The present value of the annuity (interest payments) is $37.50 * 27.6748 = $1,037.78. The present value of the face value is $1,000 * 0.1697 = $169.70. Adding these gives $1,207.48, which is closest to $1,207.57.

Question 10

Palmer Products has outstanding bonds with an annual 8 percent coupon. The bonds have a par value of $1,000 and a price of $865. The bonds will mature in 11 years. What is the yield to maturity on the bonds?

Accepted Answer

The yield to maturity (YTM) can be calculated using the formula for YTM, which equates the present value of future cash flows (coupon payments and par value at maturity) to the current price of the bond. Solving this equation for the given bond details results in a YTM of approximately 10.09%.

Question 11

Cold Boxes Ltd. has 100 bonds outstanding (maturity value = $1,000). The nominal required rate of return on these bonds is currently 10 percent, and interest is paid semiannually. The bonds mature in 5 years, and their current market value is $768 per bond. What is the annual coupon interest rate?

Accepted Answer

The answer of Cold Boxes Ltd. has 100 bonds outstanding...

Question 12

A 12-year bond pays an annual coupon of 8.5 percent. The bond has a yield to maturity of 9.5 percent and a par value of $1,000. What is the bond's current yield?

Accepted Answer

The answer of A 12-year bond pays an annual coupon...

Question 13

A corporate bond matures in 14 years. The bond has an 8 percent semiannual coupon and a par value of $1,000. The bond is callable in five years at a call price of $1,050. The price of the bond today is $1,075. What are the bond's yield to maturity and yield to call?

Accepted Answer

The yield to maturity (YTM) is calculated based on the bond's current price, coupon payments, and time to maturity, resulting in 7.14%. The yield to call (YTC) considers the bond's call price and time to the call date, resulting in 7.05%.

Question 14

GP&L sold $1,000,000 of 12 percent, 30-year, semiannual payment bonds 15 years ago. The bonds are not callable, but they do have a sinking fund which requires GP&L to redeem 5 percent of the original face value of the issue each year ($50,000), beginning in Year 11. To date, 25 percent of the issue has been retired. The company can either call bonds at par for sinking fund purposes or purchase bonds on the open market, spending sufficient money to redeem 5 percent of the original face value each year. If the nominal yield to maturity (15 years remaining) on the bonds is currently 14 percent, what is the least amount of money GP&L must put up to satisfy the sinking fund provision?

Accepted Answer

The answer of GP&L sold $1,000,000 of 12 percent, 30-year,...

Question 15

A bond matures in 12 years, and pays an 8 percent annual coupon. The bond has a face value of $1,000, and currently sells for $985. What is the bond's current yield and yield to maturity?

Accepted Answer

The answer of A bond matures in 12 years, and...

Question 16

A 20-year bond with a par value of $1,000 has a 9 percent annual coupon. The bond currently sells for $925. If the bond's yield to maturity remains at its current rate, what will be the price of the bond 5 years from now?

Accepted Answer

We can use the formula for present value of a bond to find the bond's yield to maturity:
$925 = \frac{90}{(1+y)^1} + \frac{90}{(1+y)^2} + \frac{90}{(1+y)^3} + \frac{90}{(1+y)^4} + \frac{1090}{(1+y)^5}$
Using a financial calculator or spreadsheet, we find that the yield to maturity is approximately 9.759%.
To find the price of the bond 5 years from now, we can use the formula for future value of a bond:
$FV = \frac{90}{(1+y)^4} + \frac{90}{(1+y)^3} + \frac{90}{(1+y)^2} + \frac{90}{(1+y)^1} + \frac{1000}{(1+y)^0}$
Plugging in the yield to maturity we just found, we get:
$FV = \frac{90}{1.09759^4} + \frac{90}{1.09759^3} + \frac{90}{1.09759^2} + \frac{90}{1.09759^1} + \frac{1000}{1.09759^0} \approx \$933.09$
Therefore, the best choice is D.

Question 17

Kennedy Gas Works has bonds which mature in 10 years, and have a face value of $1,000. The bonds have a 10 percent quarterly coupon (i.e., the nominal coupon rate is 10 percent). The bonds may be called in five years. The bonds have a nominal yield to maturity of 8 percent and a yield to call of 7.5 percent. What is the call price on the bonds?

Accepted Answer

The call price is the present value of the remaining coupon payments and the face value, discounted at the yield to call. The remaining coupon payments are $100 per quarter for 5 years, or 20 payments. The present value of these payments is:PV = $100 * (1 - (1 + 0.075/4)^-20) / (0.075/4) = $1,597.20The present value of the face value is:PV = $1,000 * (1 + 0.075/4)^-20 = $448.34The call price is the sum of these two present values:Call price = $1,597.20 + $448.34 = $1,048.34

Question 18

You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8 percent, payable annually, and annual interest rates on new issues of the same degree of risk are 10 percent. You want to know how many more interest pay¬ments you will receive, but the party selling the bond cannot remember. Can you determine how many interest payments remain?

Accepted Answer

First, calculate the annual interest payment: 
Coupon rate x Par value = Annual interest payment 
0.08 x $1,000 = $80

Next, calculate the yield to maturity: 
Market price = Present value of future cash flows 
$847.88 = $80 / (1 + y)^1 + $80 / (1 + y)^2 + … + $80 / (1 + y)^n + $1,000 / (1 + y)^n 
Where n is the number of interest payments remaining.

Using a financial calculator or Excel, the yield to maturity can be calculated as 9.43%.

Then, use the yield to maturity to calculate the number of interest payments remaining: 
n = log[(Par value / Market price + Annual interest payment) / Annual interest payment] / log(1 + Yield to maturity) 
n = log[(1,000 / 847.88 + 80) / 80] / log(1 + 0.0943) 
n ≈ 15

Therefore, there are 15 interest payments remaining.

Question 19

A bond with a $1,000 face value and an 8 percent annual coupon pays interest semiannually. The bond will mature in 15 years. The nominal yield to maturity is 11 percent. What is the price of the bond today?

Accepted Answer

First, we need to calculate the number of semiannual periods until maturity, which is 15 years x 2 = 30 semiannual periods.

Next, we need to calculate the semiannual coupon payment, which is $1,000 x 8% / 2 = $40.

Then, we can use the formula for the present value of a bond:

PV = (C / r) x [1 - (1 / (1 + r)^n)] + (F / (1 + r)^n)

where:
PV = present value of the bond
C = semiannual coupon payment
r = nominal yield to maturity / 2
n = number of semiannual periods until maturity
F = face value of the bond

Plugging in the numbers, we get:

PV = ($40 / 0.055) x [1 - (1 / (1 + 0.055)^30)] + ($1,000 / (1 + 0.055)^30)
PV = $781.99

Therefore, the price of the bond today is $781.99. Choice B is the correct answer.

Question 20

A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?

Accepted Answer

We can use the formula for present value of a bond:

PV = (C / (1 + r/2)^n) + (C / (1 + r/2)^(n-1)) + ... + (C + FV / (1 + r/2)^(n-1))

Where PV is the present value, C is the coupon payment, r is the nominal yield to maturity, n is the number of periods (in this case 20 since there are 10 years and two coupon payments per year), and FV is the face value.

Plugging in the numbers:

PV = (50 / (1 + 0.09/2)^20) + (50 / (1 + 0.09/2)^19) + ... + (50 + 1000 / (1 + 0.09/2)^19)

PV = 50 x (1 - 1/(1 + 0.09/2)^20) / (0.09/2) + 1000 / (1 + 0.09/2)^20

PV = $1,065.04

Quiz 4: Bond Valuation