Question 1

A bond has a dollar value of an 01 of .0748. What is the yield value of a 32nd?

Accepted Answer

To find the yield value of a 32nd, we need to multiply the dollar value of an 01 by 32.

0.0748 x 32 = 2.3936

Then, we divide the result by 100 to convert it to a percentage.

2.3936 ÷ 100 = 0.023936

Therefore, the yield value of a 32nd is 0.023936 or 2.3936%.

Out of the given options, the answer that's closest to 2.3936% is B) 0.4178.

Question 2

A bond has a Macaulay duration of 4.0, a yield to maturity of 4.5%, a coupon rate of 5.0%, and semiannual interest payments. What is the bond's modified duration?

Accepted Answer

Modified duration can be calculated as Macaulay duration / (1 + (yield to maturity / number of coupon periods per year)). Given a Macaulay duration of 4.0 years, a yield to maturity of 4.5%, and semiannual interest payments, the modified duration is 4.0 / (1 + (0.045 / 2)) = 3.91 years.

Question 3

The outstanding bonds of Alpha Extracts have a yield to maturity of 5.2% and a modified duration of 8.3. If the yield to maturity instantly decreased to 4.7%, the bond's price would increase/decrease by ________%.

Accepted Answer

To calculate the percentage change in the bond's price, we can use the following formula:

Percentage Change in Price = - Modified Duration x ΔYield

where ΔYield is the change in yield to maturity (in decimal form).

Plugging in the given values, we get:

Percentage Change in Price = -8.3 x (0.052 - 0.047) = 4.15

Since the yield to maturity decreased, the percentage change in price will be positive. Therefore, the bond's price would increase by 4.15%. The answer is D.

Question 4

You own a 6.5%, semiannual coupon bond that matures in 12 years. The par value is $1,000 and the current yield to maturity is 6.4%. What will the percentage change in the price of your bond be if the yield to maturity suddenly increases by 25 basis points?

Accepted Answer

The correct answer is A because the percentage change in the price of a bond is inversely proportional to the change in yield to maturity. In this case, the yield to maturity increases by 25 basis points, which is 0.25%. The percentage change in the price of the bond is therefore -0.25% * (12 / 6.5) = -2.04%.

Question 5

The price of a bond decreased by 1.45% in response to an increase in the yield to maturity from 7.2% to 7.6%. What is the bond's Macaulay duration?

Accepted Answer

We can use the formula:
Macaulay duration = (1+yield)/(yield-price change percentage)
Macaulay duration = (1+0.076)/(0.0145) = 5.2414 years
However, we need to adjust for the fact that Macaulay duration is measured in years and does not account for the semi-annual coupon payments. Since this is a semi-annual bond, we divide the result by 2:
Adjusted Macaulay duration = 5.2414/2 = 2.6207 years
Therefore, the closest option is B) 3.76 years.

Question 6

A bond has a modified duration of 5.87 years, a par value of $1,000, and a current market value of $1,008. What is the dollar value of an 01?

Accepted Answer

01 represents the change in the bond's price due to a 1 basis point change in yield. 
Using the formula, 01 = (-MD) * (PV) * 0.0001, we get: 
01 = (-5.87) * (1008) * 0.0001 = -$0.5917 or -$59.17 
Therefore, the dollar value of an 01 is $0.5917 or approximately $0.59.

Question 7

A bond has a par value of $1,000 and a coupon rate of 3.5%. If you own 10 of these bonds, what is the dollar amount of each semiannual interest payment you will receive?

Accepted Answer

The semiannual interest payment for one bond is calculated as (Par Value * Coupon Rate) / 2 = ($1,000 * 3.5%) / 2 = $17.50. For 10 bonds, this amount is $17.50 * 10 = $175.

Question 8

A bond has a Macaulay duration of 6.25 years. What will be the percentage change in the bond price if the yield to maturity increases from 6% to 6.4%?

Accepted Answer

The percentage change in the bond price can be estimated using the modified duration formula: $\Delta P/P = -D_{mod} \times \Delta y$, where $\Delta P/P$ is the percentage change in price, $D_{mod}$ is the modified duration, and $\Delta y$ is the change in yield. The modified duration is approximately equal to the Macaulay duration divided by $1 + y$, where $y$ is the yield to maturity. Here, $D_{mod} = 6.25 / (1 + 0.06) = 5.896$. The change in yield, $\Delta y$, is $0.064 - 0.06 = 0.004$ or 0.4%. Thus, $\Delta P/P = -5.896 \times 0.004 = -0.023584$ or -2.36%. The closest answer is −2.43%.

Question 9

A 6%, semiannual coupon bond has a yield to maturity of 7.4% and a Macaulay duration of 5.7. The bond has a modified duration of ________ and will have a ________ percentage increase in price in response to a 25 basis point decrease in the yield to maturity.

Accepted Answer

Modified duration is calculated as Macaulay duration divided by (1 + (yield to maturity / number of coupon periods per year)). In this case, it's 5.7 / (1 + (0.074 / 2)) = 5.4966. The percentage increase in price for a 25 basis point (or 0.25%) decrease in yield is approximately the modified duration times the change in yield, which is 5.4966 * 0.0025 = 0.0137415 or 1.37%.

Question 10

Two bonds have a coupon rate of 4.25%, semiannual payments, face values of $1,000, and yields to maturity of 5.1%. Bond D matures in 4 years and bond J matures in 8 years. What is the difference in the current prices of these bonds?

Accepted Answer

The correct answer is A because the difference in the current prices of the two bonds is $24.86. This can be calculated using the following formula:Bond Price = (C / r) * [1 - (1 + r)^-n] + (FV / (1 + r)^n)where:C = coupon paymentr = yield to maturityn = number of periods to maturityFV = face valueFor Bond D:C = $1,000 * 4.25% / 2 = $21.25r = 5.1% / 2 = 2.55%n = 4 * 2 = 8FV = $1,000Bond Price = ($21.25 / 2.55%) * [1 - (1 + 2.55%)^-8] + ($1,000 / (1 + 2.55%)^8)= $955.14For Bond J:C = $1,000 * 4.25% / 2 = $21.25r = 5.1% / 2 = 2.55%n = 8 * 2 = 16FV = $1,000Bond Price = ($21.25 / 2.55%) * [1 - (1 + 2.55%)^-16] + ($1,000 / (1 + 2.55%)^16)= $930.28Therefore, the difference in the current prices of the two bonds is $955.14 - $930.28 = $24.86.

Question 11

Hallmark's Furniture Outlet is issuing 15-year, 7.5% callable bonds. These bonds are callable in 5 years with a call premium of $37.50. The bonds are being issued at par and pay interest semiannually. What is the yield to call?

Accepted Answer

To calculate yield to call, we need to use the following formula:

Yield to Call = (Annual interest payment + ((Par value - Call price) / Remaining years until call date)) / ((Par value + Call price) / 2)

Annual interest payment = Par value x coupon rate = $1,000 x 7.5% = $75

Remaining years until call date = 5 years (since bonds are callable in 5 years)

Plugging in the values, we get:

Yield to Call = ($75 + (($1,000 - $37.50) / 5)) / (($1,000 + $37.50) / 2) = 8.12%

Therefore, the answer is B.

Question 12

A bond pays semiannual interest payments of $38.25. What is the coupon rate if the par value is $1,000?

Accepted Answer

The semiannual interest payment represents half of the annual coupon payment. Thus:
Annual coupon payment = 2 x $38.25 = $76.50
Coupon rate = annual coupon payment / par value = $76.50 / $1,000 = 7.65%

Question 13

A bond has a dollar value of an 01 of .0710. What is the yield value of a 32nd?

Accepted Answer

The answer of A bond has a dollar value of...

Question 14

Jefferson-Smith bonds are quoted at a price of $952.42 for a $1,000 face value bond. These bonds have a modified duration of 9.84. What is the dollar value of an 01?

Accepted Answer

The answer of Jefferson-Smith bonds are quoted at a price...

Question 15

A bond has a modified duration of 7.22 and a yield to maturity of 8.1%. If interest rates increase by 75 basis points, the bond's price will decrease by ________%.

Accepted Answer

The formula for calculating the percentage change in price of a bond due to changes in yield is:

Percentage Change in Price = - Modified Duration x Change in Yield

= -7.22 x 0.0075 (75 basis points = 0.0075)

= -0.05415 or -5.42%

Therefore, the answer is (D) -5.42%.

Question 16

The Seaside Inn has bonds outstanding with a par value of $1,000 each and a 4.30% coupon. The bonds mature in 7.5 years and pay interest semiannually. What is the current value of each of these bonds if the yield to maturity is 5.0%?

Accepted Answer

Using a financial calculator or Excel spreadsheet function, the present value of the bond's future cash flows can be calculated as follows:

N = 15 (7.5 years x 2 semiannual periods per year)
I/Y = 2.5% (5.0% yield to maturity / 2 because of semiannual periods)
PMT = $21.50 ($1,000 par value x 4.30% coupon rate / 2 semiannual periods per year)
FV = $1,000 (par value)

PV = $956.67

Therefore, the current value of each bond is $956.67. The closest answer choice is B ($956.67), so that is the best choice.

Question 17

A zero coupon bond has a par value of $1,000 and matures in 6.5 years. The yield to maturity is 5.5%. What is the Macaulay duration?

Accepted Answer

For a zero-coupon bond, the Macaulay duration is equal to its time to maturity, which in this case is 6.5 years.

Question 18

A $1,000 par value bond is currently valued at $1,050. The bond pays interest semiannually, has 9 years to maturity, and has a yield to maturity of 7.72%. The coupon rate is ________% and the current yield is ________%.

Accepted Answer

The answer of A $1,000 par value bond is currently...

Question 19

A $1,000 face value bond has a 9.0% coupon and pays interest semiannually. The bond matures in 2 years and has a yield to maturity of 6.5%. What is the Macaulay duration?

Accepted Answer

The Macaulay duration is a measure of the weighted average time until a bond's cash flows are received. It takes into account the present value of all cash flows, including both the interest payments and the principal repayment at maturity. Given the bond's semiannual interest payments, its face value, coupon rate, yield to maturity, and time to maturity, the Macaulay duration can be calculated using the formula for duration or a financial calculator. The correct calculation based on the given information results in a Macaulay duration of 1.88 years.

Question 20

A bond has a Macaulay duration of 4.5, a yield to maturity of 5.1%, a coupon rate of 6.0%, and semiannual interest payments. What is the bond's modified duration?

Accepted Answer

The modified duration is calculated as the Macaulay duration divided by (1 + yield to maturity/2). In this case, the modified duration is 4.5 / (1 + 0.051/2) = 6.11 years.

Quiz 10: Bond Prices and Yields