Question 1

A US Government 4% coupon bond has 10 years remaining to maturity. The bond pays annual coupons and the next coupon is due in one year. The face value of the bond is $100. The bond is currently trading for $74.43 and yields 6%. Calculate your capital gain return if you buy the bond today, hold it for one year and sell it after the next coupon. (Assume that yields are expected to remain constant at the current level over the bond's life.)

Accepted Answer

Capital gains rate = yield - coupon yield.
Capital gains rate = .06 - 11ea7fdb_fc02_83f8_a768_abb65552a7a7_TB2902_11 = .6%

Question 2

Consider two recent bond issues by Microsoft: both have face values of $1,000 and coupon rates of 10% but one bond (call it the short bond)has five years to maturity and the other, the long bond, has twenty years to maturity. Which bond do you expect to be more sensitive to a change in yields? That is, for a given change in yield which bond (the long or the short)will experience a greater change in price?

Accepted Answer

The long bond is expected to be more sensitive to a change in yields because it has a longer time to maturity. A longer time to maturity means that the cash flows of the bond are spread out over a longer period of time, making it more sensitive to changes in interest rates. In contrast, the short bond has a shorter time to maturity, and its cash flows are concentrated over a shorter period, making it less sensitive to changes in interest rates.

Question 3

A US Government bond has 15 years remaining to maturity, pays annual coupons (yesterday)of $90, and has a face value of $1,000. The current price of the bond is $923.94 to yield 10%. Calculate your return if you buy the bond today, hold it for one year and sell it after the next coupon. What percentage of your return will be attributable to coupon interest (as opposed to capital gain)? (Assume that yields are expected to remain constant at the current level over the bond's life.)

Accepted Answer

Coupon yield as a proportion of yield = coupon yield / yield 11ea7fdb_fc02_ab09_a768_8d80061b3cb5_TB2902_11 = .9741 or 97.41%

Question 4

Assume that the Microsoft bonds have a face value of $1,000, 5-years to maturity and pay annual coupons of $100. The next coupon is due in one year. The yield on equivalently risky corporate bonds is currently 5%. Assume the yield stays at 5% over the life of the bond. Determine the price of the bond today and after each of the first four coupon payments. Plot those prices on a graph with price on the y-axis and time on the x-axis. (The x-axis starts at time 0 and ends on the date of the fourth coupon.)What do you note about the time path (slope of the line)of the bond price?

Accepted Answer

The price of a bond decreases as time passes, as the bond's remaining life gets shorter. As a result, the time path (slope of the line) of the bond price is downward sloping.

Question 5

A $1,000 face value bond has a coupon rate of 5%. Bonds of similar risk currently yield 7%. This bond should be selling

Accepted Answer

The bond has a lower yield (5%) than current market rates (7%), indicating that it is not as attractive to investors. As a result, the bond should be selling at a discount to its face value in order to compensate for the lower yield.

Question 6

Microsoft just issued a bond with annual coupons and twenty years to maturity. The bond has a face value of $1,000 and a coupon rate of 10%. If the yield on equivalently risky corporate bonds is currently 10%, then what were the proceeds to Microsoft from the bond issue?

Accepted Answer

If the yield on the bond is 10% and the coupon rate is also 10%, the bond was issued at its face value of $1,000. Therefore, the proceeds to Microsoft from the bond issue were $1,000.

Question 7

Consider a 3-year bond maturing Sept 30, 2019. Assume that you bought the bond on Sept 30, 2016, at a price of $1,074.56 ($1,000 face value). If rates stay as they are for the rest of the year, what percentage change in price do you expect over the next year based on your estimate of the bond price after the second coupon is paid (Sept 30, 2017)? Assume that the bond pays semi-annual coupons (4.5% annual coupon rate)and has a bond equivalent yield of 1.93% per annum.

Accepted Answer

First, let's calculate the amount of the semi-annual coupons:

Coupon payment = Face value x Coupon rate/2 = $1,000 x 4.5%/2 = $22.50

The bond will pay two coupons over the next year (on March 31, 2017 and September 30, 2017), so the total cash flow you will receive is:

Cash flow = Coupon payment + Face value = $22.50 + $1,000 = $1,022.50

Next, let's calculate the bond's yield to maturity (YTM) using its bond equivalent yield (BEY):

BEY = (1 + YTM/2)^2 - 1

1.93% = (1 + YTM/2)^2 - 1

YTM = 3.82%

We can use this YTM to calculate the bond's price after the second coupon is paid (i.e., on Sept 30, 2017):

Price = ($22.50 / (1 + 1.91%/2)^1) + ($22.50 / (1 + 1.91%/2)^2) + ($1,000 / (1 + 1.91%/2)^2) = $1,041.43

Therefore, the percentage change in price over the next year is:

Percentage change = (New price - Old price) / Old price = ($1,041.43 - $1,074.56) / $1,074.56 = -3.07%

Rounding to one decimal, we get -3.1%, which is closest to answer choice A (-2.3%). So, the answer is A.

Question 8

A $1,000 face value bond has a 9% annual coupon rate. The next coupon is due in one year. The bond matures in 15 years and the yield on the bond is 10%. What is the difference in price if the yield rises to 11%?

Accepted Answer

P_bond = C × 11ea7fdb_fc02_5ce2_a768_8f20efa8e7f8_TB2902_11 + 11ea7fdb_fc02_5ce3_a768_5ba0b4105d75_TB2902_11 P_10% = 90 × 11ea7fdb_fc02_5ce4_a768_5580e4829b32_TB2902_11 + 11ea7fdb_fc02_5ce5_a768_efb34fb81431_TB2902_11 = $923.94 Using a financial calculator: N = 15, I/Y = 10, PMT = -90, FV = -1,000, CPT PV = $923.94 P_11% = 90 × 11ea7fdb_fc02_83f6_a768_2fdb7122ee0d_TB2902_11 + 11ea7fdb_fc02_83f7_a768_bd961639c9f5_TB2902_11 = $856.18 Using a financial calculator: N = 15, I/Y = 11, PMT = -90, FV = -1,000, CPT PV = $856.18 Difference = $856.18 - $923.94 = -$67.76

Question 9

$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Bond } & \text { Coupon Rate } & \text { Maturity } & \text { Price } & \text { Yield } \
\hline \text { T-Note Strip } & 0 & 10 & 70.69 & 3.5 \% \
\hline \text { T-Bill } & 0 & 1 & 96.62 & 3.5 \% \
\hline \text { 8-year T-Note } & 5 \% & 8 & 110.31 & 3.5 \% \
\hline \text { 7-year T-Note } & 6.5 \% & 7 & 118.34 & 3.5 \% \
\hline
\end{array}$$ Each bond in the table has a face value of $100. The coupon bonds pay annual coupons, and the next coupon is due in one year. Assume that the yield curve is flat and all yields are currently 3.5%. If interest rates are forecast to rise to 4% from 3.5%, then what is the percentage change in price for the bond whose price changes the most?

Accepted Answer

The bond with the longest duration will experience the largest percentage change in price when interest rates change. The T-Note Strip has the longest maturity and zero coupon, making it the most sensitive to interest rate changes. The percentage change in price for the T-Note Strip when rates rise from 3.5% to 4% is approximately -4.4%.

Question 10

A US Government bond has 10 years remaining to maturity, pays annual coupons (yesterday)of $40, and has a face value of $1,000. The current price of the bond is $1,085.30 to yield 3%. If you buy the bond today, hold it for one year and sell it after the next coupon, then what return will you earn for the year? (Assume that yields are expected to remain constant at the current level over the bond's life.)

Accepted Answer

Holding period return = Capital gains rate + coupon yield, which equals the yield.
Yield = 3%.

Question 11

The economy is slowing and many forecasters predict a recession. You expect the monetary authorities to relax monetary policy which will cause interest rates to fall. You expect the yield on the Walt Disney 10-year bond to fall from 5% to 4%. The bond has a face value of $1,000, and a coupon of 3.25%. If you want to make $5,000 by investing in bonds to profit from the interest rate change, what position do you take?

Accepted Answer

Step 1 - Calculate the price of the bonds before and after the expected change in interest rates, and find the difference. P_bond = C × 11ea7fdb_fc03_2044_a768_7354fc8f7b1b_TB2902_11 + 11ea7fdb_fc03_2045_a768_058c02b8efa5_TB2902_11 P_{new 4%} = 32.5 × 11ea7fdb_fc03_2046_a768_8f4489500e41_TB2902_11 + 11ea7fdb_fc03_4757_a768_5743a4c41ab8_TB2902_11 = $939.17 P_{old 5%} = 32.5 × 11ea7fdb_fc03_4758_a768_fdb8599dc968_TB2902_11 + 11ea7fdb_fc03_4759_a768_5bb8b0a9d24a_TB2902_11 = $864.87 939.17 - 864.87 = 74.30 Step 2 - Determine how many bonds you need to profit $5,000. 11ea7fdb_fc03_475a_a768_f9c6b235d83b_TB2902_11 = 67.29 Since interest rates will fall, bond prices will rise, so you should buy 67 bonds.

Question 12

$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Bond } & \text { Coupon Rate } & \text { Maturity } & \text { Price } & \text { Yield } \
\hline \text { T-Note Strip } & 0 & 10 & 70.69 & 3.5 \% \
\hline \text { T-Bill } & 0 & 1 & 96.62 & 3.5 \% \
\hline \text { 8-year T-Note } & 5 \% & 8 & 110.31 & 3.5 \% \
\hline \text { 7-year T-Note } & 6.5 \% & 7 & 118.34 & 3.5 \% \
\hline
\end{array}$$ Each bond in the table has a face value of $100. The coupon bonds pay annual coupons, and the next coupon is due in one year. Assume that the yield curve is flat and all yields are currently 3.5%. If interest rates are forecast to rise to 4% from 3.5%, what is your profit if you short-sell the bond with the biggest anticipated (percentage)decline. (Assume you short-sell only one bond.)

Accepted Answer

The bond with the biggest anticipated percentage decline when interest rates rise is the 7-year T-Note with a 6.5% coupon. When rates rise, longer-duration bonds with higher coupons tend to decline more in price. The profit from short-selling is the difference in price due to the rate change, which is approximately $3.13.

Question 13

A bond with an annual coupon of $100 originally sold at par for $1,000. The current yield to maturity on this bond is 9%. Assuming no change in risk, this bond would sell at a ________ in order to compensate ________.

Accepted Answer

Since the coupon rate (10%) is greater than the yield (9%), the bond trades at a premium to offset the above market coupon rate.

Question 14

A bond sells at a discount when

Accepted Answer

When a bond sells at a discount, it means its price is lower than its face value. This can happen for various reasons such as a decrease in the creditworthiness of the issuer, an increase in interest rates, or a decrease in market demand for the bond. Investors buying a bond at a discount receive a higher yield than the coupon rate, but they will not receive the full face value of the bond at maturity.

Question 15

In general, if interest rates ________, bond prices ________.

Accepted Answer

Bond prices move inversely with interest rates, meaning that if interest rates rise bond prices fall and vice versa. Therefore both answers C and D are correct.

Question 16

$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Bond } & \text { Coupon Rate } & \text { Maturity } & \text { Price } & \text { Yield } \
\hline \text { T-Note Strip } & 0 & 10 & 70.69 & 3.5 \% \
\hline \text { T-Bill } & 0 & 1 & 96.62 & 3.5 \% \
\hline \text { 8-year T-Note } & 5 \% & 8 & 110.31 & 3.5 \% \
\hline \text { 7-year T-Note } & 6.5 \% & 7 & 118.34 & 3.5 \% \
\hline
\end{array}$$ Each bond in the table has a face value of $100. The coupon bonds pay annual coupons, and the next coupon is due in one year. Assume that the yield curve is flat and all yields are currently 3.5%. If interest rates are forecast to rise to 4% from 3.5%, then which bond's price will decline by the greatest percentage amount?

Accepted Answer

The T-Note Strip, being a zero-coupon bond with the longest maturity, is most sensitive to interest rate changes, leading to the greatest percentage price decline when rates rise.

Question 17

Assume that the Microsoft bonds have 5-years to maturity and pay annual coupons of $100. The next coupon is due in one year. The yield on equivalently risky corporate bonds is currently 15%. Assume the yield stays at 15% over the life of the bond. Determine the price of the bond today and after each of the first four coupon payments. Plot those prices on a graph with price on the y-axis and time on the x-axis. (The x-axis starts at time 0 and ends on the date of the fourth coupon.)What do you note about the time path (slope of the line)of the bond price?

Accepted Answer

The coupon rate is smaller than the yield to maturity, the bond trades at a discount to face value and rises over its life (assuming no change in yield).

Question 18

Consider two recent bond issues by Microsoft: both have face values of $1,000 and coupon rates of 10% but one bond (call it the short bond)has five years to maturity and the other, the long bond, has twenty years to maturity. Assume that yields fall from 15% to 5%. Which bond will experience a greater price increase, and by how much?

Accepted Answer

P_bond = C × 11ea7fdb_fc02_d21a_a768_19f0fb7cc410_TB2902_11 + 11ea7fdb_fc02_d21b_a768_994ff6046d88_TB2902_11 P_{long 5%} = 100 × 11ea7fdb_fc02_d21c_a768_273691f7aade_TB2902_11 + 11ea7fdb_fc02_d21d_a768_05bd2415d1e7_TB2902_11 = $1,623.11 P_{long 15%} = 100 × 11ea7fdb_fc02_f92e_a768_277eff927cd5_TB2902_11 + 11ea7fdb_fc02_f92f_a768_cf2d0d4d0cbe_TB2902_11 = $687.03 Change in the long bond's price = 1,623.11 - 687.03 = $936.08 P_{short 5%} = 100 × 11ea7fdb_fc02_f930_a768_f1e7b123fff9_TB2902_11 + 11ea7fdb_fc02_f931_a768_514dda508ba7_TB2902_11 = $1,216.47 P_{short 15%} = 100 × 11ea7fdb_fc02_f932_a768_753939fdc82a_TB2902_11 + 11ea7fdb_fc02_f933_a768_575bfc0e4949_TB2902_11 = $832.39 Change in the short bond's price = 1,216.47 - 832.39 = $384.08

Question 19

Suppose that you are reviewing a price sheet for bonds and see the following prices (per $100 face value)reported. Without calculating the price of each bond, which bond seems to be reported incorrectly? $$\begin{array} { | c | c | c | c | } 
\hline \text { Bond } & \text { Price } & \text { Coupon Rate } & \text { Yield } \
\hline \mathrm { V } & 100 & 6 \% & 6 \% \
\hline \mathrm { W } & 110 & 8 \% & 6 \% \
\hline \mathrm { X } & 95 & 0 \% & 5 \% \
\hline \mathrm { Y } & 107 & 7 \% & 9 \% \
\hline \mathrm { Z } & 90 & 6 \% & 9 \% \
\hline
\end{array}$$

Accepted Answer

Bond Y is reported incorrectly because a bond with a coupon rate of 7% and a yield of 9% should be priced below its face value, not above it at 107.

Question 20

Which of the following bonds carries the greatest amount of interest rate risk?

Accepted Answer

The 25-year bond carries the greatest amount of interest rate risk because when interest rates change, long-term bond prices change more than those of short term bonds.
This is due to the fact that the present value of a short-term cash flow doesn't change as much as that of a more distant, long-term cash flow. Short-term cash flows are only discounted a few periods, whereas long-term cash flows are discounted over many periods.
PV = 11ea7fdb_fc03_e3a3_a768_e3275dd53048_TB2902_11 Looking at the equation for present value, we can see that when n is very large (i.e. many periods) the change in interest rates has a compounding effect and will drastically change the present value (or price) of the bond.

Quiz 7: Interest Rates and Bond Valuation

A $1,000 face value bond has a coupon rate of 5%. Bonds of similar risk currently yield 7%. This bond should be selling

Microsoft just issued a bond with annual coupons and twenty years to maturity. The bond has a face value of $1,000 and a coupon rate of 10%. If the yield on equivalently risky corporate bonds is currently 10%, then what were the proceeds to Microsoft from the bond issue?

A $1,000 face value bond has a 9% annual coupon rate. The next coupon is due in one year. The bond matures in 15 years and the yield on the bond is 10%. What is the difference in price if the yield rises to 11%?

A bond with an annual coupon of $100 originally sold at par for $1,000. The current yield to maturity on this bond is 9%. Assuming no change in risk, this bond would sell at a in order to compensate .

A bond sells at a discount when

In general, if interest rates , bond prices .

Which of the following bonds carries the greatest amount of interest rate risk?