Question 1
You are purchasing a 15 year, zero coupon bond with a face value of $1000. The yield to maturity is 6.6% based
I/Y 6.60%
N 15
PMT 0
FV $1,000.00
Solve for
PV $383.39
Question 2
Company ABC offers a 6.5% coupon bond with annual payments and a yield to maturity of 11.12 %. The bonds
YTM 11.12%
N 12
Coupon Rate 6.50%
PMT $65.00
FV 1,000
PV of par value $282.16
PV of coupons $419.60
Solve for
PV of bond $701.76
Question 3
Company XYZ has a bond issue outstanding that pays an 7.25% coupon semiannually with a maturity o
$957.20. What is the yield to maturity?
Coupon rate 7.25%
PMT $36.25
N 36
Market value of bond = PV of par value + PV of coupons
PV of bond -$957.20
FV $1,000.00
Solve for
I/Y 3.847%
YTM 7.69%
Question 4
Consider a 10 year bond making annual coupon payments at a rate of 8% with a face value of $10
a) Suppose you decide to buy the bond today and hold it for 10 years. What is the price of the bo
a)
I. Under annual payments and a flat term structure, interest rate = YTM
II. When YTM = coupon rate, the bond is sold at par
III. Without calculations, price of bond = $1,000 and retun = YTM = 8%
Suppose you decide to sell the bond at the end of year 4. If the interest rate stays at 8% for the nex
what price can you sell the bond at the time of transaction and what is your (holding period) return
b)
I. At the end of Y4, there are 6 years and coupon payments remaining
II. These payments are discounted at 5%
N 6
I/Y 5%
FV -$1,000.00
PMT -$80.00
Solve for
PV $1,152.27
Price of bond at Y4 $1,152.27
III. To find the holding period return (HPY), add in received payments and discount
PV -$1,000.00
N 4
PMT $80.00
FV $1,152.27
Solve for
I/Y 11.22%
Question 5
You are a bond trader and observe the following three US government bonds trading in the market: (Face
A: A ten-year zero coupon bond trading at $508.35.
B: A ten-year 7% annual coupon bond trading at $1,000.00.
C: A ten-year 4% semi-annual coupon bond trading at $794.13.
The term structure is flat.
a) What is the market interest rate?
b) What is the YTM on the three bonds?
Suppose now you see the following bond selling on the market:
A ten-year 6% annual coupon bond trading at $925.00.
B: A ten-year 7% annual coupon bond trading at $1,000.00.
C: A ten-year 4% semi-annual coupon bond trading at $794.13.
The term structure is flat.
a) What is the market interest rate?
b) What is the YTM on the three bonds?
Suppose now you see the following bond selling on the market:
A ten-year 6% annual coupon bond trading at $925.00.
c) Are you surprised by the market price? Why or why not?
a) Use the zero coupon bond to find the market rate
Using Bond A
PV -$508.35
N 10
PMT 0
FV $1,000.00
Solve for
I/Y 7.00%
I. Since the yield curve is flat, the interest rate is constant across time
II. Market rate is constant at 7%
III. Because the yield curve is flat, you could have solved for YTM using any of the
Using Bond B Selling at par => YTM = coupon rate
Annual payments => market rate = YTM
Using Bond C
PMT $20
N 20
PV -$794.13
FV $1,000.00
Solve for
I/Y 3.44%
EAR 7.00%
b)
Bond A YTM = market rate b/c cash flows are annual, so YTM = 7%
Bond B YTM = market rate b/c cash flows are annual, so YTM = 7%
Bond C YTM = 2*semi-annual rate = 2*3.44% = 6.88%, EAR = 7%
c)
Bond D
Annual coupon pmt $60
Market interest rate 7%
PV $929.76
I. We should be surprised
II. Bond is worth $929.76 but the market is selling it at $925
III. The bond is mispriced/undervalued; good buying opportunity
Alternative method
N 10
PV -$925.00
PMT $60
FV $1,000
Solve for
I/Y 7.07%
I. This bond offers a return of 7.07% > 7% market rate
II. Bond is mispriced/undervalued; good buying opportunity
d) Buy the underpriced bond
IGNORE the information below
I. Since we know that Bond D is mispriced, there is an arbitrage opportunity in the
II. Bond D should equal to (6/7)*Bond A +(1/7)*Bond B
III. In the market, Bond D < (6/7)*Bond A +(1/7)*Bond B
IV. To take advantage of this arbitrage:
i. Buy Bond D from the market (pay $925)
ii. Sell (6/7) of Bond A and (1/7) of Bond B (earn $929.76)
iii. This gives us a risk-free profit of $4.76
iv. Repeat lots of times to reap more profits
NOTES
I. An arbitrage opportunity is one where you can make profits without incurring ad
II. i.e A "free-lunch" opportunity
III. By doing the above buy-sell, you have perfectly canceled your risk (offset the ca
IV. And making a profit
V. Ideally, you would repeat step iv) infinite times to reap infinite profits
VI. Why would you not be able to do so? (Ch. 12)
o maturity is 6.6% based on annual coupon payments. What is the current market price?
y of 11.12 %. The bonds mature in 12 years. What is the market price of the bond if the face value is $1,000?
OR, = 282.16 + 419.60
ually with a maturity of 18 years. The bonds have a par value of $1,000 and a market price of
% with a face value of $1000. The market interest rate is 8%. (15 points)
hat is the price of the bond and your (holding period) return (in percentages) if the term structure stays flat at 8% for the enti
rate = YTM
= YTM = 8%
e stays at 8% for the next two years from now (time 0) and then shifts down to 5% and stays at 5% for the remainder of the 1
r (holding period) return (in percentages)?
remaining
ayments and discount back to Y0
ding in the market: (Face value = $1000.) (25 points)
cross time
YTM using any of the 3 bonds and obtained the market rate
rage opportunity in the market
ts without incurring additional risk
your risk (offset the cash flows)
nite profits
ue is $1,000?
ice of
e stays flat at 8% for the entire 10 years during which you hold the bond?
% for the remainder of the 10 years,
