Homework: Valuing Bonds Assignment
1.A 30-year Treasury bond is issued with face value of $1,000, paying interest of $42 per year. If
market yields increase shortly after the T-bond is issued, what is the bond’s coupon rate?
42/1000= 4.2%
More
3.One bond has a coupon rate of 7.4%, another a coupon rate of 9.2%. Both bonds pay interest
annually, have 11-year maturities, and sell at a yield to maturity of 8.0%.
a.If their yields to maturity next year are still 8.0%, what is the rate of return on each bond? (Do
not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal
place.)
Bond 1 8% and Bond 2 8%
b.Does the higher-coupon bond give a higher rate of return over this period?
d. If the yield to maturity falls to 6.5%, will the current yield be less, or more, than the yield to
maturity?
2.A General Power bond carries a coupon rate of 8.5%, has 9 years until maturity, and sells
at a yield to maturity of 7.5%. (Assume annual interest payments.)
a.What interest payments do bondholders receive each year?
.085*1000=$85
b.At what price does the bond sell? (Do not round intermediate calculations. Round
your answer to 2 decimal places.)
85 x ((1/.075)-(1/(.075(1+.075)^9)))+1000/(1+.075)^9
=1063.79
c.What will happen to the bond price if the yield to maturity falls to 6.5%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
85 x ((1/.065)-(1/(.065(1+.065)^9)))+1000/(1+.065)^9
=1133.12-1063.79=69.33 rise
No
4. General Matter’s outstanding bond issue has a coupon rate of 9.0%, and it sells at a yield to
maturity of 7.40%. The firm wishes to issue additional bonds to the public. What coupon rate
must the new bonds offer in order to sell at face value? (Enter your answer as a percent rounded
to 2 decimal places.)
7.40 (YTM) BECAUSE
When the bond is selling at face value, its yield to maturity equals its coupon rate. This firm's
bonds are selling at a yield to maturity of 7.40%. So the coupon rate on the new bonds must be
7.40% if they are to sell at face value
b. What will be the price of the 8-year bond if its yield increases to 7.20%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
c. What will be the price of the 30-year bond if its yield increases to 7.20%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
d. What will be the price of the 4-year bond if its yield decreases to 5.20%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
e. What will be the price of the 8-year bond if its yield decreases to 5.20%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
f. What will be the price of the 30-year bond if its yield decreases to 5.20%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
g. Comparing your answers to parts (a), (b), and (c), are long-term bonds more or less affected
than short-term bonds by a rise in interest rates?
h. Comparing your answers to parts (d), (e), and (f), are long-term bonds more or less affected
than short-term bonds by a decline in interest rates?
Consider three bonds with 6.20% coupon rates, all making annual coupon payments and all
selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond
has a maturity of 8 years, and the long-term bond has a maturity of 30 years.
a.What will be the price of the 4-year bond if its yield increases to 7.20%? (Do not round
intermediate calculations. Round your answer to 2 decimal places.)
The following table shows the prices of a sample of Treasury strips. Each strip makes a single payment
at maturity.
a. What is the 1-year interest rate? (Do not round intermediate calculations. Enter your
answer as a percent rounded to 2 decimal places.)
b. What is the 2-year interest rate? (Do not round intermediate calculations. Enter your
answer as a percent rounded to 2 decimal places.)
c. What is the 3-year interest rate? (Do not round intermediate calculations. Enter your
answer as a percent rounded to 2 decimal places.)
d. What is the 4-year interest rate? (Do not round intermediate calculations. Enter your
answer as a percent rounded to 2 decimal places.)
e. Is the yield curve upward-sloping, downward-sloping, or flat?
f. Is this the usual shape of the yield curve?
a) Face Value = 100
c) 100 = 91.344 * ( 1 + r) ^ 3
Thus, 100 = 98.652 * ( 1 + r)
b) 100 = 95.151 * ( 1 + r) ^ 2
d) c) 100 = 87.280 * ( 1 + r) ^ 4
r = (100 / 95.151)^(1/2) - 1 = 2.5164%
r = (100 / 91.344)^(1/3) - 1 = 3.0639%
r = (100 / 87.280)^(1/4) - 1 = 3.4597%
r = (100 / 98.652) - 1 = 1.0137 - 1 = 1.37%
Since the bonds were issued at par (face value), Coupon rate = yield to maturity = 6%
Semi annual coupon rate = (6%/2)*1000 = 30
Yield to maturity(r) = 11%/2 = 5.5% = 0.055
Upward sloping
7. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of
6%. Now, with 6 years left until the maturity of the bonds, the company has run into hard times and the
yield to maturity on the bonds has increased to 11%. What is the price of the bond now? (Assume
semiannual coupon payments.) (Do not round intermediate calculations. Round your answer to 2
decimal places.)
Par value=FV=85%*1000= 850
Coupon rate= 6%
Semi-annual Coupon amount=6%*1000/2=
30 No of semi-annual periods= n= 6*2=12
Price= 784.5370538
Using financial calculator enter
FV=850
PMT=30
N=12
PV= -784.5370538
Solve for I/Y as 4.36762496
YTM=2*4.36762496%= 8.74%
Period(n) = 6*2 = 12
Price of the bond now = Coupon*((1-(1+r)^-n)/r) + F/(!+r)^n
Price of the bond now = 30*((1-1.055^-12)/0.055 +
1000/1.055^12 Price of the bond now = 258.56 + 525.98
Price of the bond now = $784.54
784.54= ((.06*1000)/2)*((1/(r/2))-(1/((r/2)(1+(r/2))^8)))+8600*1000)/(1+(r/2))^8
Suppose that investors believe that Castles can make good on the promised coupon payments but that
the company will go bankrupt when the bond matures and the principal comes due. The expectation is
that investors will receive only 85% of face value at maturity. If they buy the bond today, what yield to
maturity do they expect to receive? (Do not round intermediate calculations. Enter your answer as a
percent rounded to 2 decimal places.)
