FINA 351 – Managerial Finance, Chapter 6, (Ref. 6b)
Answer the following questions. Instructions for determining bond prices are in your textbook and in the instructor
notes.
1.
Suppose the following bond price quotes were listed in the Wall Street Journal. If each bond has a face value of
$1,000, determine the price of each bond in dollars. Also, state whether the bond is priced at a premium, discount or
at par.
(A) 98.39
(B) 104.65
(C) 100.00
2.
What factors would need to exist for a bond to be priced at par (100%)?
3.
Suppose a bond with $1,000 face value paid interest of $50 per year but the market demanded an annual yield of 8%
(YTM). Will this bond be priced at a premium or discount? How can you tell?
4.
(A) In the example below, the coupon rate in all cases is 10%. What was the bond price when the market rate
(YTM) was the same as the coupon rate?
(B) What happened to the price of the bond when the market rate moved up by 2%?
(C) What happened to the price of the bond when the market rate moved down by 2%?
(D) Why did the bond price move inversely with the change in interest rates? (See Bond Theorem #2 in the notes)
EXAMPLE: Suppose you purchased a $1,000 face-value bond that matures in 5 years and promises to pay a fixed rate of 10% in
annual interest payments (coupon rate). What would be the present value of the bond if the market rate (or YTM) today was (A)
10%, (B) 12%, or (C) 8%?
CASE A -- bond sold at face value, market rate (YTM) = 10%
PVA(5,10%)
ANN x IF = 100 x 3.7908
379.08
PVSS(5,10%)
SS x IF = 1,000 x .6209
620.90
Present value =
1,000.00
CASE B -- bond sold at discount, market rate (YTM) = 12%
PVA(5,12%)
ANN x IF = 100 x 3.6048
PVSS(5,12%)
SS x IF = 1,000 x .5674
Present value=
360.48
567.40
927.88
CASE C -- bond sold at premium, market rate (YTM) = 8%
PVA(5,8%)
ANN x IF = 100 x 3.9927
399.27
PVSS(5,8%)
SS x IF = 1,000 x .6806
680.60
Present value=
1,079.80
5.
Assume the following terms for the purchase of ABC bonds. Calculate the total cash price you would pay to buy
these bonds. Show your work.
Number of bonds purchased: 6
Face value of each bond: $1,000
Maturity: 12 years
Coupons: 8% rate, paid semi-annually (Hint: 4% per semi-annual period, 24 periods)
Market rate (YTM): 6% per year (3% per semi-annual period, 24 periods)
6.
Assume the following information about a bond: Face value is $1,000; annual coupons at a fixed rate of 8%; current
market rate (YTM) is 10% per year. Determine the prices of the bond assuming:
(A) 30 years until maturity
(B) 15 years until maturity
(C) 1 year until maturity.
(D) 0 years until maturity.
If you pictured the price of this bond over time (from left to right), describe in words what you see. (See Bond
Theorem #3 in the notes).
7.
Bond Theorem #4 (see notes) states the price of a long-term bond is more sensitive to a change in interest rates than
the price of a short-term bond. Let’s prove this theorem. Assume you own two different corporate bonds, LT and
ST. Both bonds have a face value of $1,000 and pay coupons at a fixed rate of 10% annually. However, bond LT is
a 30-year bond and bond ST is a 10-year bond. Furthermore, assume that market interest rates unexpectedly moved
from 10% to 12%.
(A) Find the values in the yellow-highlighted cells below [i.e. calculate the prices of both bonds assuming the
current market rate (YTM) move from 10% to 12%, and the percentage change in price].
(B) Which bond was more sensitive to the 2% increase in market rates?
(C) Which bond experienced more interest rate risk?
Type of Bond
LT bond (30 year)
ST bond (10 year)
8.
10% YTM
$1,000.00
$1,000.00
12% YTM
$?
$?
% change
%?
%?
Bond Theorem #5 (see notes) states the price of a low-coupon bond is more sensitive to a change in interest rates
than the price of a high-coupon bond. Let’s see if this is true. Suppose you own two different corporate bonds, Low
and Hi. Both bonds have a face value of $1,000 and a maturity of 30 years. However, bond Low pays a fixed
coupon of 4% per year, and bond Hi pays a fixed coupon of 12% per year. Furthermore, assume that market interest
rates unexpectedly climbed from 4% to 12%.
(A) Find the values in the yellow-highlighted cells below [i.e. calculate the prices of the Hi bond assuming 4%
market rate and Low bond assuming 12% market rate, and the percentage change in price].
(B) Which bond was more sensitive to the 8% increase in market rates?
(C) Which bond experienced interest rate risk?
Type of Bond
Low bond (4% coupon)
Hi bond (12% coupon)
9.
Change 
Market rates increase from 10% to 12%
4% YTM
$1,000
$?
Change 
Market rates Increase from 4% to 12%
12% YTM
$?
$1,000
% change
%?
%?
Suppose you manage WWU’s investment portfolio of bonds (e.g. a good portion of scholarship endowment funds
are invested in bonds).
(A) If market interest rates are headed up over the next year, would you want to increase or reduce the average
maturity of your bond portfolio in order to minimize losses in the prices of bonds?
(B) If market interest rates are headed up over the next year, would you want to increase or reduce the average
coupon rate of your bond portfolio in order to minimize losses in the prices of bonds?