The University of Manchester
Manchester Business School
Manchester Accounting & Finance Group
BMAN23000 Foundations of Finance – Kostakis/Marchica
SOLUTIONS
WORKSHOP 2:
STOCK AND BOND VALUATION
Question 1.
HMK Enterprises would like to raise $10 million to invest in capital expenditures.
The company plans to issue five-year bonds with a face value of $1,000 and a coupon
rate of 6.5% (annual payments). The following table summarizes the yield to maturity
for five-year (annual-pay) coupon corporate bonds of various ratings:
Rating AAA AA A BBB BB
YTM 6.20 % 6.30 % 6.50 % 6.90 % 7.50 %
a) If a similar U.S. Treasury security has a YTM of 6.10%, what is the credit
spread of corporate bonds of various ratings given in a table above?
b) Assuming the bonds will be rated AA, what will the price of the bonds be?
c) What must the bond rating be for them to sell at par?
d) Suppose that when the bonds are issued, the price of each bond is $959.54.
What is the likely rating of the bonds? Are they junk bonds?
, Solution:
a)
Credit spread (or default spread) is the difference between yields on Treasury
securities and yields on corporate bonds.
It can be expressed in % or in basis points (basis point is one hundredth of a
percentage point).
Rating AAA AA A BBB BB
Credit spread in % 0.10% 0.20% 0.40% 0.80% 1.40%
Credit spread in basis points 10 20 40 80 140
b)
The price of a coupon bond is calculated using the following formula:
1 1 FV
P CPN 1
y (1 y ) N (1 y ) N
So the price for AA-rated bond will be:
1 1 1000
P 65 1 $1008.36
0.063 (1 0.063) 5 (1 0.063) 5
c)
For the bonds to sell at par, the coupon must be equal to the yield-to-maturity. Since
the coupon is 6.5%, the yield-to-maturity must also be equal to 6.5%, as it is for the
A-rated bond.
d)
First we can find the yield-to-maturity for the bond priced at $959.54 (using a trial-
and-error method, or a function in Excel):
65 65 1000
959.54 ... YTM 7.5%
(1 YTM) (1 YTM)5
Given a yield of 7.5%, these bonds are BB rated. Yes, BB-rated bonds are junk bonds.
Alternative solution:
You can calculate the price for a bond of each rating:
Rating AAA AA A BBB BB
Price, $ 1012.57 1008.36 1000.00 983.56 959.54
Since when the bonds are issued, the price of each bond is $959.54, it is likely these
bonds are BB rated. Yes, BB-rated bonds are junk bonds.
Question 2.
Manchester Business School
Manchester Accounting & Finance Group
BMAN23000 Foundations of Finance – Kostakis/Marchica
SOLUTIONS
WORKSHOP 2:
STOCK AND BOND VALUATION
Question 1.
HMK Enterprises would like to raise $10 million to invest in capital expenditures.
The company plans to issue five-year bonds with a face value of $1,000 and a coupon
rate of 6.5% (annual payments). The following table summarizes the yield to maturity
for five-year (annual-pay) coupon corporate bonds of various ratings:
Rating AAA AA A BBB BB
YTM 6.20 % 6.30 % 6.50 % 6.90 % 7.50 %
a) If a similar U.S. Treasury security has a YTM of 6.10%, what is the credit
spread of corporate bonds of various ratings given in a table above?
b) Assuming the bonds will be rated AA, what will the price of the bonds be?
c) What must the bond rating be for them to sell at par?
d) Suppose that when the bonds are issued, the price of each bond is $959.54.
What is the likely rating of the bonds? Are they junk bonds?
, Solution:
a)
Credit spread (or default spread) is the difference between yields on Treasury
securities and yields on corporate bonds.
It can be expressed in % or in basis points (basis point is one hundredth of a
percentage point).
Rating AAA AA A BBB BB
Credit spread in % 0.10% 0.20% 0.40% 0.80% 1.40%
Credit spread in basis points 10 20 40 80 140
b)
The price of a coupon bond is calculated using the following formula:
1 1 FV
P CPN 1
y (1 y ) N (1 y ) N
So the price for AA-rated bond will be:
1 1 1000
P 65 1 $1008.36
0.063 (1 0.063) 5 (1 0.063) 5
c)
For the bonds to sell at par, the coupon must be equal to the yield-to-maturity. Since
the coupon is 6.5%, the yield-to-maturity must also be equal to 6.5%, as it is for the
A-rated bond.
d)
First we can find the yield-to-maturity for the bond priced at $959.54 (using a trial-
and-error method, or a function in Excel):
65 65 1000
959.54 ... YTM 7.5%
(1 YTM) (1 YTM)5
Given a yield of 7.5%, these bonds are BB rated. Yes, BB-rated bonds are junk bonds.
Alternative solution:
You can calculate the price for a bond of each rating:
Rating AAA AA A BBB BB
Price, $ 1012.57 1008.36 1000.00 983.56 959.54
Since when the bonds are issued, the price of each bond is $959.54, it is likely these
bonds are BB rated. Yes, BB-rated bonds are junk bonds.
Question 2.
