Gapenski case 11.2 solutions
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Finance
Date
Feb 20, 2024
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PROBLEM 1
Version B
Assume HCA sold bonds that have a ten-year maturity, a 13 percent coupon rate with
annual payments, and a $1,000 par value.
a. Suppose that two years after the bonds were issued, the required interest rate fell to 12 percent. W
would be the bond's value?
b. Suppose that two years after the bonds were issued, the required interest rate rose to 14 percent
would be the bond's value?
ANSWER
a.
Interest rate
rate
12%
Years to maturity
nper
8
Annual coupon payment
pmt
$130 Par value
FV
$1,000 Bond value
PV
($1,049.68)
b.
Interest rate
rate
14%
Years to maturity
nper
8
Annual coupon payment
pmt
$130 Par value
FV
$1,000 Bond value
PV
($953.61)
PROBLEM 2
Tenet Healthcare, has a bond issue outstanding with eight years remaining to maturity,
a coupon rate of 9 percent with interest paid annually, and a par value of $1,000. The current marke
price of the bond is $1,251.22.
a. What is the bond's yield to maturity?
b. Now, assume that the bond has semiannual coupon payments. What is its yield to maturity in this
situation?
ANSWER
a.
Years to maturity
nper
8
Annual coupon payment
pmt
$90
Current price
pv
-$1,251.22
Par value
fv
$1,000
Yield to maturity
rate
5.10%
b.
Semiannual periods to maturity
nper
16
Semiannual coupon payment
pmt
$45
Current price
pv
-$1,251.22
Because interest rates have fallen since the bond was issued, it is selling at a premium
.
Because interest rates have risen since the bond was issued, it is selling at a discount
.
Par value
fv
$1,000
Yield to maturity
rate
2.57%
5.13%
higher than under annual interest. Note that the effective annual YTM is still higher. PROBLEM 3
United Health Group has bonds outstanding that have four years remaining to maturity,
a coupon interest rate of 8 percent paid annually, and a $1,000 par value.
a. What is the yield to maturity on the issue if the current market price is $829?
b. If the current market price is $1,104?
c. Would you be willing to buy one of these bonds for $829 if you required a 12 percent rate of return
the issue? Explain your answer.
ANSWER
a.
Years to maturity
nper
4
Annual coupon payment
pmt
$80
Current price
pv
-$829.00
Par value
fv
$1,000
Yield to maturity
rate
13.85%
b.
Years to maturity
nper
4
Annual coupon payment
pmt
$80
Current price
pv
-$1,104.00
Par value
fv
$1,000
Yield to maturity
rate
5.06%
c. Therefore, the YTM, which is expressed as a stated annual rate, is 2 x 2.57% = 5.13%
, w
Yes
, the YTM > the 12% required rate of return.
What
t. What
et
s
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n on
which is slightly
PROBLEM 1
Version B
Liberty Rehab Corporation has a current stock price of $56, and its last dividend (D0) was
$5.00. In view of the company's strong financial position, its required rate of return is 10 percent. If Liber
dividends are expected to grow at a constant rate in the future, what is the firm's expected stock price in
five years?
ANSWER
First, given the current stock price, find the stock's constant growth rate:
D0 + P0
5 + 55
E(g) = 0.8%
Spreadsheet solution:
D0
$5.00
R(Rs)
10%
P0
$56.00
E(g)
1.0% =((C23*C22)-C21)/(C21+C23)
Now, under constant growth assumptions, stock price increases each year at the growth rate, E(g), so t
expected stock price in five years is $45.95:
E(P5) = $55 x (1.008)5 = $57.33
Spreadsheet solution:
P0
$56
E(g)
0.984%
n
5
E(P5)
($58.81)
=FV(C32,C33,,C31)
PROBLEM 2
Your personal financial advisor is trying to get you to buy the stock of Eagle Healthcare, a
local drug and alcohol rehabilitation company. The stock has a current market price of $35, its last divid
and the company's earnings and dividends are expected to increase at a constant growth rate of 8 perc
required return on this stock is 15 percent. From a strict valuation standpoint, should you buy the
stock?
ANSWER
With a current price of $35.00, the stock is undervalued and hence should be purchased. Spreadsheet solution:
D0
$2.50
E(g)
8%
R(Rs)
15%
E(P0)
$38.57 =(C22*(1+C23))/(C24-C23)
E(g) = [(P0 * R(Rs)] - D0
E(g) = (55*.10) - 5
rty's
n
the
dend (D0) was $2.50, cent. The
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PROBLEM 1
Version B
St. David's Hospital in Austin, Texas has a target capital structure of 35 percent debt and 65
equity (fund capital) estimate is 13.5 percent and its cost of debt is 7 percent. If it has a 35%
is the hospital's corporate cost of capital?
ANSWER
The corporate cost of capital is merely the weighted average (blend) of the comp
Spreadsheet solution:
wd =
35%
R(Rd) =
7%
T =
35%
we =
65%
R(Re) =
13.5%
CCC =
10.4% Double click on this cell to see the formula.
PROBLEM 2
The capital structure for HCA is provided below. If the firm has a 5% after tax cost of debt, 9
a 11.5% cost of preferred stock, an 15% cost of common stock, and given the dollar amount
weighted average cost of capital (WACC)? Capital Structure (in K's)
Weights
Individual Costs
Bonds
$ 1,083 13.75%
5.00%
Commercial Loans
$ 2,845 36.12%
9.00%
Preferred Stock
$ 268 3.40%
11.50%
Common Stock
$ 3,681 46.73%
15.00%
$ 7,877 100.00%
5 percent equity. Its cost of
% tax rate, what
ponent costs:
9% commerical loan rate, ts provided below, what is the firm's Weighted Costs
0.69%
3.25%
0.39%
7.01%
11.34%
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K
Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods):
0
2
5
Period
$19.53
a. What is the maturity of the bond (in years)?
b. What is the coupon rate (as a percentage)?
c. What is the face value?
Cash Flows
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★
a. What is the maturity of the bond (in years)?
The maturity is years. (Round to the nearest integer.)
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6
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Question 4
Both Bond A and Bond B have 8% coupon rate. Bond A has 4 years to maturity, while Bond
B is 14 years to maturity. Both bonds have 10% yield to maturity (YTM), and make semi-
annually payment
i.
If interest rates increase by 4%, determine the percentage price change of both
bonds.
ii.
If interest rate decrease by 4%, determine the percentage price change for both
bonds
iii.
Explain the concept of maturity and coupon bonds based on the answer in part
and ii.
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K
Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods):
Period
2
Cash Flows
1
$20.34
a. What is the maturity of the bond (in years)?
b. What is the coupon rate (as a percentage)?
c. What is the face value?
$20.34
a. What is the maturity of the bond (in years)?
The maturity is years. (Round to the nearest integer.)
b. What is the coupon rate (as a percentage)?
The coupon rate is%. (Round to two decimal places.)
c. What is the face value?
The face value is $
(Round to the nearest dollar.)
19
$20.34
20
$20.34 + $1,000
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Question 2
a. A bond that matures in one year has a $500 face value and a $60 coupon. What is the price of the bond if the interest rate is 6 percent and the bond was purchased by the present owner for $450?
b. A bond that matures in two years has a face value equal to F and a coupon equal to R. Suppose that the yield to maturity, i, is such that i = ( R / F ). The price of the bond equals...
F
F/(1+i)
F(1+i)
F/i
Answer both otherwise don't do that I will Dounvote
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K
Assume that a bond will make payments every six months as shown on the following
timeline (using six-month periods):
Period
0
2
Cash Flows
$19.12
$19.12
a. What is the maturity of the bond (in years)?
b. What is the coupon rate (as a percentage)?
c. What is the face value?
a. What is the maturity of the bond (in years)?
The maturity is
years. (Round to the nearest integer.)
39
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Question 1. Duration and Banking
Consider a 5-year bond with annual coupon payments. The bond has a face value (prin-
cipal) of $100 and sells for $95. Its coupon rate is 3%. (The coupon rate is the ratio
between the coupon value and the face value). The face value is paid at the maturity
year in addition to the last coupon payment.
1. Calculate the bond's yield to maturity (YTM) and duration using its YTM.
2. Suppose the bond's YTM changes in the same way as a 5-year T-bill interest rate.
Use the bond's modified duration to evaluate the relative change in the 5-year bond's
value if the interest rate on 5-year T-bills falls by one basis point, that is, by 0.0001.
This part was extracted from the balance sheet of the First Bank of Australia:
Assets (Billion AUD)
Bond 80
Liabilities (Billion AUD)
Fixed-rate liabilities 60
where "Bond" here refers to the bond we specified above and the fixed-rate liabilities
(banks future payment obligations) have an average duration of 4 years and YTM of…
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9
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Question 2
Two bonds are available for purchase in the financial markets. The first bond is a two-year,
50,000 AUD bond that pays an annual coupon of 6 per cent. The second bond is a two-
year, 10,000 AUD, zero-coupon bond.
(a) What is the duration of the coupon bond if the current yield-to-maturity (R) is 6
per cent? And 8 per cent? How does the change in the current yield to maturity affect
the duration of this coupon bond?
(b) Calculate the duration of the zero-coupon bond with a yield to maturity of 5 per
cent, and 8 per cent.
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Question 1
: Consider a coupon bond with an 8% annual coupon rate, a 10% interest rate, and a
$1000 face value. The bond will mature in 4 years. What is the duration of this bond? Duration is
defined as a weighted average of the maturities of the cash payments. Suppose the weight
assigned to the maturity of 1 year is W.
Show your work. No work, no credit
A: Duration 2.28 and W=7.77%
B: Duration=3.56 and W-20.5%
C. Duration 3.56 and W-23.1%
D. Duration=3,56 and W-7.77%
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Question 7
You hold an annual coupon bond for 1 year, receiving the 0.14 coupon before selling. When bought it had 6 years to maturity, and the YTM was 0.095. Over the year, interest rates ROSE by 0.002What is the total holding period return for this investment?
Group of answer choices
0.0939
0.0856
0.0903
0.0879
0.0820
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Question 6
Assume that a bond makes 10 equal annual payments of \$1,000$1,000 starting one year from today. The bond will make an additional payment of \$100,000$100,000 at the end of the last year, year 10. (This security is sometimes referred to as a coupon bond.)
If the discount rate is 3.5\%3.5% per annum, what is the current price of the bond?
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Question content area top
Part 1
(Yield to maturity) A bond's market price is
$1,200.
It has a
$1,000
par value, will mature in
12
years, and has a coupon interest rate of
8
percent annual interest, but makes its interest payments semiannually. What is the bond's yield to maturity? What happens to the bond's yield to maturity if the bond matures in
24
years? What if it matures in
6
years?
Question content area bottom
Part 1
a. The bond's yield to maturity if it matures in
12
years is
enter your response here%.
(Round to two decimal places.)
Part 2
b. The bond's yield to maturity if it matures in
24
years is
enter your response here%.
(Round to two decimal places.)
Part 3
c. The bond's yield to maturity if it matures in
6
years is
enter your response here%.
(Round to two decimal places.)
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Question 1: Valuing Bonds
a. A firm issues a zero-coupon bond with a face value of $1,000, maturing in five years.
Bonds with similar risk are currently yielding 5 percent per year. What is the value of
the bond?
b. A firm issues a bond with a face value of $1,000 and a coupon rate of 5 percent per
year, maturing in five years. Bonds with similar risk are currently yielding 5 percent
per year. What is the value of the bond?
c. A firm issues the same bond as in part (b) but with an annual coupon rate of 4 percent
per year. What is the value of the bond?
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QUESTION 1
"A coupon bond that pays interest annually has a par value of $1000, matures in 6 years, and has a yield to maturity of 6%. If the coupon rate is 15%, the value of the bond today will be __________. Note: Express your answers in strictly numerical terms. For example, if the answer is $500, write enter 500 as an answer."
QUESTION 2
"A coupon bond that pays interest quarterly has a par value of $1000, matures in 4 years, and has a yield to maturity of 15%. If the coupon rate is 8%, the value of the bond today will be __________. Note: Express your answers in strictly numerical terms. For example, if the answer is $500, write enter 500 as an answer."
QUESTION 3
"What is the coupon payment of a 4-year $1000 bond, 9% YTM, and with a 2% coupon rate and semiannually payments? Note: Express your answers in strictly numerical terms. For example, if the answer is $500, write enter 500 as an answer."
QUESTION 4
"Consider a zero-coupon bond with $100 face value and 5…
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* Assignment 3 i
Assume coupons are paid annually. Here are the prices of three bonds with 10-year maturities. Assume face value is $100.
Bond Coupon
(%)
248
a. What is the yield to maturity of each bond?
b. What is the duration of each bond?
Price (%)
80.36
96.95
135.22
Complete this question by entering your answers in the tabs below.
Required A
Bond Coupon
(%)
2
4
8
Required B
What is the yield to maturity of each bond?
Note: Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.
YTM
%
%
%
Saved
22255
35445
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H5.
Show proper step by step calculation
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Question 4
The following is a list of prices today for bonds with different maturities. Face value is 100. Assume that the bonds pay their coupons annually, and that the YTMs in the table are annualized and compounded annually. Both coupon rate and yield to maturity (YTM) is in percent.
Maturity (years) Price Coupon rate YTM 1 98.00 0 ?2 100 ? 5.00 3?9 6.00
Fill in the missing values in the table.What are the annualized spot rates for years 1 & 2 (r1 & r2)?
Given r1 & r2, what is the price of a 2-year coupon bond with annual coupon rate of 7%? What is the duration of this bond?
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2:37
a. Compute the bond's yield to maturity.
b. Determine the value of the bond to you, given your required rate of return.
c. Should you purchase the bond?
(Related to Checkpoint 9.2 and Checkpoint 9.3) (Bond valuation) Fingen's 14-year, $1,000 par value bonds pay 9
percent interest annually. The market price of the bonds is $850 and the market's required yield to maturity on a
comparable-risk bond is 13 percent.
a. What is your yield to maturity on the Fingen bonds given the market price of the bonds?
% (Round to two decimal
places.)
|||
Vo) 1
LTE2
=
O
4Gl 41%
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Need help with C Approximate yield to maturity
An investor must choose between two bonds:
Bond A pays $90 annual interest and has a market value of $815. It has 15 years to maturity.
Bond B pays $81 annual interest and has a market value of $700. It has eight years to maturity.
Assume the par value of the bonds is $1,000.
a. Compute the current yield on both bonds. (Do not round intermediate calculations. Input your answers as a percent rounded to 2 decimal places.)
Current Yield
Bond A11.04%
Bond B11.57%
c. A drawback of current yield is that it does not consider the total life of the bond. For example, the approximate yield to maturity on Bond A is 11.51 percent. What is the approximate yield to maturity on Bond B? The exact yield to maturity? (Use the approximation formula to compute the approximate yield to maturity and use the calculator method to compute the exact yield to maturity. Do not round intermediate calculations. Input your answers as a percent rounded to 2…
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Finance
ISBN:9780077861759
Author:Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:McGraw-Hill Education