TESTBANK
FINANCIAL MANAGEMENT
FINANCE 301
JAMES T. LINDLEY
PROFESSOR OF FINANCE
FALL 2004
DEPARTMENT OF ECONOMICS, FINANCE
& INTERNATIONAL BUSINESS
COLLEGE OF BUSINESS ADMINISTRATION
& ECONOMIC DEVELOPMENT
THE UNIVERSITY OF SOUTHERN MISSISSIPPI
JAMES T. LINDLEY
PROFESSOR OF FINANCE
DEPARTMENT OF ECONOMICS AND FINANCE & INTERNATIONAL BUSINESS
COLLEGE OF BUSINESS & ECONOMIC DEVELOPMENT
OFFICE: 314-H Greene Hall
PHONE 266-4637
FAX: 266-4920
EMAIL: t.lindley@usm.edu
WEB SITE
http://ocean.otr.usm.edu/~jindley/
TABLE OF CONTENTS FOR TESTBANK
FIN 301
FINANCIAL MANAGEMENT
TO BE USED IN CONJUNCTION WITH
Corporate Financial Management, Douglas Emery, John
Finnerty and John Stowe, Prentice-Hall, 2004
PROBLEMS
1-39
40-66
67-95
96-131
132-142
143-159
160-164
165-173
174-192
193-198
199-205
206-209
210-211
AREA
CHAPTER IN CORPORATE
FINANCIAL MANAGEMENT
Time Value of Money
Bond Evaluation
Stock Evaluation
Capital Budgeting
Risk and Return
Financial Analysis
Break Even – Leverage
Cost of Capital
Capital Structure
Dividend Policy
Additional Funds Needed
Leasing
Bond Refunding
4
5 & 24
5 & 24
10 Thru 13
6
1 & 2
10
10
15 & 16
17 & 18
15 & 16
25
24
FUTURE VALUE AND PRESENT VALUE FORMULAS
WHERE
K = Nominal Yearly Rate Of Interest
m = Portion Of The Year
n = number of years
Effective annual rate
[1 + (K/m)]m −
Sum * (1 + K) n
FUTURE VALUE OF A SUM
FUTURE VALUE OF AN ANNUITY
PRESENT VALUE OF A SUM
1
 (1 + K) n − 1 
Payment * 

K


1
Sum * ( 1 + K ) n
PRESENT VALUE OF AN ANNUITY
1

1 −
Payment * 



1

(1 + K) n 

K

TIME VALUE OF MONEY
1. If you buy a factory for $250,000 and the terms are 20% down, the balance to be paid
off over 30 years at a 12% rate of interest on the unpaid balance, what are the 30 equal
annual payments? [$24,828.73]
2. You start saving now for your college education. You will begin college at age 18 and will
need $4,000 per year at the end of each of the next 4 years. You will make a deposit 1
year from today into an account that pays 6% compounded annually and an identical
deposit each year until you start college. If an annual deposit of $1,987 will allow you to
reach your goal, how old are you now? [12 Years Old]
3. On January 1, 1985, a graduate student developed a financial plan that would provide
enough money at the end of his graduate work (January 1, 1990) to open a business of his
own. His plan was to deposit $8,000 per year, starting immediately, into an account
paying 10% compounded annually. His activities proceeded according to plan except that
at the end of his third year he withdrew $5,000 to take a Caribbean cruise, at the end
of the fourth year he withdrew $5,000 to buy a used Camaro, and at the end of the
fifth year he had to withdraw $5,000 to pay to have his dissertation typed. His account,
at the end of the fifth year, will be less than the amount he had originally planned on by
how much? [$16,550]
4. You plan on working for 10 years and then leaving for the Alaskan back country. You
figure you can save $1,000 a year for the first 5 years and $2,000 a year for the last 5
years. In addition, your family has given you a $5,000 graduation gift. If you put the
gift and your future savings in an account paying 8% compounded annually, what will your
'stake' be when you leave for the wilderness 10 years hence? [$31,147.50]
5. You have $1,000 invested in an account that pays 8% compounded annually. You have
found an equally safe deposit that will pay 8%, quarterly compounding, for 2 years. How
much additional interest will you earn by shifting accounts? [$5.26]
6. If $100 is placed into an account that earns a nominal 4% compounded quarterly, what
will it be worth 5 years from today? [$122.05]
7. Visser Distributors is financing a new truck with a loan of $10,000 to be repaid in 5
annual installments of $2,505. What annual interest rate is the company paying? [8%]
2
8. Suppose you have $2 million in a 2-year account paying a 6% nominal rate, compounded
annually. Another bank offers you an account for 2 years paying a 6% nominal rate, but
compounded bimonthly (that is, 6 times a year). If you move your account, how much
additional interest will you earn over the 2 years? [$6,450.06]
9. You have the opportunity to buy a perpetuity paying $1,000 annually. Your demanded
rate of return on this investment is 15%. You would be essentially indifferent to buying
or not buying the investment if it were offered at what price? [$6,666.67]
10. You have decided to deposit your scholarship money ($1,000) in a savings account paying
8% interest, compounded quarterly. Eighteen months later, you decide to go to the
mountains rather than school and you close out your account. How much money will you
receive? [$1,126.16]
11. The present value (t = 0) of the following cash flow stream is $5,979.04 when discounted
at 12% annually. What is the value of the MISSING (t = 2) cash flow? [$2,999.93]
0
1
2
3
4
---|---------|----------|----------|----------|----$0
$1,000
$?
$2,000 $2,000
12. You want to set up a trust fund. If you make a payment at the end of each year for
twenty years and earn 10% per year, how large must your annual payments be so that the
trust is worth $100,000 at the end of the twentieth year? [$1,745.96]
13. Starting on January 1, 1987, and then on each January 1 until 1996 (10 payments), you
will make payments of $1,000 into an investment which yields 10 percent. How much will
your investment be worth on December 31 in the year 2006? [$45,468.85]
14. Your 69-year old aunt has savings of $35,000. She has made arrangements to enter a
home for the aged upon reaching the age of 80. Before going into the home, she wants
to decrease the account balance by a constant amount each year for ten years, with a
zero balance remaining. How much can she withdraw each year if she earns 6 percent
annually on her savings?
Her first withdrawal would be one year from today.
[$4,755.37]
15. A rich aunt promises you $35,000 exactly 5 years after you graduate from college.
What is the value of the promised $35,000 if you could negotiate payment upon
graduation? Assume an interest rate of 12 percent. [$19,859.94]
3
16. John Roberts is retiring one year from today. How much should John currently have in a
retirement account earning 10 percent interest to guarantee withdrawals of $25,000
per year for 10 years? [$153,615]
17. You place $5,000 in your credit union at an annual interest rate of 12 percent
compounded monthly. How much will you have in 2 years if all interest remains in the
accounts? [$6,348.67]
18. Find the present value for the following income stream if the interest rate is 12 percent
and the payments occur at the end of each year. [$5,001.74]
YEARS
1-4
5-10
11-15
CASHFLOW
$ 500
$ 800
$1,200
19. You have just had your thirtieth birthday. You have two children. One will go to college
10 years from now and require four beginning-of-year payments for college expenses of
$10,000, $11,000, $12,000, and $13,000. The second child will go to college 15 years
from now and require four beginning-of-year payments of $15,000, $16,000, $17,000,
and $18,000. In addition, you plan to retire in 30 years. You want to be able to
withdraw $50,000 per year (at the end of each year) from an account throughout your
retirement. You expect to live 20 years beyond retirement. The first withdrawal will
occur on your sixty-first birthday. What equal, annual, end-of- year amount must you
save for each of the next 30 years to meet these goals, if all savings earn a 15 percent
annual rate of return? [$3,123.10]
20. Find the present value of the cash flows shown using a discount rate of 8 percent.
Assume that each payment occurs at the end of the year. [$1,166.80]
YEAR
1-4
5
6
7-15
16
CASHFLOW
$100/yr.
200
300
100/yr.
400
21. According to a local department store, the store charges its customers 1% per month on
the outstanding balances of their charge accounts. What is the effective annual rate on
such customer credit? Assume the store recalculates your account balance at the end
of each month. [12.68%]
4
22. Your bank has offered you a $15,000 loan. The terms of the loan require you to pay
back the loan in five equal annual installments of $4,161.00. The first payment will be
made a year from today. What is the effective rate of interest on this loan? [12.00%]
23. You have agreed to pay a creditor $5,000 one year hence, $4,000 two years hence,
$3,000 three years hence, $2,000 four years hence, and a final payment of $1,000 five
years from now. Due to budget considerations you would like to make five equal annual
payments to satisfy your contract. If the agreed upon interest is 5% effective per
year, what should the equal annual payments be? [$3,097.43]
24. You have purchased a new sailboat and have the option of paying the entire $8,000 now
or making equal, annual payments for the next 4 years, the first payment due one year
from now. If your time value of money is 7 percent, what would be the largest amount
for the equal, annual payments that you would be willing to undertake? [$2,361.83]
25. You are 35 years old and wish to provide for your old age. Suppose you invest $1,000 per
year at an effective rate of 5 percent per year for the next 25 years, with the first
deposit beginning one year hence. Beginning one year after your last $1,000 deposit you
start withdrawing $X per year for the next 20 years. How large must $X be in order to
use up all of your funds? [$3,829.74]
26. Your grandmother is thrilled that you are going to college and plans to reward you at
graduation in 4 years with a new car. She would like to set aside an equal amount at the
completion of each of your college years. If her account earns 11.5 percent and the new
car will cost $30,000, how much must she deposit each year? Assume her first deposit
is in exactly one year. [$6,323.22]
27. Robert Smith's son Joseph is ten years old today. Joseph is already making plans to go
to college on his eighteenth birthday and his father wants to start putting away money
now for that purpose. Smith estimates that Joseph will need $16,000, $17,000,
$18,000, and $19,000 for his freshman, sophomore, junior, and senior years. He plans on
making these amounts available to Joseph at the beginning of each of these years.
Smith would like to make eight deposits (the first of which would be made on Joseph's
eleventh birthday, 1 year from now) in an account earning 10 percent. He wants the
account to eventually be worth enough to pay for Joseph's college expenses. Any
balances remaining in the account will continue to earn 10 percent. How much will Smith
have to deposit in this planning account each year to provide for Joseph's education?
[$5,299.46]
28. What is the present value of an investment that promises to pay $10,000 for the first
five years and $20,000 for the second five years if the discount rate is 18 percent?
[$58,610]
5
29. Suppose that a local savings and loan association advertises a 6 percent annual rate of
interest on regular accounts, compounded monthly. What is the effective annual
percentage rate of interest paid by the savings and loan? [6.17%]
30. How much would you pay for a joint venture that is expected to yield $20,000 per year
for 5 years, and then $50,000 per year for the next 10 years, but will require an
expenditure of $100,000 to terminate the venture at the end of its productive life?
Assume that you require a 20 percent return on the investment because of its high risk.
[$137,565]
31. Alphonzo Provenzono has been married 20 years. He is planning a surprise for his 50th
wedding anniversary to take himself and his wife back to the old country. He plans to
save $1,000 per year that will earn 9 percent. He expects to withdraw $15,000 per year
in the old country. How many years will Alphonzo and his wife be able to stay?
[20
Years]
32. Mr. Lewis, age 29, wants to begin planning for his retirement at age 65. Upon retiring,
he wants to be able to withdraw $15,000 per year on each birthday for 10 years. The
first withdrawal will be on his 66th birthday. He will receive a large inheritance on his
30th birthday in two weeks, and he wants to know how much he needs to invest on that
day to be able to attain his retirement income. He will invest the money in an account
paying 10 percent annual interest for the life of the investment. How much does he need
to deposit on his 30th birthday? [$3,280]
33. Jason and Bryan McNutt are presently 3 and 5 years old, respectively. Their parents
plan to send them to college when each turns 18 at a cost of $10,000 per year for each,
with the payments to be made at the beginning of each year. How much must the
parents contribute annually to a college fund to ensure the boys' college education if the
interest rate is 12 percent compounded annually? The deposits start in one year and end
when the older brother starts college. [$2,181.24]
34. If you have $5,436 in an account that has been paying an annual rate of 10%,
compounded continuously, since you deposited some funds 10 years ago, how much was
the original deposit? [$1,999.79]
35. For a 10-year deposit, what annual rate payable semi-annually will produce the same
effective rate as 4% compounded continuously? [4.04%]
36. How much should you be willing to pay for an account today that will have a value of
$1,000 in 10 years under continuous compounding if the nominal rate is 10%? [$367.88]
6
37. In 1975, its first year of operations, The Coffee Mill had earnings per share (EPS) of
$0.26. Four years later, in 1978, EPS was up to $0.38, and 7 years later, in 1985, EPS
was up to $0.535. It appears that the first 4 years represented an unusual growth
situation and that since then a more normal growth rate has been sustained. What are
the two rates of growth? [10% and 5% respectively]
38. Digger O'Dell is the local friendly undertaker. His business has improved since he
adopted his new motto, "I will be the last man to ever let you down." Given his expanded
business, he wishes to build a new establishment financed with a short-term mortgage.
He can borrow for eight years at 9 percent. He will pay monthly payments on the
$50,000 he will borrow. Determine his monthly payment and develop an amortization
schedule for the first four months. [Monthly Payment = $732.51]
39. On December 1, 1998, Otto Van Auto borrowed $25,000 for his new car. The loan terms
were: 48 month loan, payments beginning January 1, 1999, 10.5% interest. However, as a
marketing promotion, a monthly payment will not be required on the month of his
birthday, October. What will be the monthly payment for the loan? How much larger is
this payment than a standard 48 month loan?
[Monthly Payment = $696.35 :
Difference = $56.26]
7
BOND VALUE FORMULAS
ANNUAL BOND PRICE =
1


 M 

1 −
C 
(1 + K)n  + 
n
(1 + K ) 


K


1


 M 


SEMIANNUAL BOND PRICE = C / 2 1 − (1 + K) n  + 
n
(1 + K ) 


.5
(1 + K) − 1 
WHERE
K = Yearly Rate Of Interest
n = Number Of Years
C = Coupon Payment
M = Maturity Value
DURATION FOR ANNUAL BOND
D = N - (C/Py)[N - (1+y)AN]
N = years to maturity
C = yearly coupon payment
P = market price of the bond
y = yield to maturity in annual terms
AN = present value of an annuity yielding y for N years.
DURATION FOR SEMIANNUAL BOND
D = N - (C'/Py')[N - (1+y')AN'/2]
C' = C/2
y' = [(1+y)
1/2
] - 1
AN' = present value of an annuity yielding [(1+y)
kN years.
ELASTICITY OF A BOND
(-1.0)IEit = MDit [YTM/(1 + YTM)]
where,
IEit = ELASTICITY
MDit = DURATION
YTM = YIELD TO MATURITY
8
1/2
- 1] for
BOND VALUATION
40. USM bonds pay an annual coupon rate of 10%. They have 8 years before maturity. The
maturity value is $1,000. The yield to maturity (market interest rate) on these class of
bonds is 12%. Determine the price of these bonds. [$900.65]
41. Liddy Corporation has bonds that pay a coupon rate of 8% and a maturity value of
$1,000. The yield on comparable new bonds is 9.5% The bonds have 7 years before they
mature. Determine the value of one of Liddy's bonds. [$925.76]
42. Hamblin Inc. has bonds that pay a coupon rate of 11% and a maturity value of $1,000.
The yield in the market for this risk class of bonds is 10.5 %. The bonds have 18 years
before maturity.
How much would one Hamblin bond be worth on the market?
[$1,039.73]
43. Calculate the yield to maturity (on an annual basis) of an 8% coupon, 10 year bond that
pays interest semiannually if its price is now $787.17. [12%]
44. Adeline Corporation just issued a zero coupon bond with a life of 15 years. The face
value of these bonds is $100,000 and the market rate is 9.6%. What would be the price
of these bonds? {25,283.76]
45. The Athletic Association has decided to build new bleachers for the baseball field.
Total costs are estimated to be $1 million, and financing will be through a bond issue of
the same amount. The bond will have a coupon rate of 8%, and the Association must set
up a reserve to pay off the loan by making equal annual payments in an account paying 8%
annually. The interest-accumulated amount in the reserve will be used to retire the
entire issue at its maturity date (20 years). The Association plans to meet the payment
requirements by selling season tickets at $10 net profit per ticket. Approximately how
many tickets must be sold each year to meet the interest and principal retirement
requirements? [10,185 Tickets]
46. Mary Parker was left some bonds (face value $100,000) by her late husband Norman.
She has recently become engaged to Slick Jones, who wants her to cash in the bonds and
use the money to 'live like royalty' for a couple of years in Monte Carlo. The 15% bonds
mature on January 1, 2007, and it is now January 1, 1987. Interest on these bonds is
paid annually on December 31 each year and new bonds issued by the same company with
the same maturity are currently showing a 12% coupon rate. If Mary sells her bonds now
and puts the proceeds in an account paying 10% compounded annually, what would be the
largest equal annual amounts they could withdraw for two years beginning January 1,
1988? [$70,530]
9
47. Easton, Inc., has two bond issues outstanding, both selling for $701.22. The first issue
has a coupon rate of 8% and 20 years to maturity. The second has an identical yield to
maturity as the first but only 5 years until maturity. Both issues are payable annually.
What is the interest payment on the second issue? [$37.12]
48. You are the owner of 100 bonds issued by Georgia Corporation. These bonds have 8
years remaining to maturity, an annual coupon payment of $80, and a par value of $1,000.
Unfortunately, Georgia Corp. is on the brink of bankruptcy, and the creditors, including
yourself, have agreed to a postponement of the next 4 interest payments. The
remaining interest payments will be made as scheduled. The postponed payments will
accrue interest at an annual rate of 6% and will be paid as a lump sum at maturity 8
years hence. The required rate of return on these bonds, considering their substantial
risk, is now 28%. What is the present value of each bond? [$266.91]
49. Robert Baron is considering two 5 year bonds. One pays a coupon rate of 10% and is taxexempt and the other pays a coupon rate of 13% and is fully taxable for Bob at a 34%
tax rate. If the tax-exempt bond sells for $1000, at what maximum price must the
taxable bond sell for in order to induce Robert to purchase it instead of the tax-exempt
(par value is $1000)? NOTE: There is capital gain at end. [$ 931.77]
50. RFK, Inc., plans to issue bonds with a par value of $1,000 and 10 years to maturity.
These bonds will pay $45 every 6 months. Current market conditions are such that the
bonds will be sold to net $952.05. If RFK is in the 34% tax bracket, what is its AFTERTAX cost of debt? (The after-tax cost of debt is equal to the interest rate times (1 –
tax rate), and it recognizes the tax deductibility of interest.) [6.6%]
51. Assume that you own 100 bonds, $1,000 par value, with a total face value of $100,000.
These bonds have a 4% coupon, pay interest semiannually, and have 5 years remaining
until they mature. New bonds with the same risk and maturity provide yields to maturity
of 14%. You are considering selling your bonds and depositing the proceeds in a savings
account which pays interest at a rate of 6%, compounded annually. If you do make the
transaction, you will liquidate the savings account by making 5 equal withdrawals, the
first coming 1 year from now. How large will each annual withdrawal be? [$15,700]
52. Recently, JFK, Inc., filed bankruptcy papers. The firm was reorganized as PQ, Inc., and
the court permitted a new indenture on an outstanding bond issue to be put into effect.
The issue has 10 years to maturity and a coupon rate of 10%, paid annually. The new
agreement allows the firm to pay no interest for 5 years and then at maturity to repay
principal and any unpaid interest (no interest on the unpaid interest). If the required
return is 20%, what should such bonds sell for in the market today? [$362.44]
10
53. Joe Don Brigham has a choice of buying bonds that pay annual coupons at a rate of 9.4%
per year with a life of 10 years or bonds that pay a coupon rate of 9.1% per year with
semiannual payments and a life of 8 years. The market rate for both bonds is 14%.
Which bond will sell at the highest price? If he has $1,000,000 to invest in these bonds,
approximately how many annual bonds could he purchase and how many semiannual bonds
could Joe Don purchase?
[Price annual = 760.06; Price semiannual = 786.99; Annual
bonds purchased would be 1316 while semiannual bonds purchased would be 1,271]
54. A major auto manufacturer has experienced a market re-evaluation lately due to a
number of lawsuits. The firm has a bond issue outstanding with 15 years to maturity and
a coupon rate of 8% (paid semiannually). The required rate has now risen to 16%. At
what price can these securities be purchased on the market? [$571.15]
55. Calculate the price change in a semiannual municipal bond with a coupon rate of 9% and
10 years to maturity when the market rate of interest increases from 8.25% to 10.75%
[$ 151.96]
56. What is the value of a government bond that pays semiannual payments of $50 (coupon
rate of 10%) and has a maturity value of $1,000 if the annual market interest rate is
10% and the bond has 20 years until maturity? [$1,020.78]
57. Commonwealth Company has 100 bonds outstanding (maturity value = $1,000). The
required rate of return on these bonds is currently 10%, and interest is paid
semiannually. The bonds mature in 5 years, and their current market value is $768 per
bond. What is the annual coupon interest rate? [3.78%]
58. The current market price of a Johnson Company bond is $1,305.28. A 10% coupon
interest rate is paid semi-annually, and the par value is equal to $1,000. What is the
YTM (on an annual basis) if the bonds mature 10 years from today? [6%]
59. Golden bonds pay a semi-annual coupon rate of 10%. They have 8 years before maturity.
The maturity value is $1,000. The yield to maturity (market interest rate) on these
class of bonds is 10%. Determine the price of these bonds. [$1,013.02]
60. What is the coupon payment on a corporate bond that has semiannual payments if the
price of the bond is $1,141.57, the interest rate is 7.75%, and there are 8 years left
until the bond matures. (Assume a maturity value of $1,000). [$50]
61. The Banzai Auto Company has experienced a market re-evaluation lately due to a number
of lawsuits. The firm has a bond issue outstanding with 15 years to maturity and a
coupon rate of 8% (paid semiannually). The required rate has now risen to 12.25%. At
what price can these securities be purchased on the market? [$ 730.35]
11
62. Ford and GM have similar bond issues outstanding. The Ford bond has interest payments
of $80 paid annually and matures in the year 2007 (20 years from today). The GM bond
has interest payments of $80 per year, paid semiannually and also matures in the year
2007. If the required rate of return (kd ) is 12%, what is the difference in current
selling price of the two bonds? [$17.42]
63. Calculate the yield to maturity (on an annual basis) of an 8% coupon, 10 year bond that
pays interest semiannually if its price is now $787.17. [12%]
64. McDougal Corporation has a 15 year bond with a coupon rate of 15 percent paid annually
and yields 12% (par value= $1000). What is the duration elasticity of the bond?
[Duration = 7.35
IE = -.79]
65. King Incorporated has a twenty-year bond with a coupon rate of 12 percent paid
semiannually. The market rate of interest is 10.5 percent and the bond has a maturity
value of $1,000. Determine the duration of the bond. [Duration = 8.647]
66. Determine the price elasticity of Bolin Corporation's semiannual bond with twelve years
to maturity and a maturity value of $1,000. The coupon rate is 10% and the market rate
of interest is 11.5 percent. [Duration = 7.04 IE = -.73]
67. Two bonds have identical terms except that one pays annual coupon payments while the
other pays semiannual payments. The coupon rates are 11%, the market yield is 12%, and
the time to maturity is 20 years. What is the difference in the prices and duration of
the two bonds? [Price Difference $23.95, Duration Difference .27 years]
12
STOCK VALUE FORMULAS
GORDON DIVIDEND MODEL (PRICE)
D1
P0 =
Re − g
GORDON DIVIDEND MODEL (RETURN)
Re =
WHERE
Re = Yearly Rate Of Return
P0 = Price Of Stock At Time Zero
D1 = Expected Dividend = D0 (1 + g)
g = Growth Rate of Stock
CAPITAL ASSET PRICING MODEL (CAPM)
R e = R f + β (R m − R f)
CAPM
WHERE
Re = Yearly Rate Of Return
Rf = Risk Free Rate
β
= Beta
Rm = Return On Market
β
= Beta
COV M , S
VAR M
Where M = Market Returns, S = Returns on Stock
13
D1
P0
+ g
STOCK VALUATION
68. Cuomo Corporation has had dividends grow from $2 to $5 over the last five years. This
growth is expected to continue well into the foreseeable future. If the current market
price is $38 per share, what annual rate of return do investors expect to receive from
buying Cuomo stock? [35.91%]
69. Suppose a firm is facing a rather difficult financial future in which it expects to
experience an indefinite period of contraction with earnings (and dividends) decreasing
at an annual rate of 5%. If the last dividend was $1.00 and the stock price is $10 per
share, what is the return expected by investors who buy this stock? [4.5%]
70. SOS, Inc., has experienced a recent resurgence in business as it has gained new national
identity. Management is forecasting rapid growth over the next 4 years (annual rate of
15%). After that, it is expected that the firm will revert to its historical growth rate of
2% annually. The last dividend paid was $1.50 per share, and the required return is 10%.
What is the current price per share, assuming equilibrium? [$29.56]
71. SOS, Inc., has experienced a recent resurgence in business as it has gained new national
identity. Management is forecasting rapid growth over the next 4 years (annual rate of
15%). After that, it is expected that the firm will revert to its historical growth rate of
2% annually. The last dividend paid was $1.50 per share, and the required return is 10%.
What will be the equilibrium price of SOS stock at the end of the second year (P2)?
[$31.88]
72. The Crapola Company has decided to make a major investment. The investment will
require a substantial early cash out-flow, and inflows will be relatively late. As a result,
it is expected that the impact on the firm's earnings for the first 2 years will be a
negative growth of 5% annually. Further, it is anticipated that the firm will then
experience 2 years of zero growth after which it will begin a positive annual sustainable
growth of 6%. If the firm's cost of capital is 10% and its current dividend (D0) is $2
per share, what should be the current price per share? [$38.48]
73. The ACE Auto Parts Company has just recently been organized. It is expected to
experience no growth for the next 2 years as it identifies its market and acquires its
inventory. However, ACE will grow at an annual rate of 5% in the third and fourth years
and, beginning with the fifth year, should attain a 10% growth rate which it will sustain
thereafter. The last dividend paid was $0.50 per share. ACE has a cost of capital of
12%. What should be the present price per share of ACE common stock? [$20.84]
14
74. The ACE Auto Parts Company has just recently been organized. It is expected to
experience no growth for the next 2 years as it identifies its market and acquires its
inventory. However, ACE will grow at an annual rate of 5% in the third and fourth years
and, beginning with the fifth year, should attain a 10% growth rate which it will sustain
hereafter. The last dividend paid was $0.50 per share. ACE has a cost of capital of
12%. What should be the price per share of ACE stock at the beginning of the third year
(P2)? [$25.08]
75. AT&E, Inc., a large conglomerate, has decided to acquire another firm. Analysts are
forecasting that there will be a period (2 years) of extraordinary growth (20%) followed
by another 2 years of unusual growth (10%), and that finally the previous growth pattern
of 6% annually will resume. If the last dividend was $1 per share and the required
return is 8%, what should the market price be today? [$72.76]
76. The Pet Company has recently discovered a type of rock which, when crushed, is
extremely absorbent. It is expected that the firm will experience (beginning now) an
unusually high growth rate (20%) during the period (3 years) when it has exclusive rights
to the property where this rock can be found. However, beginning with the fourth year
the firm's competition will have access to the material, and from that time on the firm
will assume a normal growth rate of 8% annually. During the rapid growth period, the
firm's dividend payout ratio will be relatively low (20%), to conserve funds for
reinvestment. However, the decrease in growth will be accompanied by an increase in
dividend payout to 50%. Last year's earnings were $2.00 per share (E0) and the firm's
cost of equity is 10%. What should be the current price of the common stock? [$71.54]
77. A share of JTL, Inc., stock paid a dividend of $1.50 last year, and the dividend is
expected to grow at a constant rate of 4% in the future. The appropriate rate of return
on this stock is believed to be 12%. What should the stock sell for today? [$19.50]
78. A share of JTL, Inc., stock paid a dividend of $1.50 last year, and the dividend is
expected to grow at a constant rate of 4% in the future. The appropriate rate of return
on this stock is believed to be 12%. What would be the price of one share of JTL stock
1 year from today? [$20.28]
79. The BB Company has fallen on hard times. Its management expects to pay no dividends
for the next 2 years. However, the dividend for Year 3 (D3) will be $1.00 per share, and
it is expected to grow at a rate of 3% in Year 4, 6% in Year 5, and 10% in Year 6 and
thereafter. If the required return for BB Co. is 20%, what is the current equilibrium
price of the stock? [$6.35]
15
80. ICBM is currently selling at $65 per share. Next year's dividend is expected to be
$2.60. If investors on this particular day expect a return of 12% on their investment,
what do they think ICBM's growth rate will be? [8%]
81. In your analysis of MBI Corporation you find that the current earnings per share are
$5.00 per share and most analysts are projecting the earnings per share to grow at a 12
percent rate annually. What can you expect the earnings per share of this firm to be in
7 years?
[$11.05]
82. The Teetertotter Company is expecting both earnings and dividends to grow by -5% in
Year 1, 0% in Year 2, 5% in Year 3, and 10% in Year 4 and thereafter. The required
return on Teetertotter is 15%, and the equilibrium price (P0) is $49.87. What is the
expected value of the next dividend (D1)? [$2.85]
83. Negative Limited is expected to grow for four years at a rate of 50 percent. After four
years, the product fad is expected to decline, and Negative will grow at a negative
growth rate of 5 percent. Negative currently pays a dividend of $1.00 per share and
stockholders have a required rate of return of 18 percent. What should be the market
value for a share of Negative Limited stock? [$18.34}
84. Assume that AA Co. has been growing at a 15% annual rate and is expected to continue
to do so for 3 more years. At that time, growth is expected to slow to a constant 4%
rate. The firm maintains a 30% payout ratio, and this year's retained earnings were $1.4
million. The firm's beta is 1.25, the risk-free rate is 8%, and the market risk premium is
4%. If the market is in equilibrium, what is the market value of the firm's common
equity (1 million shares outstanding)? [$9,170,000]
85. EMBA, Inc., has a beta coefficient of 0.7 and a required rate of return of 15%. The
market risk premium is currently 5%. If we expect the inflation premium to increase 2
percentage points and EMBA to add assets to his firm that will increase the beta by
50%, what will be EMBA's new required rate of return? [18.75%]
86. Thomas, Inc., has just paid a dividend of $2.00. Its stock is now selling for $48 per
share. The firm is half as volatile as the market. The expected return on the market is
14% and the yield on U.S. Treasury bonds is 11%. If the market is in equilibrium, what
rate of growth is expected? [8%]
16
87. GWK Corp. stock is currently paying a dividend of $2.00 per share (D0 = $2) and is in
equilibrium. The company has a growth rate of 5% and beta equal to 1.5. The required
rate of return on the market is 15%, and the risk-free rate is 7%. GWK is considering a
change in policy which will increase its beta coefficient to 1.75. If market conditions
remain unchanged, what new growth rate will cause the common stock price of GWK to
remain unchanged? [6.76%]
88. USA Paper's stock is currently in equilibrium selling at $30 per share. The firm has
been experiencing a 6% annual growth rate. Earnings per share (E0) were $4.00 and the
dividend payout ratio is 40%. The risk-free rate is 8% and the market risk premium is
5%. If systematic risk increases by 50%, all other factors remaining constant, the stock
price will increase/decrease by how much? [$7.33 (Decrease)]
89. Overflow Oil Company is currently selling at its equilibrium price of $100 per share. The
beta coefficient currently is 2. The risk-free rate is 10%. The following events will soon
occur: (1) top management will lower Overflow's beta to 1.2 by investing in several low
risk projects; (2) the Federal Reserve Board will reduce the money supply causing the
inflation premium to be reduced by 3 percentage points; and (3) decreased world
stability due to global politics will cause the market risk premium to increase 2
percentage points to 5%. The company has a constant growth rate of 5%. What will be
the new equilibrium price for a share of Overflow Oil common stock after the above
events have taken place? (Assume the expected dividend will not change.) [$137.50]
90. As financial manager of Crayon, Inc., you have recently concurred with a general
management decision to enter into the plastics business. Much to your surprise, the
price of the firm's common stock has subsequently declined from $40 per share to $30
per share. While there have been several changes in financial markets during this
period, you are anxious to determine how the market perceives the relevant risk of the
firm. From the following data you find that the beta value associated with your firm has
changed from __________(old beta) to __________(new beta).
1. The real rate is 0.02, but the inflation premium has increased from 0.04 to 0.06.
2. The expected growth rate has been re-evaluated and a 0.105 rate is more realistic
than the previous 0.05 rate.
3. Risk aversion attitude of the market has shifted so that the market risk premium is
now 0.03 instead of 0.02.
4. Current dividend (D0) is $1.90 per share. [Old Beta = 2.00; New Beta = 3.17]
17
91. Consider the following information and calculate the required rate of return for the
Infidelity Investment Fund. The market required rate of return is 15% and the risk-free
rate is 7%. The total investment fund is $2 million. [13.1%]
Stock
A
B
C
D
Investment
$ 200,000
300,000
500,000
1,000,000
Beta
1.50
-0.50
1.25
0.75
92. You are an investor in common stock and currently hold a well-diversified portfolio which
has an expected return of 0.12 with a beta of 1.2. You are planning on buying 100 shares
of PM&R at $10 a share. This stock has an expected return of 0.20 with a beta of 2.0.
The total value of your current portfolio is $9,000. What will be the expected return of
the portfolio after the purchase of the new stock? [12.8% ]
93. You are holding a stock which is in equilibrium and the required return on the stock is
15% when the return on the average asset is 10%. What will be the percentage change in
the return on the stock if the return on the average asset increases by 30% and the
stock has a beta of 2? [40%]
94. An investor holds a diversified portfolio consisting of a $5,000 investment in each of 20
different common stocks. The portfolio beta is equal to 1.12. The investor has decided
to sell a lead mining stock (beta = 1.0) at $5,000 net and use the proceeds to buy a like
amount of a steel company stock (beta = 2.0). What is the new beta for the portfolio?
[1.17]
95. Over the past few years, NBC Company has retained, on the average, 70% of earnings in
the business. The future retention rate is expected to remain at 70% of earnings, and
long-run earnings growth is expected to be 10%. If the risk-free rate (kRF) is 8%, the
expected return on the market (kM) is 12%, NBC's beta is 2.0, and the current dividend
(D0) is $1.50, what is a fair market price and the P/E ratio for NBC's stock today
(P0/E0) [Market Price = $27.50 P/E Ratio = 5.5 Times]
18
96. You are given the following data:
1.
2.
3.
4.
5.
The risk-free rate is 0.05.
The required return on the market is 0.08.
The expected growth rate for the firm is 0.04.
The last dividend paid was $0.80 per share.
Beta is 1.3.
Now assume the following changes occur:
1. The inflation premium decreases by the amount of 0.01.
2. An increased degree of risk aversion causes the
required return on the market to go to 0.10 after
adjusting for the changed inflation premium.
3. The expected growth rate increases to 0.06.
4. Beta rises to 1.5.
What will be the change in price per share assuming the stock was in equilibrium before
the changes? [-$4.87 (Decrease)]
19
CAPITAL BUDGETING FORMULAS
PAYBACK = THE NUMBER OF YEARS TO RECOVER THE INVESTMENT DOLLARS
NPV
= NET PRESENT VALUE
OUTFLOW
n
NPV
=
∑
=
PRESENT VALE OF INFLOW - PRESENT VALUE OF
CFt
t
t =0 (1 + K)
WHERE
n=
t=
CF =
K=
number of periods
an index number indexing from 0 to n
the amount of each t numbered cashflow
the rate of interest in each time period t
IRR
= INTERNAL RATE OF RETURN
IRR
= NPV = 0
20
CAPITAL BUDGETING
97. MTM Inc., is considering the purchase of a new machine which will reduce manufacturing
costs by $5,000 annually. MTM will use the straight-line method to depreciate the
machine, and it expects to sell the machine at the end of its 5 year life for $10,000.
The firm expects to be able to reduce working capital by $15,000 when the machine is
installed. The firm's marginal tax rate is 34% and it uses a 12% cost of capital to
evaluate projects of this nature. If the machine costs $60,000, what is the NPV of the
project's cash flows? [-$23,685]
98. It is now December 31, 1986. Your company is planning to build an exhibit at the 198788 World's Fair. The exhibit will cost $3.024 million to build today, will bring year-end
after-tax cash inflows of $2.0 million in 1987 and 1988, and cost $0.5 million to tear
down at the end of 1989. What is this project's IRR? [IRR = 12%]
99. After a disastrous ski season last year, Valley, Inc., is considering the installation of a
snow machine. The machine has an invoice price of $100,000, and it will cost $10,000 to
install the machine. It is estimated that the machine will increase revenues by $25,303
annually, although operating expenses other than depreciation will also increase by
$5,000. The machine will be depreciated on a straight-line basis over its useful life (10
years) to a zero salvage value. If the tax rate on ordinary income is 34%, what is the
project's IRR (approximately)? [IRR = 9%]
100. As the capital budgeting director for Harding Industries, Inc., you are evaluating the
construction of a new plant. The plant has a net cost of $4.921 million in year 0, and it
will provide net cash inflows of $1 million in year 1, $1.5 million in year 2, and $2 million in
years 3 through 5. As a first approximation, you may assume that all cash flows occur at
year-end. What is the plant's approximate IRR? [IRR = 19%]
101. Ferrari of Ohio is considering the purchase of land and the construction of a new plant.
The land, which would be bought immediately, has a cost of $100,000 and the building,
which would be erected at the end of the year, would cost $500,000. It is estimated
that the firm's after-tax cash flow will be increased by $100,000 beginning at the end
of the second year and this incremental flow would increase at a 10% rate annually over
the next 10 years. What would be the payback period (approximately)? [6 years]
21
102. Two projects being considered are mutually exclusive and have the following projected
cash flows:
Year
0
1
2
3
4
5
Project A
-$50,000
15,625
15,625
15,625
15,625
15,625
Project B
-$50,000
0
0
0
0
99,263
Beyond what level of required return (approximately) would you change your selection?
[12%]
103. Two projects being considered by MTX are mutually exclusive and have the following
projected cash flows:
Year
0
1
2
3
Project A
-$100,000
39,550
39,550
39,550
Project B
-$100,000
0
0
133,500
Based ONLY on the information given, what is the IRR for the two projects? Which
would you chose? What are the NPV’s of the two projects if the cost of capital is 7%?
[IRR A = 9% IRR B = 10% B Has Higher Irr; NPV Project A = $3,791.70, NPV Project
B = $8,975.77]
104. Calculate the NPV when the cost of capital is 12% and, calculate the internal rate of
return of the following flow stream. [NPV = $477.05 ,IRR = 14%]
YEAR
0
1
2
3
4
CASHFLOW
-10,000
2,780
3,600
4,000
3,500
22
105. What are the respective IRRs for Projects A, B, C, and D?
13%: IRR C = 24% : IRR D = 14%]
Project
Cost
A
$10,000
B
5,000
C
12,000
D
3,000
Annual
Cash Inflows
$11,700
2,997
6,057
1,030
Life
(years)
1
2
3
4
[IRR A = 17% : IRR B =
IRR
?
?
?
?
106. As the DCB for Midterm INC., you are evaluating two mutually exclusive projects with
the following net cash flows:
Year
0
1
2
3
4
Project X
-$100,000
50,000
40,000
30,000
10,000
Project Z
-$100,000
10,000
30,000
50,000
60,000
If Midterm's cost of capital is 15%, which of the machines (if either) would the firm
accept? [NPV X = -$832.97 NPV Z = -$1,439.03 BOTH NEGATIVE]
107. Two projects being considered are mutually exclusive and have the following projected
cash flows:
Year
0
1
2
3
4
5
Project A
-$50,000
15,625
15,625
15,625
15,625
15,625
Project B
-$50,000
0
0
0
0
99,500
If the required return on these projects is 10%, which would be chosen and why?
[NPV A = $9,231 NPV B = $11,782; CHOSE B]
23
108. Tyler Products, Inc., requires a new machine to produce a part for a heat generator.
Two companies have submitted bids, and you have been assigned the task of choosing
one of the machines. Cash flow analysis indicates the following:
Year
0
1
2
3
4
Machine A
-$1,000
0
0
0
1,938
Machine B
-$1,000
417
417
417
417
What is the internal rate of return for each machine?
24%]
[(A) IRR = 18%
(B) IRR =
109. Tyler Products, Inc., requires a new machine to produce a part for a heat generator.
Two companies have submitted bids, and you have been assigned the task of choosing
one of the machines. Cash flow analysis indicates the following:
Year
0
1
2
3
4
Machine A
-$1,000
0
0
0
1,938
Machine B
-$1,000
417
417
417
417
If the cost of capital for Tyler Products is 5%, which of the machines (if either) would
be accepted and why? [NPV A $594.40 NPV B $478.66 A Is Superior To B]
110. Tyler Products, Inc., requires a new machine to produce a part for a heat generator.
Two companies have submitted bids, and you have been assigned the task of choosing
one of the machines. Cash flow analysis indicates the following:
Year
0
1
2
3
4
Machine A
-$1,000
0
0
0
1,938
Machine B
-$1,000
417
417
417
417
If a net present value profile were developed for these two investments, at what
discount rate would the profiles cross? [10%]
24
111. Consider the following set of investment alternatives.
A.
B.
C.
D.
E.
NPV
$15
$25
$10
$ 8
$45
IRR
18%
29%
15%
12%
25%
PAYBACK INITIAL INVESTMENT
6.0 YRS.
$150
2.5 YRS.
$ 85
3 3 YRS.
$160
4.0 YRS.
$ 45
3.0 YRS.
$365
Assuming the capital budget is fixed at $400, which projects should be accepted?
[Projects A, B, And C]
112. Gold and Black, Inc., is considering replacing its old bottling machine with a new, more
efficient machine. Relevant data for this decision are given below:
INITIAL COST
CURRENT AGE
REMAINING USEFUL LIFE
SALVAGE VALUE AT END
MAINTENANCE COSTS
REQUIRED INCREASE IN
WORKING CAPITAL
CURRENT MARKET VALUE
OLD
NEW
$ 60,000
$ 80,000
20 YRS
0
10 YRS
10 YRS
$
0
$ 10,000
$ 15,000/YR $ 3,000/YR
$ 2,000
$ 25,000
$ 6,000
$ 80,000
Assuming a 34% tax rate, straight-line depreciation, and a 6% required rate of return,
what is the NPV of this replacement decision? [$17,921.56]
113. What is the internal rate of return of the following project?
PERIOD
0
1-16
NET CASH FLOW
$ -41,500
$ 4,393
114. What is the IRR of a project with the following cash flows?
TIME
0
1
2
3
4
5
[IRR = 7%]
CASH OUTFLOW
CASH INFLOWS
$ 43,295
--$ 10,000
-10,000
-10,000
-10,000
-10,000
25
[IRR = 5%]
115. Missouri Metals, Inc. is considering the replacement of its existing lathe, which cost
$200,000 at the time of purchase five years ago, and which now has a remaining life of
five years with no salvage value. It can be sold currently for $100,000. A new, more
operationally efficient lathe costs $300,000 and has a useful life of five years with a
salvage value of $50,000. It is expected to reduce operating costs by $66,000 annually.
The firm's required rate of return for replacement decisions is 12%. Assume straightline depreciation and a tax rate of 34 percent. What is the net present value of this
capital budgeting decision? [$22,164.05]
116. UT Company is faced with two mutually exclusive investment alternatives, Project A
versus Project B, each of which has an initial cost of $100 million. The following
information is related to the two investment alternatives.
YEAR
1
2
3
4
NET CASH
A
$ 50
$ 40
$ 30
$ 10
FLOW
B
$ 10
$ 30
$ 40
$ 60
(millions)
At a 5 percent discount rate, which alternative would you accept, and at a 10 percent
discount rate which alternative would you accept? [Project B at 5%; Project A at 10%]
117. Davis & Associates is considering the purchase of a new pizza oven. The original cost of
the old oven was $30,000. The machine is now 5 years old and has a current market
value of $5,000. The oven is being depreciated over a 10 year life toward a zero
estimated salvage value on a straight line basis. Management is contemplating the
purchase of a new oven whose cost is $25,000 and whose estimated salvage value is
zero. Expected cash savings from the new oven are $7,000 a year (before tax).
Depreciation is on a straight line basis over a 5 year life, and the cost of capital is 10%.
Assume a 34% tax rate. What is the net present value of the new machine?
[$3,491.17]
118. Heel & Sole, Inc., is considering the purchase of a new leather-cutting machine to
replace an existing machine that has a book value of $3,000 and can be sold for $1,500.
The estimated salvage value of the old machine in 4 years is zero. The new machine will
reduce costs (before tax) by $7,000 per year; that is, $7,000 cash savings over the old
machine. The new machine has a 4 year life, costs $14,000, and can be sold for an
expected $2,000 at the end of the fourth year (it will be depreciated to a book value of
$2,000). Assuming straight line depreciation for both machines, a 34% tax rate, and a
cost of capital of 16%, find the NPV. [$4,182.91]
26
119. Corleone, Inc., is a fast-food establishment that needs to purchase new fryolators. If
the machines are purchased, they will replace old machines purchased 10 years ago for
$100,000, being depreciated on a straight line basis to a zero salvage value (20 years
depreciable life). The old machines can be sold for $120,000. The new machines will
cost $200,000 installed and will be depreciated on a straight line basis to a zero salvage
value in 10 years. It is expected that there will be increased revenues of $28,000 per
year and increased cash expenses of $2,500 per year. If the firm's cost of capital (k)
is 10%, the ordinary income tax rate is 34%, and the capital gain tax rate is 15%, what is
the NPV of the machine? [$34,750.36]
120. DC, Inc., has a stamping machine which is 5 years old and which is expected to last
another 10 years. It has a book value of $100,000 and is being depreciated by the
straight line method to zero. Allstate Industries has demonstrated a new machine with
an expected useful life of 10 years (scrap value $50,000) that should save DC $38,000
a year in labor and maintenance costs. The firm's tax rate is 34%, and the new machine
will cost $200,000. The market value of the old machine is $10,000 and a $10,000
increase in working capital will be needed to support the new machine. If DC's cost of
capital is 10%, should the replacement be made? [$18,282.39]
121. Stork Company is considering the purchase of a new machine to replace an existing one.
The old machine was purchased 5 years ago at a cost of $50,000 and is being
depreciated on a straight line basis to a zero salvage value 5 years from today. The
current market value of the old machine is $15,000. The new machine has an estimated
life of 5 years, costs $75,000, and has an estimated zero salvage value. It is expected
to generate cash savings (before taxes) of $25,000 per year. What is the NPV of the
proposed purchase if the tax rate is 34% and the cost of capital is 11%? [$16,948]
122. What is the IRR of a project with the following cash flows?
YEAR
0
1
2
3
4
5
CASHFLOW
$ 0
$ 15
$ -2500
$ 1000
$ 1000
$ 1000
27
[IRR = 10%]
123. FIDO, Inc., is considering the replacement of its computer with a new generation model.
The IBM salesperson has demonstrated a model which would cost FIDO $750,000,
should last 10 years, and reduce costs $166,043 per year. IBM estimates that this new
computer can be sold for $15,000 at the end of its useful life. The computer FIDO
currently uses has a book value of $450,000 (remaining life of 10 years, a salvage value
of $10,000, and a current market value of $16,000. If the new machine will permit an
$8,000 decrease in working capital when the computer is installed, what is the NPV
given that k = 15%, t = 34%, and depreciation is straight line? [$21,155.42]
124. You have been asked by the CEO of Gadsden Co. to evaluate the proposed acquisition of
a new machine. The machine's price is $50,000, and it will cost $10,000 to transport
and install. It will be depreciated by the straight line method over its 5 year useful life
to a $10,000 salvage value. The machine will increase revenues by $10,000 per year,
and it will decrease operating costs by $20,000 per year. Also, the machine will allow
the firm to reduce inventories by $5,000. If the firm's cost of capital is 12%, and its
marginal tax rate is 34%, what is the new machine's NPV? [$31,468.36]
125. Yankee Brick, Inc., has an electric kiln which is 5 years old and is expected to last
another 10 years. It has a book value of $100,000, and it is being depreciated by the
straight line method to a zero salvage value. As Director of Capital Budgeting, you are
evaluating a new gas kiln that should save Yankee Brick, Inc. $45,000 a year in fuel
costs. The new kiln would cost $200,000, and it would be depreciated over its 10-year
life using the straight-line method to a $20,000 salvage value. The market value of the
old kiln is $10,000. Yankee Brick, Inc.'s marginal tax rate is 34%, and the firm's cost of
capital is 10%. What is the NPV of the replacement project? [$47,518]
126. Projects C and W are mutually exclusive, and they have the following net cash flows.
You are to use the equivalent annual annuity method for comparing these projects since
they have unequal lives. If the cost of capital is 10%, which project should be chosen?
[EAA C = $192,598.10 EAA W = $136,202.5]
Year
0
1
2
3
4
5
Project C
-$50,000
30,000
40,000
50,000
0
0
Project W
-$100,000
40,000
40,000
40,000
40,000
40,000
28
127. Magnum, Inc., purveyor of surveillance equipment, uses a weighted average cost of
capital of 13% to evaluate average risk projects, and adds/subtracts 2 percentage
points to evaluate projects of greater/less risk. Currently two mutually exclusive
projects are under consideration. Both have a cost of $200,000 and last 4 years.
Project A, a riskier-than-average project, will produce yearly cash flows of $71,104.
Project B, of less than average risk, will produce cash flows of $146,411 annually in
years 3 and 4 only. Which project(s) should Magnum select?
[NPV A = $3000.38
NPV B = $3499.92 Select B]
128. The Lewis Company is considering two mutually exclusive investments that would
increase its capacity to make strawberry tarts. The firm uses a 12 percent cost of
capital to evaluate potential investments. The projects have the following costs and cash
flow streams: What are the respective EQUIVALENT ANNUAL ANNUITIES for
alternatives A and B? [EAA A = $5,190
EAA B = $3,841]
YEAR
0
1
2
3
4
5
6
7
8
ALTERNATIVE A ALTERNATIVE B
$ -30,000
$ -30,000
10,500
6,500
10,500
6,500
10,500
6,500
10,500
6,500
-6,500
-6,500
-6,500
-6,500
129. Taco, Inc., is evaluating the introduction of a new production process. Two alternatives
are available. Process A has an initial investment of $25,000, a 4 year life, and a $5,000
salvage value. The use of Process A will increase net income after taxes by $8,000 per
year for each of the 4 years that the equipment is in use. Process B also requires an
initial investment of $25,000, will also last for 4 years, and its expected salvage value is
zero. Process B will increase net income after taxes by $8,997 per year. Taco uses
straight line depreciation on all capital assets. Management believes that risk-adjusted
discount rate of 12% should be used for Process A. If Taco is to be indifferent
between the two processes, what risk-adjusted discount rate must be used to evaluate
B? [16%]
29
130. Frankenstein Inc., is considering the development of one of two mutually exclusive new
models. Each will cost $5,000. The cash flow figures (after-tax profits plus
depreciation) for each project are shown below:
Period
1
2
3
Project A
$2,000
2,500
2,250
Project B
$3,000
2,600
2,900
Model B, which has an energy-saving sod roof, is considered a high-risk project, while
Model A is of average risk. The firm adds 2 percentage points to arrive at a riskadjusted cost of capital when evaluating a high-risk project. The cost of capital used
for average risk projects is 12%. Calculate the NPVs for Models A and B.
[NPV A =
$380.21 NPV B = $1,589.61]
131. Diversified Products Co. is faced with two mutually exclusive investment alternatives,
each of which has an initial cost of $100 million. Given the following after tax net cash
flows for the projects, which alternative would you accept at a 5 percent cost of capital
and which at a 10 percent cost of capital?
NPV A at 5% = $18,042,370 NPV B at 5% = $20,650,340 NPV A at 10% = $7,881,975
NPV B at 10% = $4,917,696]
YEAR
PROJECT A
1
$50,000,000
2
$40,000,000
3
$30,000,000
4
$10,000,000
PROJECT B
$10,000,000
$30,000,000
$40,000,000
$60,000,000
132. Marvin's Meats is considering an investment in one of two mutually exclusive projects.
The discount rate used for Project A is 12%. Further, Project A costs $15,000 and is
being depreciated on a straight line basis to an estimated salvage value of $5,000 at the
end of 5 years. Project A is expected to produce net income after taxes of $4,000 for
each of the 5 years. Project B also costs $15,000 and is being depreciated on a straight
line basis to an estimated zero salvage value at the end of its 5 year life. If Project B
is expected to produce net income after taxes of $5,180 each year for 5 years, what is
the risk-adjusted discount rate which will equate the NPV of B to that of A? [20%]
30
MEAN, VARIANCE, COVARIANCE AND PORTFOLIO
MEAN
=
n
∑ (Xi Pi)
X =
i=1
WHERE Pi IS THE PROBABILITY OF Xi OCCURRING
VARIANCE
σ
=
2 =
BETA
=
β
=
CORRELATION =
∑ ( Xi − X)
2
i=1
=
σ
COV X, Y
=
STANDARD DEVIATION
COVARIANCE =
n
Pi
.5
n
2 
 ∑ Xi − X Pi 

i=1
(
=
)
n
∑ ( Xi − X) (Yi − Y ) Pi
i=1
COV M, S
σ M2
ρ
COV X, Y
=
σX σ Y
COEFFICIENT OF VARIATION
_
_
MEAN OF PORTFOLIO
=
=
σ X/ X
(WX ) (X ) + (W Y)(Y)
STANDARD DEVIATION OF A PORTFOLIO
σP
=
 (W ) 2
X

(σX2 ) + (W Y ) 2 σ Y2  + 2 (W X ) (W Y ) (COV X, Y)
σP
=
 (W ) 2
X

(σX2 ) + (W Y ) 2 σ Y2
 + 2 (W ) (W )
X
Y

31
.5
( ρ σ X σ Y )
.5
RISK AND RETURN
THE FOLLOWING INFORMATION REFERS TO THE NEXT FOUR QUESTIONS.
THE GIFFIN INVESTMENT FUND HAS THE FOLLOWING DATA AND WISHES TO
ANSWER THE FOLLOWING QUESTIONS:
STOCK BLUE
18%
13%
14%
13%
16%
STOCK RED
17%
14%
15%
14%
17%
133. What is the expected return on STOCK BLUE?
[14.8%]
134. What is the standard deviation for STOCK BLUE?
[ 1.94%]
135. What is the coefficient of variation of STOCK BLUE returns?
[.13]
136. What is the covariance of STOCK BLUE returns with STOCK RED returns?
(Percent Squared)]
[ 2.48
137. What is the correlation coefficient between the STOCK BLUE returns and STOCK RED
returns? [.94]
THE FOLLOWING DATA PERTAINS TO THE NEXT FIVE QUESTIONS.
Stocks A and B have returns and probability distributions as given below.
STOCK A
07%
08%
07%
11%
STOCK B
11%
12%
13%
05%
138. Calculate the expected returns for Stocks A and B.
[A = 8.25% B = 10.25%]
139. What are the standard deviations of expected returns for Stocks A and B?
1.64%
B = 3.11%]
140. Compute the covariance between Stocks A and B.
[-4.81%]
141. Find the correlation coefficient between Stocks A and B.
32
[-.94]
[A =
142. Suppose you want to hold a portfolio composed of 40% of Stock A and 60% of Stock B.
What will be the expected return (mean) and risk (standard deviation) of your portfolio?
[Mean = 9.45% Std. Dev. = 1.27%]
143. You have the opportunity to purchase three stocks at a price that you consider a
bargain. You have a history of the returns on the stocks over the past six quarters. As
one can see from observation, the stocks do not yield equal rates of return. Your friend
suggests that you should purchase only the stock with the highest return. Since you
have had finance and know the value of a portfolio, demonstrate why buying all three in
equal proportions is a wiser investment.
[PORTFOLIO MEAN = 12.23% PORTFOLIO
STD DEVIATION = .4668]
STOCK A
STOCK B
13.0%
12.5%
12.0%
11.0%
10.0%
10.0%
11.0%
12.0%
13.0%
14.0%
STOCK C
13.0%
14.0%
15.0%
12.0%
11.0%
33
FINANCIAL ANALYSIS RATIOS
PROFITABILITY
1. Gross Profit Margin
Gross Profit
2. Return on Total Assets
Or
3. Return on Common Equity
Or
4. Operating Profit Margin
5. Net Profit Margin
(Sales − CGS)
Sales
Net Income (After Tax)
Total Assets
Net Income X
Sales
Total Assets
Sales
Net Income (After Tax)
Stockholder' s Equity
Return on Investment (Assets)
[1 − ( Debt / Assets)]
Net Operating Income (EBIT)
Sales
Net Income (After Tax)
Sales
Net Operating Income (EBIT)
6. Operating Income Return on Investment
7. P/E Ratio
Total Assets
Price Per Share of Stock
Net Income / Number Of Shares
34
FINANCIAL ANALYSIS RATIOS
ASSET UTILIZATION (Efficiency Ratios)
1. Receivable Turnover
2. Average Collection Period
Credit Sales
Accounts Receivable
Accounts Receivable
Annual Credit Sales / 365
3. Inventory Turnover
Sales
Inventory
4. Fixed Asset Turnover
Sales
Net Fixed Assets
5. Total Asset Turnover
Sales
Total Assets
DEBT UTILIZATION (LEVERAGE RATIOS)
1. Debt To Total Assets
2. Times Interest Earned
3. Fixed Charge Coverage
Total Debt (Liabilities)
Total Assets
EBIT
Annual Interest Expense
Income Before Fixed Charges & Taxes
Fixed Charges
35
FINANCIAL ANALYSIS RATIOS
LIQUIDITY RATIOS
1. Current Ratio
Current Assets
Current Liabilities
Current Assets - Inventory
Current Liabilites
2. Quick Ratio
MISCELLANEOUS RATIOS
Dividends
Net Income
1. Dividend Payout Ratio
2. ROE
Total Assets


Net Income (After Tax) 

 X 
 X  Sales

Sales
Total Assets
Total Equity 


Total Assets
Total Equity
=
Equity Multiplier
Net Income (After Tax) 




Sales
=
36
Profit Margin
FINANCIAL ANALYSIS
144. Cramer Corporation's expected net income for next year is $800,000. Cramer's target,
and current, capital structure is 40% debt and 60% common equity. The Director of
Capital Budgeting has determined that the optimal capital budget for next year is $1.2
million. If Cramer Corporation uses the residual theory of dividends to determine next
year's dividend payout, what is the expected PAYOUT ratio? [10%]
145. Craven Corp. has retained earnings of $1.75 million and 100,000 shares of stock
outstanding with a market value of $25 per share. If Craven declares a 15 percent
stock dividend, what will Craven's retained earnings be after the dividend?
[$1,375,000]
146. Holt Co. has a net income of $100 million and a policy of paying out 60 percent of its
earnings in dividends.How much total financing can be accomplished before thecompany
has to sell common stock? Assume a debt/equity ratio of 66.67 percent.
[$66,666,666.67]
147. Hagler Corp. has earnings of $1.5 million and a policy of paying out 60 percent of
earnings. Hagler has $1.8 million in acceptable investments but is unable to issue new
equity. Assuming a D/E of 0.4, how much will Hagler be able to spend on capital
budgeting if it wishes to stick with the 60 percent payout? [$840,000]
148. Before a 2-for-1 stock split, Splitpea Company sold for $60 a share, earning $15 and
paying $8 dividend per share. After the split, the dividend per share becomes $5.20. By
what percentage has the payout ratio risen? [30%]
149. Baldwin Corporation has declared a 10 percent stock dividend. Baldwin has 2 million
shares outstanding with a current market price of $7. Its capital stock account is $1
million, and the firm's retained earnings are $8 million. What balances will the retained
earnings and capital stock accounts show after the distribution of the stock dividend?
[RE = $6,600,000 CSA = $2,400,000]
150. If Hampshire, Inc., has sales of $2 million per year (all credit) and an average collection
period of 35 days, what is its average amount of accounts receivable outstanding
(assume a 365 day year)? [$191,781]
37
151. Calculate the market price of a share of FDR, Inc., given the following information:
[$75]
Stockholders' equity = $1,250;
price/earnings ratio = 5;
shares outstanding = 25;
market/book ratio = 1.5.
market/book ratio = market value equity/book value equity
152. Ensewmow, Inc., has earnings after interest deductions but before taxes of $300. The
company's before-tax times interest earned ratio is 7.00. Calculate the company's
interest charges. [$50.00]
153. Omega Co.'s records have recently been destroyed by fire. Given the following bits of
information saved from the inferno, determine Omega's net income for 1986.
[$65,989,847.73]
Return on equity 22%
Assets/equity
2.167
Net profit margin 5.6%
Total assets
$650 million
154. If ZZ Co. has total interest charges of $10,000 per year, sales of $1 million, a tax rate
of 34%, and a net profit margin of 6%, what is the firm's times interest earned ratio?
[10.09 Times]
155. The Jupiter Company has determined that its return on equity is 15%. Management is
interested in the various components that went into this calculation. However, the
accountants have misplaced the profit margin ratio. As a finance wizard, you know how
to calculate the profit margin, given following information: total debt/total assets =
0.35, and total asset turnover = 2.8. What is the profit margin? [3.48%]
156. Kelley Company has a debt ratio of 0.5, a capital intensity ratio (total assets/ total
sales) of 4, and a profit margin of 10%. The Board of Directors is unhappy with the
current return on equity (ROE), and they think it could be doubled. This could be
accomplished (1) by increasing the profit margin to 12% and (2) by increasing debt
utilization. Total asset turnover will not change. What new debt ratio (total debt/total
assets), along with the 12% profit margin, is required to double the ROE? [70%]
38
157. Assume that Calhoun Corporation is 100% equity financed. Calculate the return on equity
given the following information: [52.8%]
1.
2.
3.
4.
5.
Earnings before taxes = $2,000
Sales = $5,000
Dividend payout ratio = 60%
Total asset turnover = 2.0
Applicable tax rate = 34%
158. The Cigar Company is a relatively small, privately owned firm. In 1986 Cigar had an
after-tax income of $15,000, and 10,000 shares were outstanding. The owners were
trying to determine the equilibrium market value for Cigar's stock, prior to taking the
company public. A similar firm that is publicly traded had a price/earnings ratio of 5.0.
Using only the information given, estimate the market value of one share of Cigar's
stock. [$7.50]
39
BREAKEVEN, OPERATING AND FINANCIAL LEVERAGE
P (Q ) = FC + VC (Q )
P (Q ) − FC − VC
P (Q ) − FC - UNIT VC (Q)
BREAKEVEN
EBIT =
EBIT =
WHERE
P = Price
Q = Quantity
FC = Fixed Costs
VC = Variable Costs
DEGREE OF OPERATING LEVERAGE (DOL)
DOL = [ Q (P − V ) ]
[ Q (P − V ) − F ]
WHERE
P = Price
Q = Quantity
FC = Fixed Costs
VC = Variable Costs
DEGREE OF FINANCIAL LEVERAGE (DFL)
DFL = EBIT
( EBIT
− I)
WHERE
EBIT = Earnings Before Interest and Taxes
I = Interest
DEGREE OF COMBINED LEVERAGE (DCL)
DCL = [ Q (P − V ) ]
[Q (P − V ) − F − I ]
DCL = DFL * DOL
WHERE
P = Price
Q = Quantity
I = Interest
FC = Fixed Costs
VC = Variable Costs
40
BREAKEVEN, OPERATING AND FINANCIAL LEVERAGE
159. The Aquarium Company will produce 55,000 10-gallon aquariums next year. Variable
costs will equal 40% of sales while fixed costs total $110,000. At what price must each
aquarium be sold for the company to obtain an EBIT of $95,000? [$6.21 Per Unit]
160. Gulf Vineyards is considering two alternative production methods for making wine. One
uses an authentic, hand- operated oak wine press, the other an automated aluminum
machine. It is estimated that the variable cost per bottle will amount to $2.00 under
the former method and $0.50 under the latter. If the new machine is purchased, fixed
operating costs will equal $150,000 and interest charges $80,000. Fixed operating
costs of $25,000 will be incurred should the company decide to use the old press.
Assume sales (in units) will be 100,000 bottles under the automated method. What
sales price per unit would cause Gulf to be indifferent between the two methods if
expected sales are 75,000 units under the labor intensive method? [$4.20 Per Unit]
161. The Stone Company has identified two methods of producing its playing cards. One
method involves using a machine having a fixed cost of $10,000 and variable costs of
$1.00 per deck of cards. The other method would use a less expensive machine (fixed
cost = $5,000), but it would require greater variable costs ($1.50 per deck of cards).
If the selling price per deck of cards will be the same under each method, at what level
of output will the two methods produce the same net operating income? [10,000 Units]
162. JTL Publishers sells finance textbooks for $7 each. The variable cost per book is $5.
At current annual sales of 200,000 books, the publisher is just breaking even. It is
estimated that if the authors' royalties are reduced, the variable cost per book will
drop by $1. Assume authors' royalties are reduced and sales remain constant; how much
more money can the publisher put into advertising (a fixed cost) and still break even?
[$200,000]
163. Octacycles, Inc., currently sells 75,000 8-wheelers annually. At this sales level, its net
operating income (EBIT) is $4 million and the degree of combined leverage is 2.0. The
firm's debt consists of $10 million in bonds with a 9% coupon. The firm is considering
the implementation of a new production method that will entail an increase in fixed
costs, resulting in a degree of operating leverage of 1.8. Being concerned about the total
risk of the firm, the Chief Executive wants to maintain the degree of combined leverage
at 2.0. If EBIT remains at $4 million, what amount of bonds must be retired to
accomplish this? [$5,555,556]
41
COST OF CAPITAL
164. Zenon Co. recently issued 10-year 12 3/4 percent coupon bonds at face value. Zenon's
beta is .62, its target debt/equity ratio is .60, and the tax rate is 34 percent. If the
market risk premium is 8 percent and the risk-free rate is 10 percent, estimate Zenon's
weighted average required return. [12.51%]
165. The Argon Company has the following capital structure:
8% long-term debt due 1999
8% cumulative preferred stock
Common stock
$ 2,000,000
$ 2,000,000
$ 6,000,000
Other information is as follows:
Beta of Argon stock
Tax rate
Market rate of return
Risk-free rate
Market cost of debt
1.5
34%
12%
6%
10%
What is the weighted average required return for Argon?
[11.92%]
166. Assume the risk-free rate is 8 percent, beta is 1.5, and the return on the market is 12
percent. The firm has a D/A ratio of .4. The cost of debt is 10 percent and the tax rate
is 34 percent. What is the weighted average required return? [11.04%]
167. Druid Corp. has the following capital structure:
Debt $ 18,000,000
Equity $ 27,000,000
Total $ 45,000,000
Given KM of 15%, KRF of 8%, beta of 0.875, a before-tax cost of debt of 11%, and a tax
rate of 34%, calculate Druid's weighted average required return assuming that the firm
intends to use only retained earnings and debt. [11.38%]
168. Pittman Corp. has assets of $100,000 and a debt/equity ratio of 0.6. Debt carries an
interest rate of 10 percent, and new equity can be sold for $25 per share (ignoring any
flotation costs). If the $100,000 in assets generate $30,000 in EBIT and Pittman has a
34 percent tax rate, find the firm's earnings per share. [$6.93]
42
169. Neon Corp. has the following capital structure:
Debt $ 2O,000,000
Equity $ 25,000,000
Total $ 45,000,000
Neon Corp.'s profit margin, payout ratio, and sales are expected to be 10%, 40%, and
$50 million respectively. If Neon does not wish to issue any new common stock, what is
the maximum amount of new capital that can be raised for investment projects?
[$5,400,000]
170. SIPS' target debt/equity is 1.5. New debt can be raised at a cost to SIPS of 11.25
percent, and new stock can be issued at $15 per share; however, flotation costs of 6%
will be incurred on the stock issue. If SIPS' current dividend is $0.90, and dividends
are expected to grow at a 9 percent rate for the indefinite future, estimate SIPS'
weighted average required return. Assume a 34% tax rate. [10.84%]
171. CWF, Inc. had total earnings of $120,000 during the past year. The company pays out 60
percent of its earnings as dividends. CWF has determined that its optimal capital
structure is 40 percent debt and 60 percent equity. Given this information, how much
new capital (retained earnings plus new debt) can be raised before CWF is forced to
issue new common stock, assuming it stays at its target capital structure? [$80,000]
43
CAPITAL STRUCTURE
172. Given the following data and a 34 percent tax rate, indicate which capital structure
would be preferred by a firm. [100% Equity]
A.
B.
C.
Debt/Assets
0%
30%
60%
KD
8%
10%
12%
KS
10%
12%
14%
173. Pyramid Corp. is a new firm seeking to finance $20 million in assets. It is considering a
40 percent debt/equity ratio vs. an all-equity capital structure. New debt will carry
interest charges of 12 percent and new shares can be sold for $20 per share. Assuming
a 34 percent tax rate, find the level of EBIT at which both plans will have the same
EPS. [$2,400,000]
174. Wilson Co. has $2 million in assets, financed half by debt, half by equity. The cost of
debt is 10%, and the equity has a book value of $20 per share. Wilson is considering an
expansion of $500,000 which can be financed in two ways: (1) 50 percent debt at 12
percent, 50 percent equity at $20 per share, or (2) 100 percent debt financed at 13
percent. Find the EBIT breakeven point for Plan 1 compared to Plan 2. The tax rate is
34 percent. [$305,000]
175. Libra Company, an all equity firm, is considering the following expansion project, which it
judges to be 1.5 times as risky as an average project in the market:
Year
0
1
2
3
4
Cashflow
$ -150,000
50,000
55,000
60,000
45,000
If the riskless rate of interest is 8 percent and the market risk premium is 8 percent,
what is the net present value of the project? [-$13,715.28]
176. Assume that Smith Inc. expects to have $6,000,000 of retained earnings available for
use next year, and has a target capital structure of 40 percent long-term debt and 60
percent common equity. Where is the breakpoint in the MCC schedule for Smith when
it must switch from the use of retained earnings to the sale of new common stock?
[$10,000,000]
44
177. The following information applies to Winston Inc.:
1. Optimal capital structure is 50 percent debt and 50 percent equity.
2. Retained earnings are $4 million.
3. Cost of debt is 12 percent.
4. Tax rate is 34 percent.
5. Current dividend is $1.00.
6. Expected growth rate of dividends is 6 percent.
7. Current stock price is $25.00.
8. Flotation costs involved in issuing new stock are 5%.
What is Winston's marginal weighted average required return (the cost of the last
dollar raised), given a planned capital budget of $12 million? (Check for the point at
which Winston must issue new stock.) [9.19%]
178. A firm's capital structure includes 50 percent equity and it expects to have $200,000
of retained earnings at a 12 percent cost. In addition, it can raise common equity by
selling up to $500,000 of new common stock at 13 percent. If it issues more than that,
the cost will be 14 percent. At what level of total financing will the second equity
breakpoint occur? [$1,400,000]
179. The following data apply to GT Engineering: D1 = $1.35, P0 = $20.00, Kd = 12% ,
g = 15%, tax rate = 34%. GT's optimal capital structure calls for 30 percent debt and
70 percent equity. Assuming that all equity is obtained through retained earnings,
compute GT's weighted average required return (WARR). [17.6%]
180. GMAC's current (target) capital structure has a debt ratio (D/TA) of 50%. The firm
can raise up to $10 million in new debt at a before-tax cost of 8%. If more debt is
required, the cost will be 11%,. Net income (after tax) for the previous year was $10
million and is expected to increase by 10% this year. The firm expects to maintain its
dividend payout ratio of 40% on the 1 million shares of common stock outstanding. If it
must sell new common stock, it would encounter a 20% flotation cost. The tax rate is
34% and current stock price is $88 per share. What are the breakpoints for GMAC and
what is the weighted average cost of capital in each case?
BREAKPOINTS
COST
$0 TO $13,200,000
$13,200,000 TO 20,000,000
$20,200,000 AND UP
OF CAPITAL
.1014
.1097
.1196
45
181. Miller Mining had net income after interest but before taxes of $40,000 this year. The
marginal tax rate is 34%, and the dividend payout ratio is 30%. The company can raise
debt at a 12% interest rate for any amount of debt less than $8,000. If the firm
raises more than $8,000, a 17% interest rate will apply. The last dividend paid by Miller
was $0.90. Miller's common stock is selling for $8.59 per share and its growth rate
expected in earnings and dividends is 5%. If Miller issues new common stock, the
flotation cost incurred will be 10%. Miller plans to finance all capital expenditures with
20% debt and 80% equity. What is the break point due to retained earnings being used
up? [$23,100]
182. ZZZ, Inc., has a debt ratio of 0.2. It has concluded that this capital structure is in the
target capital structure range. It has analyzed its investment opportunities for the
coming year and has identified four possible additions to assets which generate IRRs
greater than zero.
Investment
A
B
C
D
Size
$ 3M
6M
12M
9M
IRR
0.20
0.185
0.19
0.18
ZZZ is forecasting net income for the coming year of $10 million and expects to pay out
50% in dividends to the 1 million outstanding shares of common stock. The earnings
have been growing at a constant rate of 10% over the past few years, and this rate is
expected to continue indefinitely. If ZZZ has to sell new common stock, it will be faced
with flotation costs of 15% (current market price = $50 per share). Any debt that is
raised will require a coupon rate of 8%. However, if the total debt required is greater
than $5 million, the coupon rate will have to be 10%. Assume the marginal tax rate is
34%. If the firm does not face capital rationing, how large should the capital budget
be? [$21,000,000]
183. Miller Mining had net income after interest but before taxes of $40,000 this year. The
marginal tax rate is 34%, and the dividend payout ratio is 30%. The company can raise
debt at a 12% interest rate for any amount of debt less than $8,000. If the firm
raises more than $8,000, a 17% interest rate will apply. The last dividend paid by Miller
was $0.90. Miller's common stock is selling for $8.59 per share, and its growth rate
expected in earnings and dividends is 5%. If Miller issues new common stock, the
flotation cost incurred will be 10%. Miller plans to finance all capital expenditures with
20% debt and 80% equity. What is the cost of new common equity raised by selling
stock? [17.22%]
46
184. Miller Mining had net income after interest but before taxes of $40,000 this year. The
marginal tax rate is 34%, and the dividend payout ratio is 30%. The company can raise
debt at a 12% interest rate for any amount of debt less than $8,000. If the firm
raises more than $8,000, a 17% interest rate will apply. The last dividend paid by Miller
was $0.90. Miller's common stock is selling for $8.59 per share, and its growth rate
expected in earnings and dividends is 5%. If Miller issues new common stock, the
flotation cost incurred will be 10%. Miller plans to finance all capital expenditures with
20% debt and 80% equity. There are two break points in Miller's MCC schedule; one
when retained earnings have been used up, and one when low-cost debt has been used up.
Therefore, there are three intervals in the MCC schedule. What is the marginal cost of
capital in each of these intervals?
[INT 1 = 14.38%
INT 2 = 15.36%
INT 3 =
16.02%]
185. Moon Corp. has a required return on debt of 10 percent, a required return on equity of
18 percent, and a 34 percent tax rate. Moon's management has concluded that a
financing mix of 50 percent debt, 50 percent equity is desirable. Given this information,
should Moon accept this investment? [NPV = $35,912.50]
YEAR
0
1
2
3
4
5
6
CASHFLOW
$ -100,000
$ 20,000
$ 30,000
$ 45,000
$ 50,000
$ 60,000
$ -5,000
186. Adams Corporation's present capital structure, which is also its target capital structure
is 40% debt and 60% common equity. Next year's net income after tax is projected to
be $21,000, and Adams' payout ratio is 30%. The company's earnings and dividends are
growing at a constant rate of 5%; the last dividend (D0) was $2.00; and the current
equilibrium stock price is $21.88. Adams can raise up to $20,000 of debt at a 12%
before-tax cost. All debt after $20,000 will cost 16%. If Adams issues new common
stock, a 20% flotation cost will be incurred. The firm's marginal tax rate is 34%. [A =
$24,500 B = 17%]
(A) What is the maximum amount of new capital that can be raised at the LOWEST
component cost of EQUITY?
(B) What is the component cost of equity by selling new common stock?
47
187. Determine the weighted average required return for Venus Corp. given the following
data: [17.07%]
SOURCES OF FINANCING
Bank loan
$ 120,000
Long-term debt
175,000
Preferred stock
15,000
Common stock
100,000
Retained earnings 250,000
Flotation Costs
8%
Tax rate
34%
Current stock price
$ 62.50
Current dividend
7.32
Required return on long-tern debt
12%
Interest on bank loan
16%
Required return on preferred stock
14%
Expected growth rate on dividends
11%
188. Canoe International is faced with the following possible investment opportunities:
1. Inflator
2. Plastic molder
3. Stopper
Cost
$10,000
6,000
15,000
Annual
Cash Inflows
$2,913
1,126
3,343
Life
(years)
5
9
8
The optimal capital structure calls for financing all projects with 90% equity and 10%
debt. If the following information applies to the future financial position of Canoe, in
which of the proposals (if any) should it invest? The last dividend (D0) was $1.75. The
growth rate of earnings and dividends is 6%. The current price per share of common
stock is $23. If new common stock is issued, a flotation cost of 5% will be incurred.
The company can raise as much debt as it wants at a coupon rate of 12%. The dividend
payout ratio is 30%. Canoe's net income last year was $15,000 and the firm is in the
34% tax bracket. [Accept Inflator and Stopper Projects since IRR > MCC]
189. The basic objective of financial management is to maximize the value of the firm. The
Austin Dog Food Company (ADFC) is trying to determine what ratio of debt to assets is
optimal. The analysts have the following information:
Debt/Assets
10%
20%
30%
40%
50%
Interest Rate
on Debt
9.0%
9.5%
10.0%
10.5%
11.0%
EPS
$2.75
2.97
3.20
3.36
3.30
P/E Ratio
7.94
7.58
7.14
6.58
5.95
Since management's desire is to maximize ADFC's value, what is the firm's optimal
debt/assets ratio? [Debt Ratio = 30%]
48
190. The following information relates to Jefferson, Inc.:
Debt/Assets
20%
30%
40%
50%
Interest Rate
on Debt
7.0%
8.0%
8.5%
9.5%
EPS
$5.11
5.97
6.52
6.70
P/E Ratio
8.3
8.0
7.6
6.8
What D/A ratio should Jefferson's management choose so that its capital structure is
optimal? [Debt Ratio = 40%]
191. TUT Enterprises is a new firm which is trying to find its optimal debt ratio based on the
following information:
DEBT/ASSETS
0%
10%
20%
30%
NET INCOME
$ 6,000
5,445
4,860
4,200
P/E RATIO
17.0
16.9
16.9
16.8
What debt ratio represents the optimal amount of financial leverage for TUT
Enterprises?
[Debt Ratio = 20%]
49
DIVIDEND POLICY
192. The Bickley Steel Company has an order backlog of $5 million. It desires to expand
production capacity by 20 percent, which will involve a $15 million investment in plant
and equipment. Management desires to maintain 40 percent debt in its capital structure.
The dividend policy has been to distribute 25 percent of the firm's after-tax earnings,
which this year were $6 million. If management wishes to maintain its dividend policy,
how much external equity must the firm seek at the beginning of the year? (Assume no
growth in net income). [$4,500,000]
193. On March 15, the directors of Evans Oil Company met and declared the regular dividend
of 48 cents a share to holders of record on March 31, payment to be made on May 15.
Of the 100 shares of Evans Oil you now own, 25 shares at a time were purchased on
each of the following dates: January 1, February 15, March 15, and April 1. What total
dividends will you receive? (Assume ex-dividend four days prior to record date.)
[$36.00]
194. The market price of Speaker Company's stock was $84 prior to a 3-for-1 split. The
firm's $3.20 dividend on the new (split) shares represents an increase of 20 percent
over last year's dividend on the presplit stock. What was last year's dividend per
share? [$8.00]
195. Taft Company expects next year's after-tax income to be $10 million. The firm's
current debt-equity ratio is 100 percent. If Taft has $12 million of profitable
investment opportunities and wishes to maintain its current debt ratio with no external
equity financing, how much should it pay out in dividends next year? [$4,000,000]
196. Stevens Corporation earned $2 million after-tax. The firm has 1.6 million shares
outstanding. If Stevens' dividend policy calls for a 40 percent payout ratio, what are
the dividends per share? [$0.50 Per Share]
197. Brickbat Baking has just announced a 100 percent stock dividend. The annual cash
dividend per share was $2.40 before the stock dividend. After the split, Brickbat
intends to pay $1.40 per share. What percentage increase in the dividend rate will
accompany the stock split? [16.67%]
50
ADDITIONAL FUNDS NEEDED (AFN)
IF THE FIRM IS AT 100% CAPACITY, FOLLOW THIS FORMULA
Required 
Additional 
Spontaneous 
Increase In 








 = Increase  − Increase In  − Retained 
Funds
In Assets
Needed 
Liabilities 
Earnings

[
] [
]
AFN = A/S0 (∆ S) − L/S0 (∆ S) − [(M) S1 (1 − d)]
WHERE
∆S = Change in Sales (S − S0 )
A = Assets
1
S0 = Old Sales
L = Spontaneous Liabilities
M = Profit Margin
d = Dividend Payout Ratio
S1 = New Sales
****************************************************************************
IF THE FIRM IS AT LESS THAN 100% CAPACITY, FOLLOW THIS FORMULA
Additional
Spontaneous
Increase In 
Partial 








Funds
 = Increase  − Increase In  − Retained 
Needed 
Liabilities 
Earnings

In Assets
[
]
[
]
AFN = CA/S0 (∆ S) + [Ω] − L/S0 (∆ S) − [(M) S1 (1 − d)]
WHERE
CA = CURRENT ASSETS
Ω = INCREASE IN FIXED ASSETS NEEDED TO ACCOMMODATE INCREASE
IN SALES
TO DETERMINE Ω
FULL CAPACITY SALES = CURRENT SALES/CURRENT CAPACITY PERCENTAGE
DIFFERENCE = NEW SALES (S1) - FULL CAPACITY SALES
IF ANSWER IS NEGATIVE, Ω WILL BE ZERO. IF ANSWER IS POSITIVE,
Ω = DIFFERENCE * (FIXED ASSETS/FULL CAPACITY SALES)
It is important to remember that the increase in fixed assets may be zero if the
increase in sales still leaves the firm at less than full capacity.
51
198. The Thorne Company is trying to determine an acceptable growth rate in sales. While
the firm wants to expand, it does not want to use any external funds to support such
expansion due to the particularly high rates in the market now. Having gathered the
following data for the firm, find the maximum growth in sales it can sustain without
using external funds. [4.76%]
Capital intensity ratio
= 1.2
(total assets/ total sales)
Profit margin
= 10%
Dividend payout ratio
= 0.5
Current sales
= $100,000
Spontaneous liabilities = $10,000
199. C. D. Dennis Inc. has the following balance sheet:
Current assets
$ 5,000
Net fixed assets
10,000
Total assets
_________
$15,000
Accounts payable $ 1,000
Accruals
1,000
Long-term debt
5,000
Common equity
8,000
________
Total claims
$15,000
Fixed assets are fully utilized. Current sales are $10,000. Next year they expect sales
to increase by 50%. The profit margin is expected to continue to be .10. The firm will
not pay dividends next year. What is next year's external (additional) funding
requirement? [$5,000]
200. Robin Inc. has the following balance sheet:
Current assets
$ 5,000
Net fixed assets
10,000
Total assets
_______
$15,000
Accounts payable $ 1,000
Accruals
1,000
Long-term debt
5,000
Common equity
8,000
______
Total claims
$15,000
Fixed assets are utilized at 75%. Current sales are $10,000. Next year they expect
sales to increase by 50%. The profit margin is expected to continue to be .12. The firm
will not pay dividends next year. What is next year's external (additional) funding
requirement? [$950]
52
201. Pete's Pizza Inc. had the following balance sheet last year:
Cash
$800
Accounts receivable
450
Inventory
950
Net fixed assets
34,000
Accounts payable
Accrued wages
Notes payable
Mortgage
Common stock
Retained earnings
______
$36,200
$350
150
2,000
26,500
3,200
4,000
_______
$36,200
Pete has just invented a new pizza which he expects to double sales and increase aftertax net income to $1,000. Since most of his business is take-out, he believes he can
handle the increase without adding any fixed assets. How much outside capital will he
need if he pays no dividends? [$700]
202. JEFFCO has the following balance sheet:
Cash
$ 10
Accounts receivable 10
Inventory
10
Fixed assets
90
Accounts payable
Notes payable
Long-term debt
Common stock
Retained earnings
_____
$120
$10
20
40
40
10
_____
$120
Fixed assets are being used at 80% of capacity. Sales for the year just ended were
$200. Sales are expected to grow at a rate of 5% next year. The profit margin is 5%
and the dividend payout ratio is 60%. What will be the outside funding requirement? [$3.20 (surplus)]
53
203. JAS Corporation's December 31, 1986 balance sheet is givenbelow:
Cash
$10
Accounts receivable 25
Inventory
40
Net fixed assets
75
Total assets
____
$150
Accounts payable
Notes payable
Accrued wages and
taxes
Long-term debt
Common equity
Total claims
$15
20
15
30
70
_____
$150
Sales during 1986 were $100, and they are expected to rise by 50% to $150 during
1987. Also, during 1986, fixed assets were being utilized to only 85% of capacity; that
is, JAS could have supported $100 of sales with fixed assets that were only 85% of the
actual 1986 fixed assets. Assuming that JAS' profit margin will remain constant at 5%
and that the company will continue to pay out 60% of its earnings as dividends, what
amount of non-spontaneous external funds will be needed during 1987? [$40.11]
204. The Karma Company has a balance sheet showing the following account amounts as of
December 31, 1986:
Cash
$10
Accounts receivable 40
Inventory
50
Net fixed assets
100
Accounts payable
Accruals
Notes payable
Bonds payable
Common stock
Retained earnings
_____
$200
$15
5
20
20
20
120
_____
$200
Last year (1986) the firm generated sales of $2,000 with a profit margin of 10% and
a dividend payout ratio of 50%. It has been operating its fixed assets at 80% of capacity.
It expects to increase sales by $750 with a decrease in the profit margin to 3% and an
increase in the dividend payout ratio to 60%. What will be the needs for external funds for
Karma? [$7.00]
54
LEASING
205. Queens Manufacturing Company has decided to acquire a new pressing machine and is
trying to decide between leasing and buying alternatives. The machine can be purchased
from the manufacturer for a delivered price of $85,000. The machine will be
depreciated over a 6-year period to a zero salvage value although the firm estimates
that it could be sold for a minimum of $5,000 at the end of the 6 years. Alternatively,
the manufacturer has offered a financial lease at $17,000 per year for the 6 years with
all operating, maintenance, and insurance expense to be borne by the lessee. The first
lease payment is at T0. The firm will retain the machine at the end of the lease. The
firm's before-tax interest rate on long-term debt is 10 percent, all depreciation is
straight-line, and the tax rate is 34 percent. What is the NAL (Net Advantage of
Leasing)? [NAL = $1,800]
206. Highlights Illuminating has decided to acquire a lighting display to use at automobile
exhibitions during the next 4 years. The display can be purchased or it can be leased
for a 4-year period. If purchased, the lighting display will require a $10,000 outlay and
Highlights Illuminating anticipates that maintenance will be $800 per year payable at
the beginning of the year. The display has an expected $1,000 market value at the end
of the 4-year period. The company will use straight-line depreciation to a zero salvage
value with a 4-year life for tax purposes. Highlights Illuminating is in the 34 percent
marginal tax bracket and has a 16 percent weighted average cost of capital. No
investment tax credit is available.
Lumenescence Leasing offers to lease the lighting display to Highlights for $3,785
annually, with payments at the beginning of each of the 4 years. Lease payments include
maintenance.
Highlights Illuminating's financial manager calls the company's commercial bank and is
told by a loan officer that the company can borrow up to $10,000 for 4 years at an
effective interest rate of 8 percent annually. What is the NAL (Net Advantage of
Leasing) in this case? [NAL = -$953]
55
207. Gomez Enterprises has decided to renovate an old production facility and equip it with
all new machinery. Gomez can borrow the entire $5 million it needs to purchase the
machinery at 12 percent from a bank, to be amortized over five years. The machinery
will be depreciated to zero value using straight-line over its six-year life. If purchased,
maintenance will cost $50,000 per year for six years payable at the beginning of the
year. As an alternative to purchasing the machinery, Gomez is considering leasing it.
The lease payments are to be $1,000,000 per year for six years, and each payment is to
be made in advance. Gomez estimates that it can purchase the equipment at the end of
the lease period for $200,000.
Gomez has a 34 percent marginal tax rate.
Maintenance is included in the lease. What is the NAL (Net Advantage of Leasing)?
[NAL = $375,658.70]
208. Noah Boatworks has decided to expand its current production facilities. The expansion
will require the purchase or lease of $400,000 of new equipment. To finance the new
equipment, Noah can either lease it or purchase it. The following information concerning
the two alternative financing methods is to be used to make the lease versus purchase
decision. That is, what is the NAL (Net Advantage of Leasing)?
Estimated maintenance cost on the equipment is $25,000 per year payable at the
beginning of the year. Noah must pay for maintenance regardless of the financing
method selected. If the equipment is purchased, Noah can borrow the necessary funds
at 15 percent interest and the loan will be amortized over a five year period. The
equipment will be depreciated to zero on a straight-line basis. The lease arrangements
call for payment of $95,000 to be paid at the beginning of each of the next five years.
The lessor will permit Noah to purchase the equipment at the end of the lease at its
fair market value. Noah estimates that value to be $30,000. Noah has a 34 percent
marginal tax rate.
NAL = $8,969.77
56
BOND REFUNDING
209. The Deadbeat Corporation is considering whether to refund its outstanding $20 million
bond obligation. Though the bonds were initially issued at 10 percent, the interest rates
on similar issues have declined to 8 percent. The bonds were originally issued for 20
years and have 16 years remaining. The new issue would be for 16 years. There is a 7
percent call premium on the old issue. The underwriting cost on the new $20,000,000
issue is $301,000 and the underwriting cost of the old issue was $400,000. The
company is in a 34 percent tax bracket, and it will use the after tax cost of debt for
discounting to analyze the refunding decision. What is the NPV of the refunding
decision? [$1,545,918]
210. The Reagan Corporation is considering whether to refund a $50 million, 11 percent
coupon, 20 year bond issue which was sold 5 years ago. It is amortizing $2 million of
flotation costs on the 11 percent issue over the life of that issue. Reagan's investment
bankers have indicated that the company could sell a new $50 million, 15 year issue at an
interest rate of 9 3/4 percent in today's market. Neither they nor Reagan's
management sees much chance that interest rates will fall below 9 3/4 percent any time
soon, but there is a chance that rates will increase. A call premium of 5 percent would
be required to retire the old bonds, and flotation costs on the new issue would amount
to $3 million. Reagan's marginal tax rate is 40 percent. The new bonds would be issued
one month before the old bonds were called, with the proceeds of the new issue being
invested in short-term government securities with a 5 percent coupon during the
interim. Calculate the NPV of the bond refunding. [$20,383]
57