Solutions Manual
Corporate Finance
Ross, Westerfield, and Jaffe
Asia Global Edition
01/30/2013
Prepared by:
Joe Smolira
Belmont University
1/30/2014
Revised by:
Joseph Lim
Singapore Management University
Ruth Tan
National University of Singapore
CHAPTER 15
LONG-TERM FINANCING: AN
INTRODUCTION
Answers to Concepts Review and Critical Thinking Questions
1.
The indenture is a legal contract and can run into 100 pages or more. Bond features which would be
included are: the basic terms of the bond, the total amount of the bonds issued, description of the
property used as security, repayment arrangements, call provisions, convertibility provisions, and
details of protective covenants.
2.
The differences between preferred stock and debt are:
a. The dividends on preferred stock cannot be deducted as interest expense when determining
taxable corporate income. From the individual investor’s point of view, preferred dividends are
ordinary income for tax purposes. For corporate investors, 70% of the amount they receive as
dividends from preferred stock are exempt from income taxes.
b. In case of liquidation (at bankruptcy), preferred stock is junior to debt and senior to common
stock.
c. There is no legal obligation for firms to pay out preferred dividends as opposed to the obligated
payment of interest on bonds. Therefore, firms cannot be forced into default if a preferred stock
dividend is not paid in a given year. Preferred dividends can be cumulative or non-cumulative,
and they can also be deferred indefinitely (of course, indefinitely deferring the dividends might
have an undesirable effect on the market value of the stock).
3.
Some firms can benefit from issuing preferred stock. The reasons can be:
a. Public utilities can pass the tax disadvantage of issuing preferred stock on to their customers, so
there is a substantial amount of straight preferred stock issued by utilities.
b. Firms reporting losses to the IRS already don’t have positive income for any tax deductions, so
they are not affected by the tax disadvantage of dividends versus interest payments. They may
be willing to issue preferred stock.
c. Firms that issue preferred stock can avoid the threat of bankruptcy that exists with debt
financing because preferred dividends are not a legal obligation like interest payments on
corporate debt.
4.
The return on non-convertible preferred stock is lower than the return on corporate bonds for two
reasons: 1) Corporate investors receive 70 percent tax deductibility on dividends if they hold the
stock. Therefore, they are willing to pay more for the stock; that lowers its return. 2) Issuing
corporations are willing and able to offer higher returns on debt since the interest on the debt reduces
their tax liabilities. Preferred dividends are paid out of net income, hence they provide no tax shield.
Corporate investors are the primary holders of preferred stock since, unlike individual investors, they
can deduct 70 percent of the dividend when computing their tax liabilities. Therefore, they are
willing to accept the lower return that the stock generates.
CHAPTER 15 -3
5.
The following table summarizes the main difference between debt and equity:
Repayment is an obligation of the firm
Grants ownership of the firm
Provides a tax shield
Liquidation will result if not paid
Debt
Yes
No
Yes
Yes
Equity
No
Yes
No
No
Companies often issue hybrid securities because of the potential tax shield and the bankruptcy
advantage. If the IRS accepts the security as debt, the firm can use it as a tax shield. If the security
maintains the bankruptcy and ownership advantages of equity, the firm has the best of both worlds.
6.
There are two benefits. First, the company can take advantage of interest rate declines by calling in
an issue and replacing it with a lower coupon issue. Second, a company might wish to eliminate a
covenant for some reason. Calling the issue does this. The cost to the company is a higher coupon. A
put provision is desirable from an investor’s standpoint, so it helps the company by reducing the
coupon rate on the bond. The cost to the company is that it may have to buy back the bond at an
unattractive price.
7.
It is the grant of authority by a shareholder to someone else to vote his or her shares.
8.
Preferred stock is similar to both debt and common equity. Preferred shareholders receive a stated
dividend only, and if the corporation is liquidated, preferred stockholders get a stated value.
However, unpaid preferred dividends are not debts of a company and preferred dividends are not a
tax deductible business expense.
9.
A company has to issue more debt to replace the old debt that comes due if the company wants to
maintain its capital structure. There is also the possibility that the market value of a company
continues to increase (we hope). This also means that to maintain a specific capital structure on a
market value basis the company has to issue new debt, since the market value of existing debt
generally does not increase as the value of the company increases (at least by not as much).
10. Internal financing comes from internally generated cash flows and does not require issuing
securities. In contrast, external financing requires the firm to issue new securities.
11. The three basic factors that affect the decision to issue external equity are: 1) The general economic
environment, specifically, business cycles. 2) The level of stock prices, and 3) The availability of
positive NPV projects.
12. When a company has dual class stock, the difference in the share classes are the voting rights. Dual
share classes allow minority shareholders to retain control of the company even though they do not
own a majority of the total shares outstanding. Often, dual share companies were started by a family,
and then taken public, but the founders want to retain control of the company.
13. The statement is true. In an efficient market, the callable bonds will be sold at a lower price than that
of the non-callable bonds, other things being equal. This is because the holder of callable bonds
effectively sold a call option to the bond issuer. Since the issuer holds the right to call the bonds, the
price of the bonds will reflect the disadvantage to the bondholders and the advantage to the bond
issuer (i.e., the bondholder has the obligation to surrender their bonds when the call option is
exercised by the bond issuer.)
4 – SOLUTIONS MANUAL
14. As the interest rate falls, the call option on the callable bonds is more likely to be exercised by the
bond issuer. Since the non-callable bonds do not have such a drawback, the value of the bond will go
up to reflect the decrease in the market rate of interest. Thus, the price of non-callable bonds will
move higher than that of the callable bonds.
15. Sinking funds provide additional security to bonds. If a firm is experiencing financial difficulty, it is
likely to have trouble making its sinking fund payments. Thus, the sinking fund provides an early
warning system to the bondholders about the quality of the bonds. A drawback to sinking funds is
that they give the firm an option that the bondholders may find distasteful. If bond prices are low, the
firm may satisfy its sinking fund obligation by buying bonds in the open market. If bond prices are
high though, the firm may satisfy its obligation by purchasing bonds at face value (or other fixed
price, depending on the specific terms). Those bonds being repurchased are chosen through a lottery.
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Basic
1.
If the company uses straight voting, the board of directors is elected one at a time. You will need to
own one-half of the shares, plus one share, in order to guarantee enough votes to win the election.
So, the number of shares needed to guarantee election under straight voting will be:
Shares needed = (850,000 shares / 2) + 1
Shares needed = 425,001
And the total cost to you will be the shares needed times the price per share, or:
Total cost = 425,001  $43
Total cost = $18,275,043
If the company uses cumulative voting, the board of directors are all elected at once. You will need
1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats
up for election. So, the percentage of the company’s stock you need is:
Percent of stock needed = 1/(N + 1)
Percent of stock needed = 1 / (7 + 1)
Percent of stock needed = .1250, or 12.50%
CHAPTER 15 -5
So, the number of shares you need to purchase is:
Number of shares to purchase = (850,000 × .1250) + 1
Number of shares to purchase = 106,251
And the total cost to you will be the shares needed times the price per share, or:
Total cost = 106,251  $43
Total cost = $4,568,793
2.
If the company uses cumulative voting, the board of directors are all elected at once. You will need
1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats
up for election. So, the percentage of the company’s stock you need is:
Percent of stock needed = 1/(N + 1)
Percent of stock needed = 1 / (3 + 1)
Percent of stock needed = .25, or 25%
So, the number of shares you need is:
Number of shares to purchase = (7,600 × .25) + 1
Number of shares to purchase = 1,901
So, the number of additional shares you need to purchase is:
New shares to purchase = 1,901 – 300
New shares to purchase = 1,601
3.
If the company uses cumulative voting, the board of directors are all elected at once. You will need
1/(N + 1) percent of the stock (plus one share) to guarantee election, where N is the number of seats
up for election. So, the percentage of the company’s stock you need is:
Percent of stock needed = 1/(N + 1)
Percent of stock needed = 1 / (3 + 1)
Percent of stock needed = .25, or 25%
So, the number of shares you need to purchase is:
Number of shares to purchase = (13,000,000 × .25) + 1
Number of shares to purchase = 3,250,001
And the total cost will be the shares needed times the price per share, or:
Total cost = 3,250,001  $10.50
Total cost = $34,125,011
6 – SOLUTIONS MANUAL
4.
Under cumulative voting, she will need 1 / (N + 1) percent of the stock (plus one share) to guarantee
election, where N is the number of seats up for election. So, the percentage of the company’s stock
she needs is:
Percent of stock needed = 1 / (N + 1)
Percent of stock needed = 1 / (6 + 1)
Percent of stock needed = .1429, or 14.29%
Her nominee is guaranteed election. If the elections are staggered, the percentage of the company’s
stock needed is:
Percent of stock needed = 1/(N + 1)
Percent of stock needed = 1 / (2 + 1)
Percent of stock needed = .3333, or 33.33%
Her nominee is no longer guaranteed election.
5.
a.
The price of the bond today is the present value of the expected price in one year. So, the price
of the bond in one year if interest rates increase will be:
P1 = $40(PVIFA5%,58) + $1,000(PVIF5%,58)
P1 = $811.80
If interest rates fall, the price if the bond in one year will be:
P1 = $40(PVIFA3%,58) + $1,000(PVIF3%,58)
P1 = $1,273.31
Now we can find the price of the bond today, which will be:
P0 = [.50($811.80) + .50($1,273.31)] / 1.0352
P0 = $973.24
For students who have studied term structure, the assumption of risk-neutrality implies that the
forward rate is equal to the expected future spot rate.
b.
6.
If the bond is callable, then the bond value will be less than the amount computed in part a. If
the bond price rises above the call price, the company will call it. Therefore, bondholders will
not pay as much for a callable bond.
The price of the bond today is the present value of the expected price in one year. The bond will be
called whenever the price of the bond is greater than the call price of $1,150. First, we need to find
the expected price in one year. If interest rates increase next year, the price of the bond will be the
present value of the perpetual interest payments, plus the interest payment made in one year, so:
P1 = ($100 / .12) + $100
P1 = $933.33
CHAPTER 15 -7
This is lower than the call price, so the bond will not be called. If the interest rates fall next year, the
price of the bond will be:
P1 = ($100 / .07) + $100
P1 = $1,528.57
This is greater than the call price, so the bond will be called. The present value of the expected value
of the bond price in one year is:
P0 = [.60($933.33) + .40($1,150)] / 1.10
P0 = $927.27
Intermediate
7.
If interest rates rise, the price of the bonds will fall. If the price of the bonds is low, the company will
not call them. The firm would be foolish to pay the call price for something worth less than the call
price. In this case, the bondholders will receive the coupon payment, C, plus the present value of the
remaining payments. So, if interest rates rise, the price of the bonds in one year will be:
P1 = C + C / .10
If interest rates fall, the assumption is that the bonds will be called. In this case, the bondholders will
receive the call price, plus the coupon payment, C. So, the price of the bonds if interest rates fall will
be:
P1 = $1,175 + C
The selling price today of the bonds is the PV of the expected payoffs to the bondholders. To find
the coupon rate, we can set the desired issue price equal to the present value of the expected value of
end of year payoffs, and solve for C. Doing so, we find:
P0 = $1,000 = [.60(C + C / .10) + .40($1,175 + C)] / 1.09
C = $88.57
So the coupon rate necessary to sell the bonds at par value will be:
Coupon rate = $88.57 / $1,000
Coupon rate = .0886, or 8.86%
8 – SOLUTIONS MANUAL
8.
a.
The price of the bond today is the present value of the expected price in one year. So, the price
of the bond in one year if interest rates increase will be:
P1 = $70 + $70 / .09
P1 = $847.78
If interest rates fall, the price if the bond in one year will be:
P1 = $70 + $70 / .06
P1 = $1,236.67
Now we can find the price of the bond today, which will be:
P0 = [.35($847.78) + .65($1,236.67)] / 1.07
P0 = $1,028.56
b.
If interest rates rise, the price of the bonds will fall. If the price of the bonds is low, the
company will not call them. The firm would be foolish to pay the call price for something
worth less than the call price. In this case, the bondholders will receive the coupon payment, C,
plus the present value of the remaining payments. So, if interest rates rise, the price of the
bonds in one year will be:
P1 = C + C / .09
If interest rates fall, the assumption is that the bonds will be called. In this case, the
bondholders will receive the call price, plus the coupon payment, C. The call premium is not
fixed, but it is the same as the coupon rate, so the price of the bonds if interest rates fall will be:
P1 = ($1,000 + C) + C
P1 = $1,000 + 2C
The selling price today of the bonds is the PV of the expected payoffs to the bondholders. To
find the coupon rate, we can set the desired issue price equal to the present value of the
expected value of end of year payoffs, and solve for C. Doing so, we find:
P0 = $1,000 = [.35(C + C / .09) + .65($1,000 + 2C)] / 1.07
C = $75.83
So the coupon rate necessary to sell the bonds at par value will be:
Coupon rate = $75.83 / $1,000
Coupon rate = .0758, or 7.58%
c.
To the company, the value of the call provision will be given by the difference between the
value of an outstanding, non-callable bond and the call provision. So, the value of a noncallable bond with the same coupon rate would be:
Non-callable bond value = $75.83 / 0.06 = $1,263.79
CHAPTER 15 -9
So, the value of the call provision to the company is:
Value = .65($1,263.79 – 1,075.83) / 1.07
Value = $114.18
9.
The company should refund when the NPV of refunding is greater than zero, so we need to find the
interest rate that results in a zero NPV. The NPV of the refunding is the difference between the gain
from refunding and the refunding costs. The gain from refunding is the bond value times the
difference in the interest rate, discounted to the present value. We must also consider that the interest
payments are tax deductible, so the aftertax gain is:
NPV = PV(Gain) – PV(Cost)
The present value of the gain will be:
Gain = $250,000,000(.09 – R) / R
Since refunding would cost money today, we must determine the aftertax cost of refunding, which
will be:
Aftertax cost = $250,000,000(.10)(1 – .35)
Aftertax cost = $16,250,000
So, setting the NPV of refunding equal to zero, we find:
0 = –$16,250,000 + $250,000,000(.09 – R) / R
R = .0845, or 8.45%
Any interest rate below this will result in a positive NPV from refunding.
10. In this case, we need to find the NPV of each alternative and choose the option with the highest
NPV, assuming either NPV is positive. The NPV of each decision is the gain minus the cost. So, the
NPV of refunding the 7 percent perpetual bond is:
Bond A:
Gain = $125,000,000(.07 – .0625) / .0625
Gain = $15,000,000
Assuming the call premium is tax deductible, the aftertax cost of refunding this issue is:
Cost = $125,000,000(.075)(1 – .35) + $11,500,000(1 – .35)
Cost = $13,568,750
Note that the gain can be calculated using the pretax or aftertax cost of debt. If we calculate the gain
using the aftertax cost of debt, we find:
Aftertax gain = $125,000,000[.07(1 – .35) – .0625(1 – .35)] / [.0625(1 – .35)]
Aftertax gain = $15,000,000
10 – SOLUTIONS MANUAL
Thus, the inclusion of the tax rate in the calculation of the gains from refunding is irrelevant.
The NPV of refunding this bond is:
NPV = –$13,568,750 + 15,000,000
NPV = $1,431,250
The NPV of refunding the second bond is:
Bond B:
Gain = $132,000,000(.08 – .0710) / .0710
Gain = $16,732,394.37
Assuming the call premium is tax deductible, the aftertax cost of refunding this issue is:
Cost = ($132,000,000)(.085)(1 – .35) + $13,000,000(1 – .35)
Cost = $15,743,000
The NPV of refunding this bond is:
NPV = –$15,743,000 + 16,732,394.37
NPV = $989,394.37
Since the NPV of refunding both bonds is positive, both bond issues should be refunded.
Challenge
11. To calculate this, we need to set up an equation with the callable bond equal to a weighted average of
the noncallable bonds. We will invest X percent of our money in the first noncallable bond, which
means our investment in Bond 3 (the other noncallable bond) will be (1 – X). The equation is:
C2
8.25
8.25
X
= C1 X + C3(1 – X)
= 6.50 X + 12(1 – X)
= 6.50 X + 12 – 12 X
= .68182
So, we invest about 68 percent of our money in Bond 1, and about 32 percent in Bond 3. This
combination of bonds should have the same value as the callable bond, excluding the value of the
call. So:
P2
P2
P2
= .68182P1 + .31819P3
= .68182(106.375) + .31818(134.96875)
= 115.4730
CHAPTER 15 -11
The call value is the difference between this implied bond value and the actual bond price. So, the
call value is:
Call value = 115.4730 – 103.50 = 11.9730
Assuming $1,000 par value, the call value is $119.73.
12. In general, this is not likely to happen, although it can (and did). The reason that this bond has a
negative YTM is that it is a callable U.S. Treasury bond. Market participants know this. Given the
high coupon rate of the bond, it is extremely likely to be called, which means the bondholder will not
receive all the cash flows promised. A better measure of the return on a callable bond is the yield to
call (YTC). The YTC calculation is the basically the same as the YTM calculation, but the number
of periods is the number of periods until the call date. If the YTC were calculated on this bond, it
would be positive.