Tutorial No 6
Bonds and their Valuation
1. A 15-year bond with a 10 percent semiannual coupon and a $1,000 face value
has a nominal yield to maturity of 7.5 percent. The bond, which may be
called after five years, has a nominal yield to call of 5.54 percent. What is
the bond’s call price?
Step 1: Find the bond price using the YTM:
Enter the following input data in the calculator:
N = 30; I = 7.5/2 = 3.75; PMT = 0.10/2 ´ 1,000 = 50; FV = 1000; and
then solve for PV = -$1,222.87. VB = $1,222.87.
Step 2: Solve for the call price:
Enter the following input data in the calculator:
N = 10; I = 5.54/2 = 2.77; PV = -1222.87; PMT = 50; and then solve for
FV = $1,039.938 ≈ $1,040.
2. A bond with a face value of $1,000 matures in 12 years
and has a
8 percent semiannual coupon. (That is, the bond pays a $45 coupon every six
months.) The bond has a nominal yield to maturity of 7.5 percent, and it can
be called in 4 years at a call price of $1,045. What is the bond’s nominal
yield to call?
Step 1: Find the price of the semiannual bond today using the YTM and other
information given:
N = 12 ´ 2 = 24; I = 7.5/2 = 3.75; PMT = 45; FV = 1000; and then
solve for PV = -$1,117.3362. VB = $1,117.3362.
Step 2: Given the bond’s price, calculate the yield to call by entering the following
data as inputs:
N = 4 ´ 2 = 8; PV = -1117.3362; PMT = 45; FV = 1045; and then solve
for I = k/2 = 3.3073% per 6 months
k = 3.3073% ´ 2 = 6.6146% ≈ 6.61%.
3. A corporate bond that matures in 12 years pays a 9 percent annual coupon,
has a face value of $1,000, and a yield to maturity of 7.5 percent. The bond
can first be called four years from now. The call price is $1,050. What is the
bond’s yield to call?
First get the price based on the YTM:
N = 12; I = 7.5; PMT = 90; FV = 1000; and then solve for PV =
-$1,116.03. VB = $1,116.03.
Now solve for the YTC:
N = 4; PV = -1116.03; PMT = 90; FV = 1050; and then solve for I = 6.73%.
4. A bond that matures in 11 years has an annual coupon rate of 8 percent with
interest paid annually. The bond’s face value is $1,000, and its yield to
maturity is 7.5 percent. The bond can be called 3 years from now at a price
of $1,060. What is the bond’s nominal yield to call?
The bond price today is found as N = 11; I = 7.5; PMT = 80; FV = 1000; and then
solve for PV = -$1,036.58. V B
= $1,036.58.
Solve for the yield to call as follows: N = 3; PV = -1036.58; PMT = 80; FV =
1060; and then solve for I = 8.41%.
5. A corporate bond with 12 years to maturity has a 9 percent semiannual
coupon and a face value of $1,000. (That is, the semiannual coupon
payments are $45.) The bond has a nominal yield to maturity of
7 percent. The bond can be called in three years at a call price of
$1,045. What is the bond’s nominal yield to call?
Step 1: Determine the stock’s current price:
Use the YTM to find the price today. Enter the following input data in
the calculator:
N = 24; I = 7/2 = 3.5; PMT = 90/2 = 45; FV = 1000; and then solve for
PV = -$1,160.58. VB = $1,160.58.
Step 2: Determine the bond’s yield to call:
Use the PV found in Step 1 to find the YTC.
Enter the following input data in the calculator:
N = 6; PV = -1160.58; PMT = 90/2 = 45; FV = 1045; and then solve for I
= 2.311% per 6 months or 2 ´
2.311% = 4.622% » 4.62%.
6. Hood Corporation recently issued 20-year bonds. The bonds have a coupon
rate of 8 percent and pay interest semiannually. Also, the bonds are callable
in 6 years at a call price equal to 115 percent of par value. The par value of
the bonds is $1,000. If the yield to maturity is
7 percent, what is the yield to call?
First, calculate the bond price as follows: N = 20 ´ 2 = 40; I = 7/2 = 3.5; PMT
= 0.08/2 ´ 1,000 = 40; FV = 1000; and
then
solve
for PV
=
-$1,106.78. VB = $1,106.78.
Now, we can calculate the YTC as follows, recognizing that the bond can be
called in 6 years at a call price of 115% ´ 1,000 = 1,150: N = 6 ´ 2 = 12; PV = 1106.78; PMT = 40; FV = 1150; and then solve for I = 3.8758% ´
2 = 7.75%.
7. A 12-year bond with a 10 percent semiannual coupon and a $1,000 par value
has a nominal yield to maturity of 9 percent. The bond can be called in five
years at a call price of $1,050. What is the bond’s nominal yield to call?
Find the current bond price using the YTM:
N = 12 ´ 2 = 24; I = 9/2 = 4.5; PMT = 100/2 = 50; FV = 1000; and then solve
for PV = -$1,072.48. VB =
$1,072.48.
Solve for the YTC:
N = 5 ´ 2 = 10; PV = -1072.48; PMT = 50; FV = 1050; I = 4.49% ´ 2 = 8.98%.
8. A bond with a face value of $1,000 has a 10-year maturity and an 8.5 percent annual
coupon. The bond has a current yield of 8 percent. What is the bonds yield to maturity?
Data given: N = 10; I = ? (This is what the problem is looking for); PMT = 85; PV
= ? (Don’t have directly, but you can calculate it from the current yield); FV =
1,000.
Step 1: Calculate the bond’s current price from information given in the current
yield.
Current yield = Coupon/Price
0.08 = $85/Price Price
= ? = $1,062.50.
Step 2: Given the bond’s price, calculate the bond’s yield to maturity using your
financial calculator by entering the following data as inputs: N = 10; PV
= -1062.50; PMT = 85; FV = 1000; and then solve for I = 7.5859% ≈
7.59%.
9. You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8
percent, payable annually, and annual interest rates on new issues of the same degree of
risk are 10 percent. You want to know how many more interest payments you will receive,
but the party selling the bond cannot remember. Can you determine how many interest
payments remain?
Time
0 Line: 1
10%
|
VB = 847.88
|
2
n = ? Years
|
···
PMT = 80 80
|
80
FV = 1,000
Financial calculator solution:
Inputs: I = 10; PV = -847.88; PMT = 80; FV = 1000.
Output: N = 15 years.
10. A 16-year bond with a 10 percent annual coupon has a current yield of
8 percent. What is the bond’s yield to maturity (YTM)?
Step 1: Calculate the price of the 16-year bond:
Current yield = Coupon/Price
8% = $100/Price
Price = $100/0.08 = $1,250.00.
This assumes a $1,000 face value. It doesn’t matter what face value you
select as long as you are consistent throughout your calculations.
Step 2: Calculate the 16-year bond’s YTM:
Enter the following input data in the calculator:
N = 16; PV = -1250; PMT = 100; FV = 1000; and then solve for I = 7.3
Tutorial No 7
Stocks and their Valuation
1.
The Jones Company has decided to undertake a large project. Consequently,
there is a need for additional funds. The financial manager plans to
issue preferred stock with a perpetual annual dividend of $5 per share and
a par value of $30. If the required return on this stock is currently 20
percent, what should be the stock’s market value?
Vp = Dp/kp = $5/0.20 = $25.
2.
Johnston Corporation is growing at a constant rate of 6 percent per
It has both common stock and non-participating preferred
outstanding. The cost of preferred stock (kp) is 8 percent. The par
of the preferred stock is $120, and the stock has a stated dividend
percent of par. What is the market value of the preferred stock?
year.
stock
value
of 10
The dividend is calculated as 10% × $120 = $12. We know that the cost of
preferred stock is equal to the dividend divided by the stock price or 8%
= $12/Price. Solve this expression for Price = $150. (Note: Non- participating preferred stockholders are entitled to just the stated dividend
rate. There is no growth in the dividend.)
3.
A share of preferred stock pays a quarterly dividend of $2.50. If the
price of this preferred stock is currently $50, what is the nominal annual
rate of return?
Annual dividend = $2.50(4) = $10.
kp = Dp/Vp = $10/$50 = 0.20 = 20%.
4.
Assume that you plan to buy a share of XYZ stock today and to hold it for
2 years. Your expectations are that you will not receive a dividend at
the end of Year 1, but you will receive a dividend of $9.25 at the end of
Year 2. In addition, you expect to sell the stock for $150 at the end of
Year 2. If your expected rate of return is 16 percent, how much should
you be willing to pay for this stock today?
0
ks = 16%
|
P0 = ?
1
|
0
2
Pˆ 2
Years
|
D2 = 9.25
= 150.00
CF2 = 159.25
Numerical solution:
P0 = $159.25 (1.16)2
= $118.35.
Financial calculator solution:
Inputs:
N = 2; I = 16; PMT = 0; FV = 159.25.
P0 = $118.35.
5.
Output: PV = -$118.35.
Womack Toy Company’s stock is currently trading at $25 per share. The
stock’s dividend is projected to increase at a constant rate of
7 percent per year. The required rate of return on the stock, ks, is 10
percent. What is the expected price of the stock 4 years from today?
The stock price will grow at 7 percent for 4 years, $25 × (1.07)4 =
$32.77.
6.
McKenna Motors is expected to pay a $1.00 per-share dividend at
the end of the year (D1 = $1.00). The stock sells for $20 per
share and its required rate of return is 11 percent. The
dividend is expected to grow at a constant rate, g, forever.
What is the growth rate, g, for this stock?
ks = D1/P0 + g
g = ks - D1/P0
g = 0.11 - $1/$20 = 0.06 = 6%.
7.
A stock with a required rate of return of 10 percent sells for $30 per
share. The stock’s dividend is expected to grow at a constant rate of 7
percent per year. What is the expected year-end dividend, D1, on the stock?
We know that P0 = D1/ks - g) and we have all the information except D1, so
we input the data into this equation.
$30 = D1/(0.10 - 0.07)
$30 = 33.33D1
D1 = $0.90.
Constant growth stock
8.
Answer: b
Diff: E
Gettysburg Grocers’ stock is expected to pay a year-end dividend, D1, of
$2.00 per share. The dividend is expected to grow at a constant rate of 5
percent, and the stock has a required return of 9 percent. What is the
expected price of the stock five years from today?
Step 1:
Calculate the price of the stock today, since it is a constant
growth stock.
D1 = $2.00; ks = 0.09; g = 0.05.
P0 = D1/(ks - g)
= $2.00/(0.09 - 0.05)
= $50.
Step 2: Determine the price of the stock five years from today: Bˆ5
= $50 × (1.05)5 = $63.81.
FCF model for valuing stock
9.
Answer: b
Diff: M
N
An analyst is trying to estimate the intrinsic value of Burress Inc. The
analyst has estimated the company’s free cash flows for the following
years:
Year
1
2
3
Free Cash Flow
$3,000
4,000
5,000
The analyst estimates that after three years (t = 3) the company’s free
cash flow will grow at a constant rate of 6 percent per year. The analyst
estimates that the company’s weighted average cost of capital is 10
percent. The company’s debt and preferred stock has a total market value
of $25,000 and there are 1,000 outstanding shares of common stock. What is
the (per-share) intrinsic value of the company’s common stock?
Time Line:
FCFs
Continuing Value
Total FCFs
0
|
0
10%
1
|
3,000
2
|
4,000
3,000
4,000
3
|
5,000
5,000(1 + 0.06)
132,500 =
0.10 – 0.06
137,500
Enter the following data as inputs in the financial calculator:
CF0 = 0; CF1 = 3000; CF2 = 4000; CF3 = 137500; I = 10; and then solve for
NPV = Total value of firm = $109,338.84.
So, the entire company is worth $109,338.84. This, less the market value
of debt and preferred stock, which was given in the problem, leaves
$109,338.84 - $25,000 = $84,338.84 as the value of the firm’s common
equity. The value of its common stock is calculated as $84,338.84/1,000
shares = $84.34/share.
Cost of Capital Tutorial
1.
The statement of financial position of BKB Co provides the following information:
Equity finance
Ordinary shares ($1 nominal value)
Reserves
Non-current liabilities
7% Convertible bonds ($100 nominal value)
5% Preference shares ($1 nominal value)
Current liabilities
Trade payables
Overdraft
$m
$m
25
15
–––
40
20
10
–––
30
10
15
–––
Total liabilities
25
–––
95
–––
BKB Co has an equity beta of 1·2 and the ex-dividend market value of the company’s equity is $125 million.
The ex-interest market value of the convertible bonds is $21 million and the ex-dividend market value of the
preference shares is $6·25 million.
The convertible bonds of BKB Co have a conversion ratio of 19 ordinary shares per bond. The conversion date and
redemption date are both on the same date in five years’ time. The current ordinary share price of BKB Co is expected
to increase by 4% per year for the foreseeable future.
The overdraft has a variable interest rate which is currently 6% per year and BKB Co expects this to increase in
the near future. The overdraft has not changed in size over the last financial year, although one year ago the
overdraft interest rate was 4% per year. The company’s bank will not allow the overdraft to increase from its
current level.
The equity risk premium is 5% per year and the risk-free rate of return is 4% per year. BKB Co pays profit tax at
anannual rate of 30% per year.
Required:
(a) Calculate the market value after-tax weighted average cost of capital of BKB Co, explaining clearly
any assumptions you make.
(b) Discuss why market value weighted average cost of capital is preferred to book value weighted average
cost of capital when making investment decisions.
(c) Comment on the interest rate risk faced by BKB Co and discuss briefly how this risk can be managed.
(d) Discuss the attractions to a company of convertible debt compared to a bank loan of a similar maturity
as a source of finance.
1
) Calculation of cost of equity
The cost of equity can be calculated using the capital asset pricing model
Ke = 4 + (1·2 x 5) = 10%
Calculation of cost of debt of convertible bonds
Market value of bond = 100 x 21m/20m = $105 per bond
Ordinary share price = 125m/25m = $5·00 per share
Share price in five years’ time = 5·00 x 1·045 = $6·08 per share
Conversion value = 6·08 x 19 = $115·52
It is assumed that conversion is likely to occur, as the conversion value is greater than the alternative $100 redemption value.
After-tax interest payment = 0·07 x 100 x (1 – 0·3) = $4·90 per bond
Using linear interpolation:
Year
Cash flow
0
1–5
5
Market price
Interest
C
i
l
Year
Cash flow
0
1–5
5
Market price
Interest
C
i
l
$
(105·00)
4·90
115 52
$
(105·00)
4·90
115 52
Discount at
7%
1·000
4·100
0 713
Discount at
6%
1·000
4·212
0 747
After-tax Kd = 6 + ((7 – 6) x 1·93)/(1·93 + 2·54)) = 6 + 0·43 = 6·43%
PV ($)
(105·00)
20·09
–––––
82
37
(2·54)
–––––
PV ($)
(105·00)
20·64
–––––
86
29
1·93
–––––
Calculation of cost of preference shares
Kp = 100 x (0·05 x 10m/6·25m) = 8%
Alternatively, the preference dividend per share can be compared with the preference share price to find the cost of preference
shares
Calculation of weighted average after-tax cost of capital
Total value of company = 125m + 6·25m + 21m = $152·25 million
After-tax WACC = ((10% x 125m) + (8% x 6·25m) + (6·43% x 21m))/152·25m = 9·4%
It is assumed that the overdraft can be ignored in calculating the WACC, even though it persists from year to year and is a
significant source of finance for BKB Co.
(b)
Market values of different sources of finance are preferred to their book values when calculating weighted average cost of
capital (WACC) because market values reflect the current conditions in the capital market. The relative proportions of the
different sources of finance in the capital structure reflect more appropriately their relative importance to a company if market
values are used as weights. For example, the market value of equity is usually much greater than its book value, so using
book values for weights would seriously underestimate the relative importance of the cost of equity in the weighted average
cost of capital.
If book values are used as weights, the WACC will be lower than if market values were used, due to the understatement of
the contribution of the cost of equity, which is higher than the cost of capital of other sources of finance. This can be seen in
the case of BKB Co, where the market value after-tax WACC was found to be 9·4% and the book value after-tax WACC is
8·7% (10% x 40 + 8% x 10 + 6·43% x 20/70).
If book value WACC were used as the discount rate in investment appraisal, investment projects would be accepted that would
be rejected if market value WACC were used. Using book value WACC as the discount rate will therefore lead to sub-optimal
investment decisions.
As far as the cost of debt is concerned, using book values rather than market values for weights may make little difference to
the WACC, since bonds often trade on the capital market at or close to their nominal (par) value. In addition, the cost of debt
is lower than the cost of equity and will therefore make a smaller contribution to the WACC. It is still possible, however, that
using book values as weights may under- or over-estimate the contribution of the cost of debt to the WACC.
(c)
BKB Co expects the variable interest rate on its overdraft to increase in the near future and therefore faces the risk of higher
interest payments. The expected increase in the overdraft interest rate may be due to the particular position of BKB Co, which
is at its overdraft limit as its bank will not allow any further increase in this borrowing facility. Alternatively, the expected
increase in the overdraft interest rate may be due to a general increase in short-term interest rates, for example, as a result
of government action to reduce inflationary pressures in the economy.
BKB Co is protected against interest rate increases to the extent that it has fixed-rate debt. The proportion of fixed-rate debt
to total debt is 57% (100 x 20/35), while the proportion of fixed-rate interest to total interest is 61% (100 x 1·4/2·3). An
increase of 1% in the overdraft interest rate will increase the annual interest payments on the overdraft of BKB Co by
$150,000 or 6·5%.
There are several ways that BKB can manage its interest rate risk. One way is to reduce the exposure of the company to the
identified risk, in this case an interest rate increase. The company could therefore look to reduce the size of its overdraft, an
action which would be welcomed by its bank. This could be achieved, for example, by using cash income to reduce the
overdraft or by replacing part of the overdraft with fixed interest debt, such as a bank loan or an issue of traded bonds. An
issue of longer-term debt, however, could potentially lead to a bigger increase in interest payments than expected from the
increase in short-term interest rates. Furthermore, maintaining a balance between fixed-rate and floating-rate debt is itself a
hedging method (smoothing) and BKB Co may already have chosen this internal hedging method over external hedging
methods due to its lower relative cost.
Forward rate agreements would not help BKB Co manage its interest rate risk as these relate to future borrowing rather than
to current debt. Interest rate futures would allow BKB Co to protect itself against an interest rate increase by locking into
current interest rates. Interest rate swaps would be more suitable for hedging a long-term interest rate exposure, rather than
the short-term interest rate exposure represented by an increase in the overdraft interest rate.
Workings
Total debt = 20m + 15m = $35 million
Fixed rate interest = 20m x 7% = $1·4 million per year
Variable rate interest = 15m x 6% = $0·9 million per year
Total interest = 1·4m + 0·9m = $2·3 million
(d)
Convertible debt is debt that, at the option of the holder, can be converted into ordinary shares. If not converted, it will be
redeemed like ordinary or straight debt on maturity. Convertible debt has a number of attractions compared with a bank loan
of similar maturity, as follows:
3
Self-liquidating
Provided that the conversion terms are pitched correctly and expected share price growth occurs, conversion will be an
attractive choice for bond holders as it offers more wealth than redemption. This occurs when the conversion value is greater than
the redemption value (if conversion and redemption are on the same date), or when the conversion value is greater than the floor
value on the conversion date (if conversion is at an earlier date than the redemption date). If the debt is converted into ordinary
shares, it will not need to be redeemed, i.e. self-liquidation has occurred. A bank loan of a similar maturity willneed to have all
of the capital repaid.
Lower interest rate
The interest rate on convertible debt will be lower than the interest rate on ordinary debt such as a bank loan because of the value
of the option to convert. The returns on fixed-interest debt will not increase with corporate profitability, so debt providers will have a
limited share of the benefits from the investment of the funds they have provided. When debt has been converted, however, bond
holders become shareholders and will potentially have unlimited returns, or at least returns that are higher than the returns on
debt finance.
Increase in debt capacity on conversion
Gearing will increase with a bank loan for the time that the debt is outstanding, and gearing will then return to its previous level
when the bank loan has been paid off. Gearing also increases when convertible debt is issued, but if conversion occurs, the gearing
will fall not only because the debt has been removed, but will fall even further because equity has replaced the debt. The capacity
of the company to service debt (debt capacity) will therefore be enhanced by conversion, compared to redemption of a bank
loan of a similar maturity.
More attractive than ordinary debt
It may be possible to issue convertible debt even when ordinary debt such as a bank loan is not attractive to lenders, since the
option to convert offers a little extra that ordinary debt does not. This is the option to convert in the future, which can be attractive
to optimists, even when the short- and medium-term economic outlook may be poor.
4
1
AMH Co wishes to calculate its current cost of capital for use as a discount rate in investment appraisal. The following
financial information relates to AMH Co:
Financial position statement extracts as at 31 December 2012
$000
Equity
Ordinary shares (nominal value 50 cents)
Reserves
4,000
18,000
–––––––
Long-term liabilities
4% Preference shares (nominal value $1)
7% Bonds redeemable after six years
Long-term bank loan
3,000
3,000
1,000
–––––––
$000
22,000
7,000
–––––––
29,000
–––––––
The ordinary shares of AMH Co have an ex div market value of $4·70 per share and an ordinary dividend of
36·3 cents per share has just been paid. Historic dividend payments have been as follows:
Year
Dividends per share (cents)
2008
30·9
2009
32·2
2010
33·6
2011
35·0
The preference shares of AMH Co are not redeemable and have an ex div market value of 40 cents per share. The
7% bonds are redeemable at a 5% premium to their nominal value of $100 per bond and have an ex interest market
value of $104·50 per bond. The bank loan has a variable interest rate that has averaged 4% per year in recent years.
AMH Co pays profit tax at an annual rate of 30% per year.
Required:
(a)
Calculate the market value weighted average cost of capital of AMH Co.
(b) Discuss how the capital asset pricing model can be used to calculate a project-specific cost of capital for
AMH Co, referring in your discussion to the key concepts of systematic risk, business risk and financial risk.
(c)
Discuss why the cost of equity is greater than the cost of debt.
5
[P.T.O.
1
(a) Cost of equity
The geometric average dividend growth rate in recent years:
(36·3/30·9)0·25 – 1 = 1·041 – 1 = 0·041 or 4·1% per year
Using the dividend growth model:
Ke = 0·041 + [(36·3 x 1·041)/470] = 0·041 + 0·080 = 0·121 or 12·1%
Cost of preference shares
As the preference shares are not redeemable:
Kp = 100 x [(0·04 x 100)/40] = 10%
Cost of debt of bonds
The annual after-tax interest payment is 7 x 0·7 = $4·9 per bond.Using
linear interpolation:
Year
0
1–6
6
Cash flow
Market price
Interest
Redemption
$
(104·50)
4·9
105
5% DF
1·000
5·076
0·746
PV ($)
(104·50)
24·87
78·33
––––––
(1·30)
––––––
4% DF
1·000
5·242
0·790
PV ($)
(104·5)
25·69
82·95
––––––
4·14
––––––
After-tax cost of debt = 4 + [((5 – 4) x 4·14)/(4·14 + 1·30)] = 4 + 0·76 = 4·8%
Cost of debt of bank loan
If the bank loan is assumed to be perpetual (irredeemable), the after-tax cost of debt of the bank loan will be its after-tax interest
rate, i.e. 4% x 0·7 = 2·8% per year.
Market values
Number of ordinary shares = 4,000,000/0·5 = 8 million shares
Equity: 8m x 4·70 =
Preference shares: 3m x 0·4 =
Redeemable bonds: 3m x 104·5/100 =
Bank loan (book value used)
$000
37,600
1,200
3,135
1,00
0
––––––
–
–––––––
WACC calculation
[(12·1 x 37,600) + (10 x 1,200) + (4·8 x 3,135) + (2·8 x 1,000)]/42,935 = 11·3%
(b)
The capital asset pricing model (CAPM) assumes that investors hold diversified portfolios, so that unsystematic risk has been
diversified away. Companies using the CAPM to calculate a project-specific discount rate are therefore concerned only with
determining the minimum return that must be generated by an investment project as compensation for its systematic risk.
The CAPM is useful where the business risk of an investment project is different from the business risk of the investing
company’s existing business operations. In such a situation, one or more proxy companies are identified that have similar business
risk to the investment project. The equity beta of the proxy company represents the systematic risk of the proxy company, and
reflects both the business risk of the proxy company’s business operations and the financial risk arising from the proxy company’s
capital structure.
Since the investing company is only interested in the business risk of the proxy company, the proxy company’s equity beta is
‘ungeared’ to remove the effect of its capital structure. ‘Ungearing’ converts the proxy company’s equity beta into an asset beta,
which represents business risk alone. The asset betas of several proxy companies can be averaged in order to removeany small
differences in business operations.
The asset beta can then be ‘regeared’, giving an equity beta whose systematic risk takes account of the financial risk of the
investing company as well as the business risk of an investment project. Both ungearing and regearing use the weighted average
beta formula, which equates the asset beta with the weighted average of the equity beta and the debt beta.
The project-specific equity beta resulting from the regearing process can then be used to calculate a project-specific cost ofequity
using the CAPM. This can be used as the discount rate when evaluating the investment project with a discounted cash (DCF) flow
investment appraisal method such as net present value or internal rate of return. Alternatively, the project-specific
cost of equity can be used in calculating a project-specific weighted average cost of capital, which can also be used in a DCF
evaluation.
(c)
The cost of equity is the return required by ordinary shareholders (equity investors), in order to compensate them for the risk
6
associated with their equity investment, i.e. their investment in the ordinary shares of a company. If the risk of an investment
increases, the return expected by the investor also increases. If the risk of a company increases, therefore, its cost of equity also
increases.
If a company is liquidated, the order in which the claims of creditors are settled is a factor in determining their relative risk. The
claims of providers of debt finance (debt holders) must be paid off before any cash can be distributed to ordinary
shareholders (the owners). The risk faced by shareholders is therefore greater than the risk faced by debt holders, and the cost
of equity is therefore greater than the cost of debt.
Interest on debt finance must be paid before dividends can be paid to ordinary shareholders, so the risk faced by ordinary
shareholders is greater than the risk faced by debt holders, since the necessity of paying interest may mean that dividends have
to be reduced.
7
[P.T.O.
CHAPTER 10
THE BASICS OF CAPITAL BUDGETING TUTORIAL
1.
Assume a project has normal cash flows (that is, the initial cash flow is
negative, and all other cash flows are positive). Which of the following
statements is most correct?
a. All else equal, a project’s IRR increases as the cost of capital
declines.
b. All else equal, a project’s NPV increases as the cost of capital
declines.
c. All else equal, a project’s MIRR is unaffected by changes in the cost
of capital.
d. Statements a and b are correct.
e. Statements b and c are correct.
2.
Which of the following statements is most correct?
a. The NPV method assumes that cash flows will be reinvested at the cost
of capital, while the IRR method assumes reinvestment at the IRR.
b. The NPV method assumes that cash flows will be reinvested at the riskfree rate, while the IRR method assumes reinvestment at the IRR.
c. The NPV method assumes that cash flows will be reinvested at the cost
of capital, while the IRR method assumes reinvestment at the risk-free
rate.
d. The NPV method does not consider the inflation premium.
e. The IRR method does not consider all relevant cash flows, particularly,
cash flows beyond the payback period.
3.
A major disadvantage of the payback period is that it
a.
b.
c.
d.
e.
Is useless as a risk indicator.
Ignores cash flows beyond the payback period.
Does not directly account for the time value of money.
Statements b and c are correct.
All of the statements above are correct.
4.
Projects A and B have the same expected lives and initial cash outflows.
However, one project’s cash flows are larger in the early years, while the
other project has larger cash flows in the later years. The two NPV
profiles are given below:
NPV
($
k (%)
Which of the following statements is most correct?
a. Project A has the smaller cash flows in the later years.
b. Project A has the larger cash flows in the later years.
c. We require information on the cost of capital in order to determine
which project has larger early cash flows.
d. The NPV profile graph is inconsistent with the statement made in the
problem.
e. None of the statements above is correct.
5.
Projects A and B both have normal cash flows. In other words, there is an
up-front cost followed over time by a series of positive cash flows. Both
projects have the same risk and a WACC equal to 10 percent. However,
Project A has a higher internal rate of return than Project B. Assume that
changes in the WACC have no effect on the projects’ cash flow levels.
Which of the following statements is most correct?
a.
b.
c.
d.
Project A must have a higher net present value than Project B.
If Project A has a positive NPV, Project B must also have a positive NPV.
If Project A’s WACC falls, its internal rate of return will increase.
If Projects A and B have the same NPV at the current WACC, Project B
would have a higher NPV if the WACC of both projects was lower.
e. Statements b and c are correct.
Chapter 10 - Page 2
NPV profiles
6.
Project A and Project B are mutually exclusive projects with equal risk.
Project A has an internal rate of return of 12 percent, while Project B has
an internal rate of return of 15 percent. The two projects have the same
net present value when the cost of capital is 7 percent. (In other words,
the “crossover rate” is 7 percent.) Assume each project has an initial
cash outflow followed by a series of inflows. Which of the following
statements is most correct?
a. If the cost of capital is 10 percent, each project will have a positive
net present value.
b. If the cost of capital is 6 percent, Project B has a higher net present
value than Project A.
c. If the cost of capital is 13 percent, Project B has a higher net
present value than Project A.
d. Statements a and b are correct.
e. Statements a and c are correct.
NPV profiles
7.
Sacramento Paper is considering two mutually exclusive projects. Project A
has an internal rate of return (IRR) of 12 percent, while Project B has an
IRR of 14 percent. The two projects have the same risk, and when the cost
of capital is 7 percent the projects have the same net present value (NPV).
Assume each project has an initial cash outflow followed by a series of
inflows. Given this information, which of the following statements is most
correct?
a. If the cost of capital is 13 percent, Project B’s NPV will be higher
than Project A’s NPV.
b. If the cost of capital is 9 percent, Project B’s NPV will be higher
than Project A’s NPV.
c. If the cost of capital is 9 percent, Project B’s modified internal rate
of return (MIRR) will be less than its IRR.
d. Statements a and c are correct.
e. All of the statements above are correct.
NPV profiles
8.
O’Leary Lumber Company is considering two mutually exclusive projects,
Project X and Project Y. The two projects have normal cash flows (an upfront cost followed by a series of positive cash flows), the same risk, and
the same 10 percent WACC. However, Project X has an IRR of 16 percent,
while Project Y has an IRR of 14 percent.
Which of the following
statements is most correct?
a. Project X’s NPV must be positive.
b. Project X’s NPV must be higher than Project Y’s NPV.
c. If Project X has a lower NPV than Project Y, then this means that
Project X must be a larger project.
d. Statements a and c are correct.
e. All of the statements above are correct.
NPV profiles
9.
Cherry Books is considering two mutually exclusive projects. Project A has
an internal rate of return of 18 percent, while Project B has an internal
rate of return of 30 percent. The two projects have the same risk, the
same cost of capital, and the timing of the cash flows is similar. Each
has an up-front cost followed by a series of positive cash flows. One of
the projects, however, is much larger than the other. If the cost of
capital is 16 percent, the two projects have the same net present value
(NPV); otherwise, their NPVs are different.
Which of the following
statements is most correct?
a.
b.
c.
d.
e.
If the cost of capital is 12 percent, Project B will have a higher NPV.
If the cost of capital is 17 percent, Project B will have a higher NPV.
Project B is larger than Project A.
Statements a and c are correct.
Statements b and c are correct.
NPV profiles
10.
Project X’s IRR is 19 percent. Project Y’s IRR is 17 percent. Both
projects have the same risk, and both projects have normal cash flows (an
up-front cost followed by a series of positive cash flows). If the cost of
capital is 10 percent, Project Y has a higher NPV than Project X. Given
this information, which of the following statements is most correct?
a. The crossover rate between the two projects (that is, the point where
the two projects have the same NPV) is greater than 10 percent.
b. If the cost of capital is 8 percent, Project X will have a higher NPV
than Project Y.
c. If the cost of capital is 10 percent, Project X’s MIRR is greater than
19 percent.
d. Statements a and b are correct.
e. All of the statements above are correct.
NPV and IRR
11.
Which of the following statements is most correct?
a. If a project’s internal rate of return (IRR) exceeds the cost of
capital, then the project’s net present value (NPV) must be positive.
b. If Project A has a higher IRR than Project B, then Project A must also
have a higher NPV.
c. The IRR calculation implicitly assumes that all cash flows are
reinvested at a rate of return equal to the cost of capital.
d. Statements a and c are correct.
e. None of the statements above is correct.
Chapter 10 - Page 4
NPV and IRR
12.
Project A has an internal rate of return (IRR) of 15 percent. Project B
has an IRR of 14 percent. Both projects have a cost of capital of 12
percent. Which of the following statements is most correct?
a. Both projects have a positive net present value (NPV).
b. Project A must have a higher NPV than Project B.
c. If the cost of capital were less than 12 percent, Project B would have
a higher IRR than Project A.
d. Statements a and c are correct.
e. All of the statements above are correct.
NPV, IRR, and MIRR
13.
A project has an up-front cost of $100,000. The project’s WACC is 12
percent and its net present value is $10,000. Which of the following
statements is most correct?
a.
b.
c.
d.
e.
The project should be rejected since its return is less than the WACC.
The project’s internal rate of return is greater than 12 percent.
The project’s modified internal rate of return is less than 12 percent.
All of the statements above are correct.
None of the statements above is correct.
NPV, IRR, MIRR, and payback
14.
A proposed project has normal cash flows. In other words, there is an upfront cost followed over time by a series of positive cash flows. The
project’s internal rate of return is 12 percent and its WACC is 10 percent.
Which of the following statements is most correct?
a. The project’s NPV is positive.
b. The project’s MIRR is greater than 10 percent but less than 12 percent.
c. The project’s payback period is greater than its discounted payback
period.
d. Statements a and b are correct.
e. All of the statements above are correct.
NPV and expected return
15.
Stock C has a beta of 1.2, while Stock D has a beta of 1.6. Assume that
the stock market is efficient. Which of the following statements is most
correct?
a.
b.
c.
d.
e.
The required rates of return of the two stocks should be the same.
The expected rates of return of the two stocks should be the same.
Each stock should have a required rate of return equal to zero.
The NPV of each stock should equal its expected return.
The NPV of each stock should equal zero.
NPV and project selection
16.
Moynihan Motors has a cost of capital of 10.25 percent. The firm has two
normal projects of equal risk. Project A has an internal rate of return of
14 percent, while Project B has an internal rate of return of 12.25
percent. Which of the following statements is most correct?
a. Both projects have a positive net present value.
b. If the projects are mutually exclusive, the firm should always select
Project A.
c. If the crossover rate (that is, the rate at which the Project’s NPV
profiles intersect) is 8 percent, Project A will have a higher net
present value than Project B.
d. Statements a and b are correct.
e. Statements a and c are correct.
IRR
17.
Project A has an IRR of 15 percent. Project B has an IRR of 18 percent.
Both projects have the same risk. Which of the following statements is
most correct?
a. If the WACC is 10 percent, both projects will have a positive NPV, and
the NPV of Project B will exceed the NPV of Project A.
b. If the WACC is 15 percent, the NPV of Project B will exceed the NPV of
Project A.
c. If the WACC is less than 18 percent, Project B will always have a
shorter payback than Project A.
d. If the WACC is greater than 18 percent, Project B will always have a
shorter payback than Project A.
e. If the WACC increases, the IRR of both projects will decline.
Chapter 10 - Page 6
IRR, payback, and missing cash flow
18.
Oak Furnishings is considering a project that has an up-front cost and a
series of positive cash flows. The project’s estimated cash flows are
summarized below:
Project
Cash Flow
?
$500 million
300 million
400 million
600 million
Year
0
1
2
3
4
The project has a regular payback of 2.25 years.
internal rate of return (IRR)?
What is the project’s
a. 23.1%
b. 143.9%
c. 17.7%
d. 33.5%
e. 41.0%
IRR and mutually exclusive projects
19.
A company is analyzing two mutually exclusive projects, S and L, whose cash
flows are shown below:
Years
0
|
1
|
2
|
3
|
1,000
0
350
300
50
1,500
k = 12%
S -1,100
L -1,100
The company’s cost of capital is 12 percent, and it can obtain an unlimited
amount of capital at that cost. What is the regular IRR (not MIRR) of the
better project, that is, the project that the company should choose if it
wants to maximize its stock price?
a.
b.
c.
d.
e.
12.00%
15.53%
18.62%
19.08%
20.46%
Chapter 10 - Page 8