Lecture 4
Homework 5 Review &
Chapter 7
Homework 5 Review
Question 1
 Sustainable Growth
Based on the following information, the
sustainable growth rate for Hendrix
Guitars, Inc., is 13.02%. The ROA is
11.52%.
Profit margin=6.4 %
Total asset turnover=1.80
Total debt ratio=0.60
Payout ratio=60 %
Question 1
We should begin by calculating the D/E ratio. We calculate the D/E
ratio as follows:
Total debt ratio = .60 = TD / TA
Inverting both sides we get:
1 / .60 = TA / TD
Next, we need to recognize that
TA / TD = 1 + TE / TD
Substituting this into the previous equation, we get:
1 / .60 = 1 + TE /TD
Subtract 1 (one) from both sides and inverting again, we get:
D/E = 1 / [(1 / .60) – 1]
D/E = 1.5
With the D/E ratio, we can calculate the EM and solve for ROE
using the DuPont identity:
Question 1
ROE = (PM)(TAT)(EM)
ROE = (.064)(1.80)(1 + 1.5)
ROE = .2880 or 28.80%
Now, we use the ROE equation:
ROE = ROA(EM)
.2880 = ROA(2.5)
ROA = .1152 or 11.52%
Now we can calculate the retention ratio as:
b = 1 – .60
b = .40
Finally, putting all the numbers we have calculated into the
sustainable growth rate equation, we get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Sustainable growth rate = [.2880(.40)] / [1 – .2880(.40)]
Sustainable growth rate = .1302 or 13.02%
Question 2
Sustainable Growth Rate
No Return, Inc., had equity of $165,000 at the
beginning of the year. At the end of the year, the
company had total assets of $250,000. During
the year the company sold no new equity. Net
income for the year was $80,000 and dividends
were $49,000. (Input answers as a percent
rounded to 2 decimal places, without the percent
sign.)
The sustainable growth rate for the company is
___ percent.
The sustainable growth rate is ____ percent if you
use the formula and beginning of period equity. If
you use end of period equity in this formula, the
sustainable growth rate is ____ percent. Is this
number too high or too low? Why?

Question 2
Since the company issued no new equity,
shareholders’ equity increased by retained
earnings.
Retained earnings for the year were:
Retained earnings = NI – Dividends
Retained earnings = $80,000 – 49,000
Retained earnings = $31,000
So, the equity at the end of the year was:
Ending equity = $165,000 + 31,000
Ending equity = $196,000
Question 2
The ROE based on the end of period equity is:
ROE = $80,000 / $196,000
ROE = 40.82%
The plowback ratio is:
Plowback ratio = Addition to retained earnings/NI
Plowback ratio = $31,000 / $80,000
Plowback ratio = .3875 or = 38.75%
Using the equation presented in the text for the sustainable
growth rate, we get:
Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
Sustainable growth rate = [.4082(.3875)] / [1 – .4082(.3875)]
Sustainable growth rate = .1879 or 18.79%
The ROE based on the beginning of period equity is
ROE = $80,000 / $165,000
ROE = .4848 or 48.48%
Question 2
Using the shortened equation for the sustainable growth rate and
the beginning of period ROE, we get:
Sustainable growth rate = ROE × b
Sustainable growth rate = .4848 × .3875
Sustainable growth rate = .1879 or 18.79%
Using the shortened equation for the sustainable growth rate and
the end of period ROE, we get:
Sustainable growth rate = ROE × b
Sustainable growth rate = .4082 × .3875
Sustainable growth rate = .1582 or 15.82%
Using the end of period ROE in the shortened sustainable growth
rate results in a growth rate that is too low. This will always occur
whenever the equity increases. If equity increases, the ROE based
on end of period equity is lower than the ROE based on the
beginning of period equity. The ROE (and sustainable growth rate)
in the abbreviated equation is based on equity that did not exist
when the net income was earned.
Question 2
Sustainable Growth Rate
No Return, Inc., had equity of $165,000 at the beginning of
the year. At the end of the year, the company had total
assets of $250,000. During the year the company sold
no new equity. Net income for the year was $80,000 and
dividends were $49,000. (Input answers as a percent
rounded to 2 decimal places, without the percent sign.)
The sustainable growth rate for the company is 18.79
percent.
The sustainable growth rate is 18.79% percent if you use
the (ROE x b) formula and beginning of period equity. If
you use end of period equity in this formula, the
sustainable growth rate is 15.82% percent. Is this
number too high or too low? This is too low because
equity has increased (see previous slide) Why?

Question 3
 Assets and costs are proportional to
sales. Debt and equity are not. A
dividend of $963.60 was paid, and
McGillicudy wishes to maintain a constant
payout ratio. Next year's sales are
projected to be $23,040. The external
financing needed is $ _____
Balance Sheet
Income Statement
Sales
$ 19,200
Costs
15,550
Assets
Taxes (34 %)
$ 3,650
1,241
========
Net income
$ 2,409
========
Debt
Equity
========
Taxable
income
$ 93,000
========
Total
$ 93,000
========
$ 20,400
72,600
========
Total
$ 93,000
========
Question 3
An increase of sales to $23,040 is an increase of:
Sales increase = ($23,040 – 19,200) / $19,200
Sales increase = .20 or 20%
Assuming costs and assets increase proportionally, the pro
forma financial statements will look like this:
Pro forma income statement
Sales
$23,040.00
Costs
18,660.00
EBIT
4,380.00
Taxes(34%)1,489.20
Net income$2,890.80
Pro forma balance sheet
Assets
$ 111,600Debt
Total
$
111,600Total
$20,400.00
Equity
74,334.48
$ 94,734.48
Question 3
The payout ratio is constant, so the dividends paid this year is the
payout ratio from last year times net income, or:
Dividends = ($963.60 / $2,409)($2,890.80)
Dividends = $1,156.32
The addition to retained earnings is:
Addition to retained earnings = $2,890.80 – 1,156.32
Addition to retained earnings = $1,734.48
And the new equity balance is:
Equity = $72,600 + 1,734.48
Equity = $74,334.48
So the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $111,600 – 94,734.48
EFN = $16,865.52
Question 4
 A 20 percent growth rate in sales is
projected. Prepare a pro forma income
statement assuming costs vary with
sales and the dividend payout ratio is
constant.
HEIR JORDAN CORPORATION
Income Statement
--------------------------------------------------------------------------------------------------------------------------Sales
$ 29,000
Costs
11,200
========
Taxable Income
$ 17,800
Taxes (34%)
6,052
========
Net income
$ 11,748
========
Dividends
Addition to retained earnings
$ 4,935
6,813
HEIR JORDAN CORPORATION
Pro Forma Income Statement
--------------------------------------------------------------------------------------------------------------------------Sales
=$29,000*1.2=$34,800
Costs
=$11,200*1.2=$13,440
========
Taxable Income
$21,360
Taxes (34%)
$7,262.40
========
Net income
$14,097.60
========
Dividends (Ratio = 4,935/11,748 = .42)
$ 5921.68
Addition to retained earnings
$ 8175.92
HEIR JORDAN CORPORATION
Balance Sheet
Assets
Liabilities and Owners' Equity
Percentage
$
Percentage
of Sales
$
Current assets
Cash
Current liabilities
$ 3,525
%
Accounts receivable
7,500
%
Inventory
6,000
%
========
========
$ 17,025
%
========
========
Total
Accounts
payable
Notes payable
Total
Long-term debt
Fixed assets
Net plant and
equipment
of Sales
$ 30,000
%
========
========
$ 3,000
%
7,500
%
========
========
$ 10,500
%
========
========
$ 19,500
%
========
========
$ 15,000
%
2,025
%
========
========
$ 17,025
%
========
========
$ 47,025
%
========
========
Owners' equity
Common stock
and paid-in surplus
Retained
earnings
Total
Total liabilities and
Total assets
$ 47,025
%
========
========
owners' equity
Question 5: Supply the missing information using the percentage of sales approach. Assume that
accounts payable vary with sales, whereas notes payable do not. (Input answers as a percent rounded
to 2 decimal places, without the percent sign.)(Enter "n/a" where needed.)
HEIR JORDAN CORPORATION
Balance Sheet
($)
(%)
Assets
Current assets
Cash
$3,525
A/R
7,500
Inventory 6,000
Total
$17,025
Fixed assets
Net P&E 30,000
($)
12.16
25.86
20.69
58.71
103.45
Total assets $47,025 162.16
Total liabilities and owners’ equity $47,025
n/a
(%)
Liabilities and Owners’ Equity
Current liabilities
A/P
$3,000
Notes payable
7,500
Total
$10,500
Long-term debt
19,500
10.34
n/a
n/a
n/a
Owners’ equity
CS & Paid surplus
Retained earnings
$15,000
2,025
n/a
n/a
Total
$17,025
n/a
Question 6: Prepare a pro forma balance sheet showing EFN, assuming a 15
percent increase in sales, no new external debt or equity financing, and a
constant payout ratio.
Assuming costs vary with sales and a 15 percent increase in sales, the pro forma income statement will
look like this:
HEIR JORDAN CORPORATION
Pro Forma Income Statement
Sales
$33,350.00
Costs
12,880.00
Taxable income
$20,470.00
Taxes (34%)
6,959.80
Net income
$ 13,510.20
The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net
income, or:
Dividends = ($4,935/$11,748)($13,510.20)
Dividends = $5,674.94
And the addition to retained earnings will be:
Addition to retained earnings = $13,240.20 – 5,674.94
Addition to retained earnings = $7,835.26
The new total addition to retained earnings on the pro forma balance sheet will be:
New total addition to retained earnings = $2,025 + 7,835.26
New total addition to retained earnings = $9,860.26
The pro forma balance sheet will look like this:
HEIR JORDAN CORPORATION
Pro Forma Balance Sheet
Assets
Current assets
Cash
$
Accounts receivable
Inventory
Total
$
4,053.75
8,625.00
6,900.00
19,578.75
Liabilities and Owners’ Equity
Current liabilities
Accounts payable
$
Notes payable
Total
$
3,450.00
7,500.00
10,950.00
Long-term debt
19,500.00
Owners’ equity
Common stock and
paid-in surplus
Retained earnings
Total
$
Total liabilities and owners’ equity $
$15,000.00
9,860.26
24,860.26
55,310.26
Fixed assets
Net plant and
equipment
Total assets
$
34,500.00
54,078.75
So the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $54,078.75 – 55,310.26
EFN = –$1,231.51
Question 7

Find the following financial ratios for Smolira
Golf Corp. (use year-end figures rather than
average values where appropriate):

For solvency and utilization ratios: (Round
answers to 2 decimal places.)

For profitability ratios: (Input answers as a
percent rounded to 2 decimal places, without a
percent sign.)
SMOLIRA GOLF CORP.
2004 and 2005 Balance
Sheets
Assets
Liabilities and Owners'
Equity
2004
2005
2004
2005
$ 983
$ 1,292
Current
liabilities
Current assets
Cash
$ 815
$ 906
Accounts
payable
Accounts
receivable
2,405
2,510
Notes payable
720
840
Inventory
4,608
4,906
Other
105
188
$ 7,828
$ 8,322
Total
$ 1,808
$ 2,320
Long-term debt
$ 4,817
$ 4,960
$ 10,000
$ 10,000
6,367
10,209
Total
$ 16,367
$ 20,209
Total liabilities
and owners'
equity
$ 22,992
$ 27,489
Total
Fixed assets
Net plant and
equipment
Total assets
$ 15,164
$ 19,167
Owners' equity
========
========
Common
stock and paidin surplus
$ 22,992
$ 27,489
Retained
earnings
SMOLIRA GOLF CORP.
2005 Income Statement
Sales
$ 33,500
Costs of goods sold
18,970
Depreciation
1,980
========
Earnings before interest and taxes
$ 12,550
Interest paid
486
========
Taxable Income
$ 12,064
Taxes (35%)
4,222
========
Net income
$ 7,842
========
Dividends
Addition to retained earnings
$ 4,000
3,842
Short-term solvency ratios:
Current ratio = Current assets / Current liabilities
Current ratio 2004 = $7,828 / $1,808 = 4.33 times
Current ratio 2005 = $8,322 / $2,320 = 3.59 times
Quick ratio = (Current assets – Inventory) / Current liabilities
Quick ratio 2004 = ($7,828 – 4,608) / $1,808 = 1.78 times
Quick ratio 2005 = ($8,322 – 4,906) / $2,320 = 1.47 times
Cash ratio = Cash / Current liabilities
Cash ratio 2004
= $815 / $1,808 = 0.45 times
Cash ratio 2005 = $906 / $2,320 = 0.39 times
Asset utilization ratios:
Total asset turnover
Total asset turnover
Inventory turnover
Inventory turnover
Receivables turnover
Receivables turnover
= Sales / Total assets
= $33,500 / $27,489 = 1.22 times
= Cost of goods sold / Inventory
= $18,970 / $4,906 = 3.87 times
= Sales / Accounts receivable
= $33,500 / $2,510 = 13.35 times
Long-term solvency ratios:
Total debt ratio
= (Total assets – Total equity) / Total assets
Total debt ratio 2004
= ($22,992 – 16,367) / $22,992 = 0.29
Total debt ratio 2005
= ($27,489 – 20,209) / $27,489 = 0.26
Debt-equity ratio
= Total debt / Total equity
Debt-equity ratio 2004
= ($1,808 + 4,817) / $16,367 = 0.40
Debt-equity ratio 2005
= ($2,320 + 4,960) / $20,209 = 0.36
Equity multiplier
= 1 + D/E
Equity multiplier 2004
= 1 + 0.40 = 1.40
Equity multiplier 2005
= 1 + 0.36 = 1.36
Times interest earned
= EBIT / Interest
Times interest earned
= $12,550 / $486 = 25.82 times
Cash coverage ratio= (EBIT + Depreciation) / Interest
Cash coverage ratio
= ($12,550 + 1,980) / $486 = 29.90 times
Profitability ratios:
Profit margin
Profit margin
Return on assets
Return on assets
Return on equity
Return on equity
= Net income / Sales
= $7,842 / $33,500 = 23.41%
= Net income / Total assets
= $7,842 / $27,489 = 28.53%
= Net income / Total equity
= $7,842 / $20,209 = 38.80%
Question 8

The most recent financial statements for Moose
Tours, Inc., follow. Sales for 2005 are projected
to grow by 20 percent. Interest expense will
remain constant; the tax rate and the dividend
payout rate will also remain constant. Costs,
other expenses, current assets, and
accounts payable increase spontaneously
with sales. If the firm is operating at full capacity
and no new debt or equity is issued, external
financing in the amount of $_____ is needed to
support the 20 percent growth rate in sales.
MOOSE TOURS, INC.
2004 Income Statement
------------------------------------------------------------------------------------------------Sales
$ 905,000
Costs
710,000
Other expenses
12,000
========
Earnings before interest and taxes
$ 183,000
Interest paid
19,700
========
Taxable Income
$ 163,300
Taxes (35%)
57,155
========
Net income
$ 106,145
========
Dividends
Addition to retained earnings
$ 42,458
63,687
MOOSE TOURS, INC.
Balance Sheet as of December 31, 2004
Assets
Liabilities and Owners' Equity
Current assets
Cash
Current liabilities
$ 25,000
Accounts
receivable
43,000
Inventory
76,000
Total
$ 144,000
Accounts payable
Notes payable
$ 65,000
9,000
Total
$ 74,000
Long-term debt
$ 156,000
Owners' equity
Common stock
and
Fixed assets
Net plant and
equipment
$ 364,000
Total assets
$ 508,000
paid-in surplus
Retained
earnings
Total
$ 21,000
257,000
$ 278,000
Total liabilities and
owners' equity
$ 508,000
Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income
statement will look like this:
MOOSE TOURS INC.
Pro Forma Income Statement
Sales
$
1,086,000
Costs
852,000
Other expenses
14,400
EBIT
$
219,600
Interest
19,700
Taxable income
$199,900
Taxes(35%)
69,965
Net income
$129,935
The payout ratio is constant, so the dividends paid this year is the payout ratio from last
year times net income, or:
Dividends = ($42,458/$106,145)($129,935)
Dividends = $51,974
And the addition to retained earnings will be:
Addition to retained earnings = $129,935 – 51,974
Addition to retained earnings = $77,961
The new addition to retained earnings on the pro forma balance sheet will be:
New addition to retained earnings = $257,000 + 77,961
New addition to retained earnings = $334,961
The pro forma balance sheet will look like this:
MOOSE TOURS INC.
Pro Forma Balance Sheet
Assets
Liabilities and Owners’ Equity
Current assets
Current liabilities
Cash
$30,000
Accounts payable
Accounts receivable 51,600
Notes payable
Inventory
91,200
Total
Total
$
172,800
Long-term debt
Fixed assets
Net plant and equipment 436,800
Total assets
$609,600
Owners’ equity
Common stock and
paid-in surplus
Retained earnings
Total
Total liabilities and owners’
equity
$78,000
9,000
$87,000
156,000
$21,000
334,961
$355,961
$598,961
Question 8

The most recent financial statements for Moose
Tours, Inc., follow. Sales for 2005 are projected
to grow by 20 percent. Interest expense will
remain constant; the tax rate and the dividend
payout rate will also remain constant. Costs,
other expenses, current assets, and
accounts payable increase spontaneously
with sales. If the firm is operating at full capacity
and no new debt or equity is issued, external
financing in the amount of $_____ is needed to
support the 20 percent growth rate in sales.
Question 8
So the EFN is:
EFN = Total assets – Total liabilities and
equity
EFN = $609,600 – 598,961
EFN = $10,639
Question 9

The most recent financial statements for Moose
Tours, Inc., follow. Sales for 2005 are projected
to grow by 20 percent. Interest expense will
remain constant; the tax rate and the dividend
payout rate will also remain constant. Costs,
other expenses, current assets, and accounts
payable increase spontaneously with sales. If
the firm is operating at full capacity and wishes
to keep its debt-equity ratio constant, external
financing in the amount of $ is needed to
support the 20 percent growth rate in sales.
Question 9
The D/E ratio of the company is:
D/E = ($156,000 + 74,000) / $278,000
D/E = .82734
So the new total debt amount will be:
New total debt = .82734($355,961)
New total debt = $294,500.11
So the EFN is:
EFN = $609,600 – ($294,500.11 + 355,961) = –$40,861.11
An interpretation of the answer is not that the company has a negative EFN. Looking
back at Question 8, we see that for the same sales growth, the EFN is $10,639. The
negative number in this case means the company has too much capital. There are
two possible solutions. First, the company can put the excess funds in cash, which
has the effect of changing the current asset growth rate. Second, the company can
use the excess funds to repurchase debt and equity. To maintain the current capital
structure, the repurchase must be in the same proportion as the current capital
structure.
At a 20 percent growth rate, and assuming the payout ratio is constant, the
dividends paid will be:
Dividends = ($42,458/$106,145)($129,935)
Dividends = $51,974
And the addition to retained earnings will be:
Addition to retained earnings = $129,935 – 51,974
Addition to retained earnings = $77,961
The new addition to retained earnings on the pro forma balance sheet will be:
New addition to retained earnings = $257,000 + 77,961
New addition to retained earnings = $334,961
The new total debt will be:
New total debt = .82734($334,961)
New total debt = $294,500
So, the new long-term debt will be the new total debt minus the new shortterm debt, or:
New long-term debt = $294,500 – 87,000
New long-term debt = $207,500
So the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $609,600 – 650,461
EFN = –$40,861
Question 10
EFN and Sustainable Growth
The most recent financial statements for Moose Tours, Inc., follow. Sales for
2005 are projected to grow by 30 percent. Interest expense will remain
constant; the tax rate and the dividend payout rate will also remain constant.
Costs, other expenses, current assets, and accounts payable increase
spontaneously with sales. If the firm is operating at full capacity and wishes
to keep its debt-equity ratio constant, external financing in the amount of
$_____ is needed to support the 30 percent growth rate in sales. (Round
answers to nearest whole dollar.)
If the projected sales growth rate for 2005 is 35 percent instead of 30 percent,
the amount of external financing needed is $_____.
At a sales growth rate of _____% percent, the EFN is equal to zero.
Note: This last question cannot be answered if you do not allow debt to
change to meet the debt-equity ratio at the beginning of the question.
MOOSE TOURS, INC.
2004 Income Statement
------------------------------------------------------------------------------------------------Sales
$ 905,000
Costs
710,000
Other expenses
12,000
========
Earnings before interest and taxes
$ 183,000
Interest paid
19,700
========
Taxable Income
$ 163,300
Taxes (35%)
57,155
========
Net income
$ 106,145
========
Dividends
Addition to retained earnings
$ 42,458
63,687
MOOSE TOURS, INC.
Balance Sheet as of December 31, 2004
Assets
Liabilities and Owners' Equity
Current assets
Cash
Current liabilities
$ 25,000
Accounts
receivable
43,000
Inventory
76,000
Total
$ 144,000
Accounts payable
Notes payable
$ 65,000
9,000
Total
$ 74,000
Long-term debt
$ 156,000
Owners' equity
Common stock
and
Fixed assets
Net plant and
equipment
$ 364,000
Total assets
$ 508,000
paid-in surplus
Retained
earnings
Total
$ 21,000
257,000
$ 278,000
Total liabilities and
owners' equity
$ 508,000
20% Sales
Growth
30% Sales
Growth
35% Sales
Growth
Sales
$1,086,000
$1,176,500
$1,221,750
Costs
852,000
923,000
958,500
14,400
15,600
16,200
$ 219,600
$ 237,900
$ 247,050
19,700
19,700
19,700
$ 199,900
$ 218,200
$ 227,350
69,965
76,370
79,573
$ 129,935
$ 141,830
$ 147,778
$
51,974
$ 56,732
$ 59,111
77,961
85,098
88,667
Other expenses
EBIT
Interest
Taxable income
Taxes (35%)
Net income
Dividends
Add to RE
Under the sustainable growth rate assumption, the company maintains a constant debtequity ratio. The D/E ratio of the company is:
D/E = ($156,000 + 74,000) / $278,000
D/E = .82734
At a 30 percent growth rate, and assuming the payout ratio is constant, the dividends paid
will be:
Dividends = ($42,458/$106,145)($141,830) = $56,732
And the addition to retained earnings will be:
Addition to retained earnings = $141,830 – 56,732 = $85,098
The new addition to retained earnings on the pro forma balance sheet will be:
New addition to retained earnings = $257,000 + 85,098 = $342,098
The new total debt will be:
New total debt = .82734($342,098) = $300,405
So, the new long-term debt will be the new total debt minus the new short-term debt, or:
New long-term debt = $300,405 – 93,500 = $206,905
So the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $660,400 – 663,503
EFN = –$3,103
At a 35 percent growth rate, and assuming the payout ratio is constant,
the dividends paid will be:
Dividends = ($42,458/$106,145)($147,778) = $59,111
And the addition to retained earnings will be:
Addition to retained earnings = $147,778 – 59,111 = $88,667
The new addition to retained earnings on the pro forma balance sheet
will be:
New addition to retained earnings = $257,000 + 88,667 = $345,667
The new total debt will be:
New total debt = .82734($366,667) = $303,357
So, the new long-term debt will be the new total debt minus the new
short-term debt, or:
New long-term debt = $303,357 – 96,750 = $206,607
So the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $685,800 – 670,024
EFN = $15,776
Question 10
EFN and Sustainable Growth
Note: At 30% growth, there is a paydown in
external financing, while at 35% growth there is
a positive need for external financing
At a sales growth rate of 30.82%, the EFN is equal
to zero.
Why is this internal growth rate different from that
found by using the equation in the text?
Chapter 7
Interest Rates and Bond
Valuation
Key Concepts and Skills





Know the important bond features and bond
types
Understand bond values and why they
fluctuate
Understand bond ratings and what they mean
Understand the impact of inflation on interest
rates
Understand the term structure of interest
rates and the determinants of bond yields
Bond Definitions
Bond
 Par value (face value)
 Coupon rate
 Coupon payment
 Maturity date
 Yield or Yield to maturity

Present Value of Cash Flows as
Rates Change
Bond Value = PV of coupons + PV of par
 Bond Value = PV annuity + PV of lump
sum
 Remember, as interest rates increase
present values decrease
 So, as interest rates increase, bond prices
decrease and vice versa

Coupon Bond—Yield to
Maturity
Using the same strategy used for the fixed-payment loan:
P = price of coupon bond
C = yearly coupon payment
F = face value of the bond
n = years to maturity date
C
C
C
C
F
P=


. . . +

2
3
n
1+i (1+i )
(1+i )
(1+i )
(1+i ) n



When the coupon bond is priced at its face value, the
yield to maturity equals the coupon rate
The price of a coupon bond and the yield to maturity
are negatively related
The yield to maturity is greater than the coupon rate
when the bond price is below its face value
Valuing a Discount Bond with
Annual Coupons

Consider a bond with a coupon rate of 10% and
annual coupons. The par value is $1000 and the
bond has 5 years to maturity. The yield to
maturity is 11%. What is the value of the bond?
 Using
the formula:
B
= PV of annuity + PV of lump sum
 B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5
 B = 369.59 + 593.45 = 963.04
 Using
N
the calculator:
= 5; I/Y = 11; PMT = 100; FV = 1000
 CPT PV = -963.04
Valuing a Premium Bond with
Annual Coupons

Suppose you are looking at a bond that has a
10% annual coupon and a face value of $1000.
There are 20 years to maturity and the yield to
maturity is 8%. What is the price of this bond?
 Using
the formula:
B = PV of annuity + PV of lump sum
 B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20
 B = 981.81 + 214.55 = 1196.36

 Using
the calculator:
N = 20; I/Y = 8; PMT = 100; FV = 1000
 CPT PV = -1196.36

Graphical Relationship Between
Price and Yield-to-maturity
1500
Bond Price
1400
1300
1200
1100
1000
900
800
700
600
0%
2%
4%
6%
Yield-to-maturity
8%
10%
12%
14%
Bond Prices: Relationship
Between Coupon and Yield
If YTM = coupon rate, then par value =
bond price
 If YTM > coupon rate, then par value >
bond price

 Why?
 Selling

at a discount, called a discount bond
If YTM < coupon rate, then par value <
bond price
 Why?
 Selling
at a premium, called a premium bond
The Bond-Pricing Equation
1

1
 (1  r) t
Bond Value  C 
r




F

t
 (1  r)

Example 7.1

Find present values based on the payment
period
 How
many coupon payments are there?
 What is the semiannual coupon payment?
 What is the semiannual yield?
 B = 70[1 – 1/(1.08)14] / .08 + 1000 / (1.08)14 =
917.56
 Or PMT = 70; N = 14; I/Y = 8; FV = 1000; CPT
PV = -917.56
Interest Rate Risk

Price Risk
 Change
in price due to changes in interest rates
 Long-term bonds have more price risk than short-term
bonds
 Low coupon rate bonds have more price risk than
high coupon rate bonds

Reinvestment Rate Risk

Uncertainty concerning rates at which cash flows can be
reinvested
 Short-term bonds have more reinvestment rate risk than
long-term bonds
 High coupon rate bonds have more reinvestment rate risk
than low coupon rate bonds
Interest-Rate Risk

Prices and returns for long-term
bonds are more volatile than those for
shorter-term bonds

There is no interest-rate risk for any bond
whose time to maturity matches the
holding period
Figure 7.2
Computing Yield-to-maturity
Yield-to-maturity is the rate implied by the
current bond price
 Finding the YTM requires trial and error if
you do not have a financial calculator and
is similar to the process for finding r with
an annuity
 If you have a financial calculator, enter N,
PV, PMT, and FV, remembering the sign
convention (PMT and FV need to have the
same sign, PV the opposite sign)

YTM with Annual Coupons

Consider a bond with a 10% annual
coupon rate, 15 years to maturity and a
par value of $1000. The current price is
$928.09.
 Will
the yield be more or less than 10%?
 N = 15; PV = -928.09; FV = 1000; PMT = 100
 CPT I/Y = 11%
YTM with Semiannual Coupons

Suppose a bond with a 10% coupon rate
and semiannual coupons, has a face value
of $1000, 20 years to maturity and is
selling for $1197.93.
 Is
the YTM more or less than 10%?
 What is the semiannual coupon payment?
 How many periods are there?
 N = 40; PV = -1197.93; PMT = 50; FV = 1000;
CPT I/Y = 4% (Is this the YTM?)
 YTM = 4%*2 = 8%
Table 7.1
Current Yield vs. Yield to Maturity



Current Yield = annual coupon / price
Yield to maturity = current yield + capital gains
yield
Example: 10% coupon bond, with semiannual
coupons, face value of 1000, 20 years to
maturity, $1197.93 price
 Current
 Price in
yield = 100 / 1197.93 = .0835 = 8.35%
one year, assuming no change in YTM =
1193.68
 Capital gain yield = (1193.68 – 1197.93) / 1197.93 =
-.0035 = -.35%
 YTM = 8.35 - .35 = 8%, which the same YTM
computed earlier
Bond Pricing Theorems
Bonds of similar risk (and maturity) will be
priced to yield about the same return,
regardless of the coupon rate
 If you know the price of one bond, you
can estimate its YTM and use that to find
the price of the second bond
 This is a useful concept that can be
transferred to valuing assets other than
bonds

Bond Prices with a Spreadsheet

There is a specific formula for finding bond
prices on a spreadsheet
 PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis)
 YIELD(Settlement,Maturity,Rate,Pr,Redemption,
Frequency,Basis)
 Settlement and maturity need to be actual dates
 The redemption and Pr need to given as % of par
value

Click on the Excel icon for an example
Differences Between Debt and
Equity

Debt





Not an ownership interest
Creditors do not have
voting rights
Interest is considered a
cost of doing business and
is tax deductible
Creditors have legal
recourse if interest or
principal payments are
missed
Excess debt can lead to
financial distress and
bankruptcy

Equity





Ownership interest
Common stockholders vote
for the board of directors
and other issues
Dividends are not
considered a cost of doing
business and are not tax
deductible
Dividends are not a liability
of the firm and stockholders
have no legal recourse if
dividends are not paid
An all equity firm can not go
bankrupt
The Bond Indenture

Contract between the company and the
bondholders and includes
 The
basic terms of the bonds
 The total amount of bonds issued
 A description of property used as security, if
applicable
 Sinking fund provisions
 Call provisions
 Details of protective covenants
Bond Classifications
Registered vs. Bearer Forms
 Security

– secured by financial securities
 Mortgage – secured by real property, normally
land or buildings
 Debentures – unsecured
 Notes – unsecured debt with original maturity
less than 10 years
 Collateral

Seniority
Bond Characteristics and
Required Returns
The coupon rate depends on the risk
characteristics of the bond when issued
 Which bonds will have the higher coupon,
all else equal?

 Secured
debt versus a debenture
 Subordinated debenture versus senior debt
 A bond with a sinking fund versus one without
 A callable bond versus a non-callable bond
Bond Ratings – Investment
Quality

High Grade
Moody’s Aaa and S&P AAA – capacity to pay is extremely
strong
 Moody’s Aa and S&P AA – capacity to pay is very strong


Medium Grade
Moody’s A and S&P A – capacity to pay is strong, but more
susceptible to changes in circumstances
 Moody’s Baa and S&P BBB – capacity to pay is adequate,
adverse conditions will have more impact on the firm’s
ability to pay

Bond Ratings - Speculative

Low Grade
 Moody’s
Ba, B, Caa and Ca
 S&P BB, B, CCC, CC
 Considered speculative with respect to capacity
to pay. The “B” ratings are the lowest degree of
speculation.

Very Low Grade
 Moody’s
C and S&P C – income bonds with no
interest being paid
 Moody’s D and S&P D – in default with principal
and interest in arrears
Government Bonds

Treasury Securities
 Federal
government debt
 T-bills – pure discount bonds with original maturity of
one year or less
 T-notes – coupon debt with original maturity between
one and ten years
 T-bonds coupon debt with original maturity greater
than ten years

Municipal Securities
 Debt
of state and local governments
 Varying degrees of default risk, rated similar to
corporate debt
 Interest received is tax-exempt at the federal level
Example 7.4

A taxable bond has a yield of 8% and a
municipal bond has a yield of 6%
 If
you are in a 40% tax bracket, which bond
do you prefer?
8%(1 - .4) = 4.8%
 The after-tax return on the corporate bond is 4.8%,
compared to a 6% return on the municipal

 At
what tax rate would you be indifferent
between the two bonds?
8%(1 – T) = 6%
 T = 25%

Zero-Coupon Bonds





Make no periodic interest payments (coupon
rate = 0%)
The entire yield-to-maturity comes from the
difference between the purchase price and the
par value
Cannot sell for more than par value
Sometimes called zeroes, deep discount bonds,
or original issue discount bonds (OIDs)
Treasury Bills and principal-only Treasury strips
are good examples of zeroes
Floating Rate Bonds



Coupon rate floats depending on some index
value
Examples – adjustable rate mortgages and
inflation-linked Treasuries
There is less price risk with floating rate bonds
 The
coupon floats, so it is less likely to differ
substantially from the yield-to-maturity

Coupons may have a “collar” – the rate cannot
go above a specified “ceiling” or below a
specified “floor”
Other Bond Types
Disaster bonds
 Income bonds
 Convertible bonds
 Put bonds
 There are many other types of provisions
that can be added to a bond and many
bonds have several provisions – it is
important to recognize how these
provisions affect required returns

Bond Markets
Primarily over-the-counter transactions
with dealers connected electronically
 Extremely large number of bond issues,
but generally low daily volume in single
issues
 Makes getting up-to-date prices difficult,
particularly on small company or municipal
issues
 Treasury securities are an exception

Work the Web Example
Bond quotes are available online
 One good site is Bonds Online
 Click on the web surfer to go to the site

 Follow
the bond search, corporate links
 Choose a company, enter it under Express
Search Issue and see what you can find!
Treasury Quotations

Highlighted quote in Figure 7.4
8
Nov 21
132:23
132:24
-12 5.14
 What is the coupon rate on the bond?
 When does the bond mature?
 What is the bid price? What does this mean?
 What is the ask price? What does this mean?
 How much did the price change from the
previous day?
 What is the yield based on the ask price?
Clean vs. Dirty Prices



Clean price: quoted price
Dirty price: price actually paid = quoted price plus
accrued interest
Example: Consider T-bond in previous slide, assume
today is July 15, 2005




Prices (based on ask):



Number of days since last coupon = 61
Number of days in the coupon period = 184
Accrued interest = (61/184)(.04*100,000) = 1326.09
Clean price = 132,750
Dirty price = 132,750 + 1,326.09 = 134,076.09
So, you would actually pay $134,076.09 for the bond
Inflation and Interest Rates
Real rate of interest – change in
purchasing power
 Nominal rate of interest – quoted rate of
interest, change in purchasing power and
inflation
 The ex ante nominal rate of interest
includes our desired real rate of return
plus an adjustment for expected inflation

The Fisher Effect
The Fisher Effect defines the relationship
between real rates, nominal rates and
inflation
 (1 + R) = (1 + r)(1 + h), where

R
= nominal rate
 r = real rate
 h = expected inflation rate

Approximation
R
=r+h
Fisher Equation
i  ir   e
i = nominal interest rate
ir = real interest rate
 e = expected inflation rate
When the real interest rate is low,
there are greater incentives to borrow and fewer incentives to lend.
The real interest rate is a better indicator of the incentives to
borrow and lend.
Example 7.6
If we require a 10% real return and we
expect inflation to be 8%, what is the
nominal rate?
 R = (1.1)(1.08) – 1 = .188 = 18.8%
 Approximation: R = 10% + 8% = 18%
 Because the real return and expected
inflation are relatively high, there is
significant difference between the actual
Fisher Effect and the approximation.

Term Structure of Interest
Rates

Bonds with identical risk, liquidity, and tax characteristics
may have different interest rates because the time
remaining to maturity is different

Yield curve—a plot of the yield on bonds with differing
terms to maturity but the same risk, liquidity and tax
considerations

Upward-sloping  long-term rates are above
short-term rates

Flat  short- and long-term rates are the same

Inverted  long-term rates are below short-term rates
Interpreting the Yield Curve
Figure 7.7
Figure 7.6 – Upward-Sloping
Yield Curve
Figure 7.6 – Downward-Sloping
Yield Curve
Factors Affecting Required
Return
Default risk premium – remember bond
ratings
 Taxability premium – remember municipal
versus taxable
 Liquidity premium – bonds that have more
frequent trading will generally have lower
required returns
 Anything else that affects the risk of the
cash flows to the bondholders will affect
the required returns

Quick Quiz






How do you find the value of a bond and why do
bond prices change?
What is a bond indenture and what are some of
the important features?
What are bond ratings and why are they
important?
How does inflation affect interest rates?
What is the term structure of interest rates?
What factors determine the required return on
bonds?