Net Present Value First Principles of FinanceAppendix 4.docx

Net Present Value: First Principles of Finance
Appendix 4A
Copyright © 2013 by the McGraw-Hill Companies, Inc. All
rights reserved.
McGraw-Hill/Irwin
*
4A-*
Key Concepts and SkillsUnderstand the theoretical foundations
of the Net Present Value (NPV) rule
*
4A-*
Appendix Outline
4A.1 Making Consumption Choices over Time
4A.2 Making Investment Choices
4A.3 Illustrating the Investment Decision
*

4A-*
Making Consumption Choices over TimeAn individual can alter
his consumption across time periods through borrowing and
lending.We can illustrate this by graphing consumption today
versus consumption in the future.This graph will show
intertemporal consumption opportunities.
*
4A-*
Intertemporal Consumption Opportunity Set
A person with $95,000 who faces a 10% interest rate has the
following opportunity set.
One choice available is to consume $40,000 now; invest the
remaining $55,000; consume $60,500 next year.
$0
$20,000
$40,000
$60,000
$80,000

$100,000
$120,000
Consumption today
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
Consumption at t+1
*
4A-*
Intertemporal Consumption Opportunity Set
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000

$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
Consumption today
Consumption at t+1
Another choice available is to consume $60,000 now; invest the
remaining $35,000; consume $38,500 next year.
*
4A-*
Taking Advantage of Our Opportunities
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$0
$20,000
$40,000
$60,000
$80,000
$100,000

$120,000
Consumption today
Consumption at t+1
A person’s preferences will determine what point on the
opportunity set she will choose.
Ms. Patience
Ms. Impatience
*
4A-*
Changing Our Opportunities
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
Consumption today
Consumption at t+1

A rise in interest rates will make saving more attractive …
…and borrowing less attractive.
Consider an investor who has chosen to consume $40,000 now
and to consume $60,000 next year.
*
The point at which the intertemporal opportunity set pivots
depends upon where your endowment is when interest rates
change. If the person had $95,000 in current consumption and
no future consumption, the pivot would have been at the x-axis
intercept.
4A-*
Illustrating the Investment DecisionConsider an investor who
has an initial endowment of income of $40,000 this year and
$55,000 next year.Suppose that she faces a 10-percent interest
rate and is offered the following investment.
Cash inflows
Time
Cash outflows
0
1
-$25,000
$30,000

*
4A-*
Illustrating the Investment Decision
$0
Consumption today
Our investor begins with the following opportunity set:
endowment of $40,000 today, $55,000 next year and a 10%
interest rate.
One choice available is to consume $15,000 now; invest the
remaining $25,000 in the financial markets at 10%; consume
$82,500 next year.
$0
$99,000
Consumption at t+1
$90,000
$55,000
$82,500
$40,000
$15,000
*

4A-*
$0
Consumption today
A better alternative would be to invest in the project instead of
the financial markets.
She could consume $15,000 now; invest the remaining $25,000
in the project at 20%; consume $85,000 next year.
$0
$99,000
Consumption at t+1
$90,000
$55,000
$82,500
$40,000
$85,000
$15,000
With borrowing or lending in the financial markets, she can
achieve any pattern of cash flows she wants—any of which is
better than her original opportunities.

*
4A-*
$0
Consumption today
Note that we are better off in that we can command more
consumption today or next year.
$0
$99,000
Consumption at t+1
$101,500
$101,500 = $15,000×(1.10) + $85,000
$90,000
$92,273
$55,000
$82,500
$40,000
$85,000

$15,000
$92,273 = $15,000 +
*
4A-*
Net Present ValueThe value created by the investment
opportunity increased our possible consumption.This
opportunity, therefore, created value.The current value of the
opportunity is the investment’s NPV.
*
4A-*
Quick QuizWhat factors determine our consumption next
year?How do investment opportunities create value?
*
1
1
)
10

.
1
(
000
,
85
$
Discounted Cash Flow Valuation
Chapter 4
Copyright © 2013 by the McGraw-Hill Companies, Inc. All
rights reserved.
McGraw-Hill/Irwin
*
4-*
Key Concepts and SkillsBe able to compute the future value
and/or present value of a single cash flow or series of cash
flowsBe able to compute the return on an investmentBe able to
use a financial calculator and/or spreadsheet to solve time value
problemsUnderstand perpetuities and annuities
*

4-*
Chapter Outline
4.1 Valuation: The One-Period Case
4.2 The Multiperiod Case
4.3 Compounding Periods
4.4 Simplifications
4.5 Loan Amortization
4.6 What Is a Firm Worth?
*
4-*
4.1 The One-Period CaseIf you were to invest $10,000 at 5-
percent interest for one year, your investment would grow to
$10,500.
$500 would be interest ($10,000 × .05)
$10,000 is the principal repayment ($10,000 × 1)
$10,500 is the total due. It can be calculated as:
$10,500 = $10,000×(1.05)
The total amount due at the end of the investment is call the
Future Value (FV).
*
4-*

Future ValueIn the one-period case, the formula for FV can be
written as:
FV = C0×(1 + r)
Where C0 is cash flow today (time zero), and
r is the appropriate interest rate.
*
It may be helpful to identify r as the opportunity cost.
4-*
Present ValueIf you were to be promised $10,000 due in one
year when interest rates are 5-percent, your investment would
be worth $9,523.81 in today’s dollars.
The amount that a borrower would need to set aside today to be
able to meet the promised payment of $10,000 in one year is
called the Present Value (PV).
Note that $10,000 = $9,523.81×(1.05).
*
4-*
Present ValueIn the one-period case, the formula for PV can be
written as:
Where C1 is cash flow at date 1, and
r is the appropriate interest rate.

*
4-*
Net Present ValueThe Net Present Value (NPV) of an
investment is the present value of the expected cash flows, less
the cost of the investment.Suppose an investment that promises
to pay $10,000 in one year is offered for sale for $9,500. Your
interest rate is 5%. Should you buy?
*
4-*
Net Present Value
The present value of the cash inflow is greater
than the cost. In other words, the Net Present
Value is positive, so the investment should be
purchased.
*
4-*
Net Present Value

In the one-period case, the formula for NPV can be written as:
NPV = –Cost + PV
If we had not undertaken the positive NPV project considered
on the last slide, and instead invested our $9,500 elsewhere at 5
percent, our FV would be less than the $10,000 the investment
promised, and we would be worse off in FV terms :
$9,500×(1.05) = $9,975 < $10,000
*
4-*
4.2 The Multiperiod CaseThe general formula for the future
value of an investment over many periods can be written as:
FV = C0×(1 + r)T
Where
C0 is cash flow at date 0,
r is the appropriate interest rate, and
T is the number of periods over which the cash is invested.
*
4-*
Future ValueSuppose a stock currently pays a dividend of
$1.10, which is expected to grow at 40% per year for the next
five years.What will the dividend be in five years?
FV = C0×(1 + r)T

$5.92 = $1.10×(1.40)5
*
4-*
Future Value and CompoundingNotice that the dividend in year
five, $5.92, is considerably higher than the sum of the original
dividend plus five increases of 40-percent on the original $1.10
dividend:
$5.92 > $1.10 + 5×[$1.10×.40] = $3.30
This is due to compounding.
*
4-*
Future Value and Compounding
0
1

2
3
4
5
*
4-*
Present Value and DiscountingHow much would an investor
have to set aside today in order to have $20,000 five years from
now if the current rate is 15%?
$20,000
PV
0
1
2
3
4

5
*
4-*
4.5 Finding the Number of Periods
If we deposit $5,000 today in an account paying 10%, how long
does it take to grow to $10,000?
*
It may be good at this point to discuss the difficulty of
calculating time periods and interest rates, particularly without
the help of a financial calculator.
Rule of 72 says that 72/r gives an estimate of the number of
periods it will take something (e.g., an investment) to double.
4-*
Assume the total cost of a college education will be $50,000
when your child enters college in 12 years. You have $5,000 to
invest today. What rate of interest must you earn on your
investment to cover the cost of your child’s education?
What Rate Is Enough?

About 21.15%.
*
4-*
Calculator KeysTexas Instruments BA-II PlusFV = future
valuePV = present valueI/Y = periodic interest rateP/Y must
equal 1 for the I/Y to be the periodic rateInterest is entered as a
percent, not a decimalN = number of periodsRemember to clear
the registers (CLR TVM) after each problemOther calculators
are similar in format
*
We are providing information on the Texas Instruments BA-II
Plus – other calculators are similar. We choose this calculator
since it is one that is allowable for use in taking the CFA exam
and TI provides a simulator software that can be used in class.
If you recommend or require a specific calculator other than
this one, you may want to make the appropriate changes.
Note: the more information students have to remember to enter,
the more likely they are to make a mistake. For this reason, I
normally tell my students to set P/Y = 1 and leave it that way.
Then I teach them to work on a period basis, which is consistent
with using the formulas. If you want them to use the P/Y
function, remind them that they will need to set it every time

they work a new problem and that CLR TVM does not affect
P/Y.
If students are having difficulty getting the correct answer,
make sure they have done the following:Set decimal places to
floating point (2nd Format, Dec = 9 enter) or show 4 to 5
decimal places if using and HPDouble check and make sure P/Y
= 1Make sure to clear the TVM registers after finishing a
problem (or before starting a problem). It is important to point
out that CLR TVM clears the FV, PV, N, I/Y and PMT registers.
C/CE and CLR Work DO NOT affect the TVM keys.
4-*
Multiple Cash Flows Consider an investment that pays $200
one year from now, with cash flows increasing by $200 per year
through year 4. If the interest rate is 12%, what is the present
value of this stream of cash flows?If the issuer offers this
investment for $1,500, should you purchase it?
*
4-*
Multiple Cash Flows
Present Value < Cost → Do Not Purchase

0
1
2
3
4
200
400
600
800
178.57
318.88
427.07
508.41
1,432.93
*
4-*
Valuing “Lumpy” Cash Flows
First, set your calculator to 1 payment per year.
Then, use the cash flow menu:
CF2
CF1

F2
F1
CF0
1
200
1
1,432.93
0
400
I
NPV
12
CF4
CF3
F4
F3
1
600
1
800
*
4-*
4.3 Compounding Periods
Compounding an investment m times a year for T years provides
for future value of wealth:
*

4-*
Compounding Periods
For example, if you invest $50 for 3 years at 12% compounded
semi-annually, your investment will grow to:
*
4-*
Effective Annual Rates of Interest
A reasonable question to ask in the above example is “what is
the effective annual rate of interest on that investment?”
The Effective Annual Rate (EAR) of interest is the annual rate
that would give us the same end-of-investment wealth after 3
years:
*
4-*
Effective Annual Rates of Interest
So, investing at 12.36% compounded annually is the same as
investing at 12% compounded semi-annually.

*
4-*
Effective Annual Rates of InterestFind the Effective Annual
Rate (EAR) of an 18% APR loan that is compounded
monthly.What we have is a loan with a monthly interest rate
rate of 1½%.This is equivalent to a loan with an annual interest
rate of 19.56%.
*
4-*
EAR on a Financial Calculator
Texas Instruments BAII Plus
keys:
description:
[2nd] [ICONV]
Opens interest rate conversion menu
[↓] [EFF=] [CPT]
19.56
[↓][NOM=] 18 [ENTER]

Sets 18 APR.
[↑] [C/Y=] 12 [ENTER]
Sets 12 payments per year
*
4-*
Continuous CompoundingThe general formula for the future
value of an investment compounded continuously over many
periods can be written as:
FV = C0×erT
Where
C0 is cash flow at date 0,
r is the stated annual interest rate,
T is the number of years, and
e is a transcendental number approximately equal to 2.718. ex
is a key on your calculator.
*
e is a transcendental number because it transcends the real
numbers.
4-*
4.4 SimplificationsPerpetuityA constant stream of cash flows
that lasts foreverGrowing perpetuityA stream of cash flows that
grows at a constant rate foreverAnnuityA stream of constant
cash flows that lasts for a fixed number of periodsGrowing
annuityA stream of cash flows that grows at a constant rate for
a fixed number of periods

*
4-*
Perpetuity
A constant stream of cash flows that lasts forever
…
0
1
C
2
C
3
C
*
4-*
Perpetuity: Example
What is the value of a British consol that promises to pay
£15 every year for ever?
The interest rate is 10-percent.

…
0
1
£15
2
£15
3
£15
*
4-*
Growing Perpetuity
A growing stream of cash flows that lasts forever
…
0
1
C
2
C×(1+g)
3
C ×(1+g)2

*
4-*
Growing Perpetuity: Example
The expected dividend next year is $1.30, and dividends
are expected to grow at 5% forever.
If the discount rate is 10%, what is the value of this
promised dividend stream?
…
0
1
$1.30
2
$1.30×(1.05)
3
$1.30 ×(1.05)2
*
It is important to note to students that in this example the year 1
cash flow was given. If the current dividend were $1.30, then
we would need to multiply it by one plus the growth rate to
estimate the year 1 cash flow.

4-*
Annuity
A constant stream of cash flows with a fixed maturity
0
1
C
2
C
3
C
T
C
*
4-*
Annuity: Example
If you can afford a $400 monthly car payment, how much car
can you afford if interest rates are 7% on 36-month loans?
0
1

$400
2
$400
3
$400
36
$400
*
4-*
What is the present value of a four-year annuity of
$100 per year that makes its first payment two years from today
if the discount rate is 9%?
0 1 2 3 4 5
$100 $100 $100 $100
$323.97
$297.22
4-*

*
Ordinary Annuity vs. Annuity Due: It should be emphasized that
annuity factor tables (and the annuity factors in the formulas)
assumes that the first payment occurs one period from the
present, with the final payment at the end of the annuity’s life.
If the first payment occurs at the beginning of the period, then
FV’s have one additional period for compounding and PV’s
have one less period to be discounted. Consequently, you can
multiply both the future value and the present value by (1 + r)
to account for the change in timing. The values can also be
computed directly by changing the setting in the financial
calculator.
4-*
Growing Annuity
A growing stream of cash flows with a fixed maturity
0
1
C
2
C×(1+g)
3
C ×(1+g)2
T
C×(1+g)T-1

*
4-*
Growing Annuity: Example
A defined-benefit retirement plan offers to pay $20,000 per year
for 40 years and increase the annual payment by 3% each year.
What is the present value at retirement if the discount rate is
10%?
0
1
$20,000
2
$20,000×(1.03)
40
$20,000×(1.03)39
*
4-*

Growing Annuity: Example
You are evaluating an income generating property. Net rent is
received at the end of each year. The first year's rent is
expected to be $8,500, and rent is expected to increase 7% each
year. What is the present value of the estimated income stream
over the first 5 years if the discount rate is 12%?
$34,706.26
0 1 2 3 4 5
*
4-*
4.5 Loan AmortizationPure Discount Loans are the simplest
form of loan. The borrower receives money today and repays a

single lump sum (principal and interest) at a future
time.Interest-Only Loans require an interest payment each
period, with full principal due at maturity.Amortized Loans
require repayment of principal over time, in addition to required
interest.
*
4-*
Pure Discount LoansTreasury bills are excellent examples of
pure discount loans. The principal amount is repaid at some
future date, without any periodic interest payments.If a T-bill
promises to repay $10,000 in 12 months and the market interest
rate is 7 percent, how much will the bill sell for in the
market?PV = 10,000 / 1.07 = 9,345.79
*
Remind students that the value of an investment is the present
value of expected future cash flows.
1 N; 10,000 FV; 7 I/Y; CPT PV = -9,345.79
4-*
Interest-Only LoanConsider a 5-year, interest-only loan with a
7% interest rate. The principal amount is $10,000. Interest is
paid annually.What would the stream of cash flows be?Years 1
– 4: Interest payments of .07(10,000) = 700Year 5: Interest +
principal = 10,700This cash flow stream is similar to the cash
flows on corporate bonds, and we will talk about them in

greater detail later.
*
4-*
Amortized Loan with Fixed Principal PaymentConsider a
$50,000, 10 year loan at 8% interest. The loan agreement
requires the firm to pay $5,000 in principal each year plus
interest for that year.Click on the Excel icon to see the
amortization table
*
Sheet1YearBeginning BalanceInterest PaymentPrincipal
PaymentTotal PaymentEnding
Balance150,0004,0005,0009,00045,000245,0003,6005,0008,600
40,000340,0003,2005,0008,20035,000435,0002,8005,0007,8003
0,000530,0002,4005,0007,40025,000625,0002,0005,0007,00020
,000720,0001,6005,0006,60015,000815,0001,2005,0006,20010,
000910,0008005,0005,8005,000105,0004005,0005,4000
4-*
Amortized Loan with Fixed PaymentEach payment covers the
interest expense plus reduces principalConsider a 4 year loan
with annual payments. The interest rate is 8% ,and the principal
amount is $5,000.What is the annual payment?4 N8 I/Y5,000
PVCPT PMT = -1,509.60Click on the Excel icon to see the
amortization table

*
Sheet1YearBeginning BalanceTotal PaymentInterest
PaidPrincipal PaidEnding
Balance15,000.001,509.60400.001,109.603,890.4023,890.401,5
09.60311.231,198.372,692.0332,692.031,509.60215.361,294.24
1,397.7941,397.791,509.60111.821,397.780.01Totals6,038.401,
038.414,999.99Note: The ending balance of .01 is due to
rounding. The last payment would actually be 1,509.61.
4-*
4.6 What Is a Firm Worth?Conceptually, a firm should be worth
the present value of the firm’s cash flows.The tricky part is
determining the size, timing, and risk of those cash flows.
*
4-*
Quick QuizHow is the future value of a single cash flow
computed?How is the present value of a series of cash flows
computed.What is the Net Present Value of an investment?What
is an EAR, and how is it computed?What is a perpetuity? An
annuity?
*

05.1
000,10$
r
C
PV
1
1
81.23$
81.523,9$500,9$
05.1
000,10$
500,9$
NPV
NPV
NPV
10.1$
4
23.4$
5
92.5$
2
16.2$
54.1$
3
02.3$

5
)15.1(
000,20$
T
rCFV )1(
0
T
2
000,5$
000,10$
T
T
years 27.7
0953.0
6931.0
)10.1ln(
)2ln(
T
rCFV )1(
0
12
10
000,5$
000,50$
)1(
12
121

2115.12115.1110
121
Tm
m
r
CFV
0
93.70$)06.1(50$
2
12.
150$
6
32
FV
93.70$)06.1(50$)
2
12.

1(50$
632
FV
93.70$)1(50$
3
93.70$)1(50$
3
50$
93.70$
)1(
3
1236.1
50$
93.70$
31
1956.1)015.1(
12
18.
11
12
12

m
m
r
32
)1()1()1( r
C
r
C
r
C
PV
r
C
£150
10.

£15
3
2
2
)1(
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gC
r
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r
C
PV
gr
C
PV
00.26$
05.10.
30.1$

T
r
C
r
C
r
C
r
C
PV
)1()1()1()1(
32
T
rr
C
PV
)1(
1
1

59.954,12$
)1207.1(
1
1
12/07.
400$
36
22.297$
09.1
97.327$
0
97.323$
)09.1(
100$
)09.1(
100$
)09.1(
100$
)09.1(
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)09.1(
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4321
4
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T
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PV
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1
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C
PV
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57.121,265$
10.1
03.1
1
03.10.
000,20$
40

500,8$
2
)07.1(500,8$
095,9$
65.731,9$
3
)07.1(500,8$
87.412,10$
4
)07.1(500,8$
77.141,11$

McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc.
All rights reserved.
Financial Statements Analysis and Financial Models
Chapter 3
*
3-*
Key Concepts and SkillsKnow how to standardize financial
statements for comparison purposesKnow how to compute and
interpret important financial ratiosBe able to develop a financial
plan using the percentage of sales approachUnderstand how
capital structure and dividend policies affect a firm’s ability to
grow
*
3-*
Chapter Outline
3.1 Financial Statements Analysis
3.2 Ratio Analysis
3.3 The DuPont Identity
3.4 Financial Models
3.5 External Financing and Growth

3.6 Some Caveats Regarding Financial Planning Models
*
3-*
3.1 Financial Statements AnalysisCommon-Size Balance
SheetsCompute all accounts as a percent of total
assetsCommon-Size Income StatementsCompute all line items
as a percent of salesStandardized statements make it easier to
compare financial information, particularly as the company
grows.They are also useful for comparing companies of
different sizes, particularly within the same industry.
*
3-*
3.2 Ratio AnalysisRatios also allow for better comparison
through time or between companies.As we look at each ratio,
ask yourself:How is the ratio computed?What is the ratio trying
to measure and why?What is the unit of measurement?What
does the value indicate?How can we improve the company’s
ratio?
*

3-*
Categories of Financial RatiosShort-term solvency or liquidity
ratiosLong-term solvency or financial leverage ratiosAsset
management or turnover ratiosProfitability ratiosMarket value
ratios
*
The ratios in the following slides will be computed using the
2012 information from the Balance Sheet (Table 3.1) and
Income Statement (Table 3.4) given in the text.
3-*
Computing Liquidity RatiosCurrent Ratio = CA / CL708 / 540 =
1.31 timesQuick Ratio = (CA – Inventory) / CL(708 - 422) / 540
= .53 timesCash Ratio = Cash / CL98 / 540 = .18 times
*
The firm is able to cover current liabilities with it’s current
assets by a factor of 1.3 to 1. The ratio should be compared to
the industry – it’s possible that this industry has a substantial
amount of cash flow and that they can meet their current
liabilities out of cash flow instead of relying solely on the
liquidation of current assets that are on the books.
The quick ratio is quite a bit lower than the current ratio, so
inventory seems to be an important component of current assets.
This company carries a low cash balance. This may be an
indication that they are aggressively investing in assets that will
provide higher returns. We need to make sure that we have
enough cash to meet our obligations, but too much cash reduces

the return earned by the company.
3-*
Computing Leverage RatiosTotal Debt Ratio = (TA – TE) /
TA(3588 - 2591) / 3588 = 28%Debt/Equity = TD / TE(3588 –
2591) / 2591 = 38.5%Equity Multiplier = TA / TE = 1 + D/E1 +
.385 = 1.385
*
Note that these are often called solvency ratios.
TE = total equity, and TA = total assets. The numerator in the
total debt ratio could also be found by adding all of the current
and long-term liabilities.
The firm finances approximately 28% of its assets with debt.
Another way to compute the D/E ratio if you already have the
total debt ratio:
D/E = Total debt ratio / (1 – total debt ratio) = .28 / .72 = .39
Note the rounding error as compared to the direct method
applied in the slide.
The EM is one of the ratios that is used in the Du Pont Identity
as a measure of the firm’s financial leverage.
3-*
Computing Coverage RatiosTimes Interest Earned = EBIT /
Interest691 / 141 = 4.9 timesCash Coverage = (EBIT +
Depreciation + Amortization) / Interest(691 + 276) / 141 = 6.9
times

*
Remember that depreciation (and amortization) is a non-cash
deduction. A better indication of a firm’s ability to meet
interest payments may be to add back the depreciation and
amortization to get an estimate of cash flow before taxes.
You can also calculate a type of inverse value as follows:
Interest Bearing Debt / EBITDA = (196 + 457) / 967 = .68
Values less than one are indicative of a stable position.
3-*
Computing Inventory RatiosInventory Turnover = Cost of
Goods Sold / Inventory1344 / 422 = 3.2 timesDays’ Sales in
Inventory = 365 / Inventory Turnover365 / 3.2 = 114 days
*
Inventory turnover can be computed using either ending
inventory or average inventory when you have both beginning
and ending figures. It is important to be consistent with
whatever benchmark you are using to analyze the company’s
strengths or weaknesses.
It is also important to consider seasonality in sales. If the
balance sheet is prepared at a time when there is a large
inventory build-up to meet seasonal demand, then the inventory
turnover will be understated and you might believe that the
company is not performing as well as it is. On the other hand, if
the balance sheet is prepared when inventory has been drawn
down due to seasonal sales, then the inventory turnover would
be overstated and the company may appear to be doing better
than it really is. Averages using annual data may not fix this

problem. If a company has seasonal sales, you may want to look
at quarterly averages to get a better indication of turnover.
3-*
Computing Receivables RatiosReceivables Turnover = Sales /
Accounts Receivable2311 / 188 = 12.3 timesDays’ Sales in
Receivables = 365 / Receivables Turnover365 / 12.3 = 30 days
*
Technically, the sales figure should be credit sales. This is often
difficult to determine from the income statements provided in
annual reports. If you use total sales instead of credit sales, you
will overstate your turnover level. You need to recognize this
bias when credit sales are unavailable, particularly if a large
portion of the sales are cash sales.
As with inventory turnover, you can use either ending
receivables or an average of beginning and ending.
You also run into the same seasonal issues as discussed with
inventory.
Probably the best benchmark for days’ sales in receivables is
the company’s credit terms. If the company offers a discount
(1/10 net 30), then you would like to see days’ sales in
receivables less than 30. If the company does not offer a
discount (net 30), then you would like to see days’ sales in
receivables close to the net terms. If days’ sales in receivables
is substantially larger than the net terms, then you first need to
look for biases, such as seasonality in sales. If this does not
provide an explanation for the difference, then the company
may need to take another look at its credit policy (who it grants
credit to and its collection procedures).

3-*
Computing Total Asset TurnoverTotal Asset Turnover = Sales /
Total Assets2311 / 3588 = .64 timesIt is not unusual for TAT <
1, especially if a firm has a large amount of fixed assets.
*
Having a TAT of less than one is not a problem for most firms.
Fixed assets are expensive and are meant to provide sales over a
long period of time. This is why the matching principle
indicates that they should be depreciated instead of immediately
expensed.
This is one of the ratios that will be used in the Du Pont
identity.
3-*
Computing Profitability MeasuresProfit Margin = Net Income /
Sales363 / 2311 = 15.7%Return on Assets (ROA) = Net Income
/ Total Assets363 / 3588 = 10.1%Return on Equity (ROE) = Net
Income / Total Equity363 / 2591 = 14.0%EBITDA Margin =
EBITDA / Sales967 / 2311 = 41.8%
*
You can also compute the gross profit margin and the operating
profit margin.
GPM = (Sales – COGS) / Sales
OPM = EBIT / Sales
Profit margin is one of the components of the Du Pont identity

and is a measure of operating efficiency. It measures how well
the firm controls the costs required to generate the revenues. It
tells how much the firm earns for every dollar in sales. In the
example, the firm earns almost $0.16 for each dollar in sales.
Note that the ROA and ROE are returns on accounting numbers.
As such, they are not directly comparable with returns found in
the marketplace. ROA is sometimes referred to as ROI (return
on investment). As with many of the ratios, there are variations
in how they can be computed. The most important thing is to
make sure that you are computing them the same way as the
benchmark you are using.
ROE will always be higher than ROA as long as the firm has
debt (and ROA is positive). The greater the leverage, the larger
the difference will be. ROE is often used as a measure of how
well management is attaining the goal of owner wealth
maximization. The Du Pont identity is used to identify factors
that affect the ROE.
3-*
Computing Market Value MeasuresMarket Capitalization = $88
per share x 33 million shares = 2904 millionPE Ratio = Price
per share / Earnings per share88 / 11 = 8 timesMarket-to-book
ratio = market value per share / book value per share88 / (2591 /
33) = 1.12 timesEnterprise Value (EV) = Market capitalization
+ Market value of interest bearing debt – cash2904 + (196 +
457) – 98 = 3465EV Multiple = EV / EBITDA3465 / 967 = 3.6
times
*
See Table 3.6, as well as the instructor’s manual (chapter 3
appendix), for a summary list of financial ratios.

3-*
Using Financial StatementsRatios are not very helpful by
themselves: they need to be compared to somethingTime-Trend
AnalysisUsed to see how the firm’s performance is changing
through timePeer Group AnalysisCompare to similar companies
or within industriesSIC and NAICS codes
*
SIC codes have been used many years to identify industries and
allow for comparison with industry average ratios. The SIC
codes are limited, however, and have not kept pace with a
rapidly changing environment. Consequently, the North
American Industry Classification System was introduced in
1997 to alleviate some of the problems with SIC codes.
Click on the web surfer to go the NAICS home page. It provides
information on the change to the NAICS and conversion
between SIC and NAICS codes.
3-*
3.3 The DuPont IdentityROE = NI / TEMultiply by 1 and then
rearrange:ROE = (NI / TE) (TA / TA)ROE = (NI / TA) (TA /
TE) = ROA * EMMultiply by 1 again and then rearrange:ROE =
(NI / TA) (TA / TE) (Sales / Sales)ROE = (NI / Sales) (Sales /
TA) (TA / TE)ROE = PM * TAT * EM
*

3-*
Using the DuPont IdentityROE = PM * TAT * EMProfit margin
is a measure of the firm’s operating efficiency – how well it
controls costs.Total asset turnover is a measure of the firm’s
asset use efficiency – how well it manages its assets.Equity
multiplier is a measure of the firm’s financial leverage.
*
Improving our operating efficiency or our asset use efficiency
will improve our return on equity. If the TAT is low compared
to our benchmark, then we can break it down into more detail
by looking at inventory turnover and receivables turnover. If
those areas are strong, then we can look at fixed asset turnover
and cash management.
We can also improve our ROE by increasing our leverage – up
to a point. Debt affects a lot of other factors, including profit
margin, so we have to be a little careful here. We want to make
sure we have enough debt to utilize our interest tax credit
effectively, but we don’t want to overdo it.
3-*
Calculating the DuPont IdentityROA = 10.1% and EM =
1.39ROE = 10.1% * 1.385 = 14.0%PM = 15.7% and TAT =
0.64ROE = 15.7% * 0.64 * 1.385 = 14.0%
*

3-*
Potential ProblemsThere is no underlying theory, so there is no
way to know which ratios are most relevant.Benchmarking is
difficult for diversified firms.Globalization and international
competition makes comparison more difficult because of
differences in accounting regulations.Firms use varying
accounting procedures.Firms have different fiscal
years.Extraordinary, or one-time, events
*
3-*
3.4 Financial ModelsInvestment in new assets – determined by
capital budgeting decisionsDegree of financial leverage –
determined by capital structure decisionsCash paid to
shareholders – determined by dividend policy
decisionsLiquidity requirements – determined by net working
capital decisions
*
3-*
Financial Planning IngredientsSales Forecast – many cash flows
depend directly on the level of sales (often estimate sales
growth rate)Pro Forma Statements – setting up the plan as
projected (pro forma) financial statements allows for
consistency and ease of interpretationAsset Requirements – the

additional assets that will be required to meet sales
projectionsFinancial Requirements – the amount of financing
needed to pay for the required assetsPlug Variable – determined
by management decisions about what type of financing will be
used (makes the balance sheet balance)Economic Assumptions –
explicit assumptions about the coming economic environment
*
3-*
Percent of Sales ApproachSome items vary directly with sales,
others do not.Income StatementCosts may vary directly with
sales - if this is the case, then the profit margin is
constantDepreciation and interest expense may not vary directly
with sales – if this is the case, then the profit margin is not
constantDividends are a management decision and generally do
not vary directly with sales – this affects additions to retained
earnings
*
3-*
Percent of Sales ApproachBalance SheetInitially assume all
assets, including fixed, vary directly with sales.Accounts
payable also normally vary directly with sales.Notes payable,
long-term debt, and equity generally do not vary with sales
because they depend on management decisions about capital
structure.The change in the retained earnings portion of equity

will come from the dividend decision.External Financing
Needed (EFN)The difference between the forecasted increase in
assets and the forecasted increase in liabilities and equity.
*
3-*
Percent of Sales and EFNExternal Financing Needed (EFN) can
also be calculated as:
*
The first term measures the increase in assets, which is based on
the capital intensity ratio. The second and third terms capture
the increase in liabilities and equity, respectively.
3-*
3.5 External Financing and GrowthAt low growth levels,
internal financing (retained earnings) may exceed the required
investment in assets.As the growth rate increases, the internal
financing will not be enough, and the firm will have to go to the
capital markets for financing.Examining the relationship
between growth and external financing required is a useful tool
in financial planning.
*

3-*
The Internal Growth RateThe internal growth rate tells us how
much the firm can grow assets using retained earnings as the
only source of financing.Using the information from the
Hoffman Co.ROA = 66 / 500 = .132b = 44/ 66 = .667
*
The information for these calculations is given in Table 3.13.
This firm could grow assets at 9.65% without raising additional
external capital.
Relying solely on internally generated funds will increase
equity (retained earnings are part of equity) and assets without
an increase in debt. Consequently, the firm’s leverage will
decrease over time. If there is an optimal amount of leverage, as
we will discuss in later chapters, then the firm may want to
borrow to maintain that optimal level of leverage. This idea
leads us to the sustainable growth rate.
3-*
The Sustainable Growth RateThe sustainable growth rate tells
us how much the firm can grow by using internally generated
funds and issuing debt to maintain a constant debt ratio.Using
the Hoffman Co.ROE = 66 / 250 = .264b = .667
*
Note that no new equity is issued.
The sustainable growth rate is substantially higher than the

internal growth rate. This is because we are allowing the
company to issue debt as well as use internal funds.
Commonly, sustainable growth is calculated as only the
numerator of our formula (ROE * b), but this assumes we
calculate ROE based on beginning, rather than ending, equity.
3-*
Determinants of GrowthProfit margin – operating
efficiencyTotal asset turnover – asset use efficiencyFinancial
leverage – choice of optimal debt ratioDividend policy – choice
of how much to pay to shareholders versus reinvesting in the
firm
*
The first three components come from the ROE and the Du Pont
identity.
It is important to note at this point that growth is not the goal of
a firm in and of itself. Growth is only important so long as it
continues to maximize shareholder value.
3-*
3.6 Some CaveatsFinancial planning models do not indicate
which financial polices are the best.Models are simplifications
of reality, and the world can change in unexpected
ways.Without some sort of plan, the firm may find itself adrift
in a sea of change without a rudder for guidance.

*
3-*
Quick QuizHow do you standardize balance sheets and income
statements?Why is standardization useful?What are the major
categories of financial ratios?How do you compute the ratios
within each category?What are some of the problems associated
with financial statement analysis?
*
3-*
Quick QuizWhat is the purpose of financial planning?What are
the major decision areas involved in developing a plan?What is
the percentage of sales approach?What is the internal growth
rate?What is the sustainable growth rate?What are the major
determinants of growth?
*
565$
)667.0125013.0()2503.0()2503(
)1(Sales) Projected(ΔSales
Sales
LiabSpon
Sales
Sales
Assets

dPM
%65.9
0965.
667.132.1
667.132.
bROA - 1
bROA
RateGrowth Internal
%4.21
214.
667.264.1
667.264.
bROE-1
bROE
RateGrowth eSustainabl

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