AFN and Growth
AFN=Increase in total assets –Addition to Retained
earnings, where p is profit margin; S sales.
Internal financing = Addition to retained earnings =
Projected net income × retention ratio (R) = Profit
margin (p) × projected sales[S×(1+g)] × retention
ratio
or
or
AFN = A×g – p×S×R×(1+g)
Internal growth rate = ROA×R/(1-ROA×R)
1
AFN
example (1)
•ROSENGARTEN CORPORATION
Initial income statement
Sales
$1,000
Costs
800(80%)
Taxable Income
$200
Taxes
68
Net Income
$132(13.2%)p
Addition to retained
earnings
$88
Dividends
$44
2
(2)
Dividend payout ratio = Cash dividends/Net income
= $ 44/$132 *100= 331/3%
Retention ratio (plowback ratio) = Retained
earnings/Net income = $88/$132*100 = 662/3%
or retention ratio = 1- dividend payout ratio =
1-0.333 = 0.667
3
(3)
Pro forma income statement (25% sales increase)
Sales
$1,250
Costs
1000(80%)
Taxable income
$250
Taxes
85
Net income
$165(13.2%) p
Projected addition to retained earnings = 165*0.667
Projected dividends paid to shareholders =165*0.333
Net income
=165
4
(4)
Assets
Current assets
Cash
A/R
Inventory
Total
Fixed assets
Net plant and
equipment
Total assets
ROSENGARTEN CORPORATION`
Balance sheet
Liabilities and Owner's
Equity
Current liabilities
$160
A/P
$300
440
Notes payable
100
600
Total
$400
$1,200
Long-term debt
$800
Owner's equity
Common stock
$800
Retained
$1,800
earnings
1,000
Total
$1,800
$3,000
Total liabilities
and shareholder's
equity
$3,000
5
(5)
ROSENGARTEN CORPORATION
Pro forma balance sheet after 25% sales increase
($)
(Δ,$)
Assets
Current assets
Cash
A/R
Inventory
Total
$200
$40
550
750
$1,500
110
150
$300
Fixed assets
Net plant and
equipment
$2,250
$450
Total assets
$3,750
$750
($)
(Δ,$)
Liabilities and Owner's Equity
Current liabilites
A/P
$375
$75
Notes payable
Total
100
$475
0
$75
Long-term debt
Owner's equity
Common stock
Retained earnings
Total
Total liabilities and
shareholder's equity
External financing
needed
$800
$0
$800
1,100
$1,910
$0
110
$110
$3,185
$185
$565
6
Example (1)
AFN = A×g – p×S×R×(1+g)-A/P*g
=3000*.25-13.2%*1,000 0.667*1.25-300*.25
= 750-.132*1,000*.667*1.25-75=565
Internal growth rate = ROA×R/(1-ROA×R)
=132/3000*.667/(1- 132/3000*.667)
=.044*.667/(1-0.293)=3.02%
7
Financial Policy and Growth
A firm may not wish to sell any new equity
Debt capacity = the ability to borrow to increase
firm value
If a firm borrows to its debt capacity sustainable
growth rate can be achieved
g* = ROE×R/(1-ROE×R)
8
Breakeven Computation
For the proposal to break even, Unilate must sell 57
million units or $855.6 million of product.
9
10
Learning Outcomes
Chapter 8
Explain what it means to take risks when investing.
Compute the risk and return of an investment, and explain how the risk
and return of an investment are related.
Identify relevant and irrelevant risk and, explain how irrelevant risk can
be reduced.
Describe how to determine the appropriate reward – that is, risk
premium – that investors should earn for purchasing a risky investment.
Describe actions that investors take when the return they require to
purchase an investment is different from the return they expect the
investment to produce.
Indentify different types of risk and classify each as relevant or irrelevant
with respect to determining an investment’s required rate of return.
11
Defining and Measuring Risk
Risk is the chance that an unexpected
outcome will occur
A probability distribution is a listing of all
possible outcomes with a probability assigned
to each
12
Probability Distributions
It either will rain, or it will not.
Only two possible outcomes.
Outcome (1)
Rain
Probability (2)
0.40
= 40%
No Rain
0.60
1.00
= 60%
100%
13
Probability Distributions
Martin Products and U. S. Electric
14
Expected Rate of Return
Rate of return expected to be realized from
an investment during its life
Mean value of the probability distribution of
possible returns
Weighted average of the outcomes, where
the weights are the probabilities
15
Expected Rate of Return
16
Measuring Risk: The Standard Deviation
17
Measuring Risk: The Standard Deviation
Calculating Martin Products’ Standard Deviation
18
Measuring Risk: Coefficient of Variation
Calculated as the standard deviation divided by
the expected return
Useful where investments differ in risk and
expected returns
19
Risk Aversion and Required Returns
Risk-averse investors require higher rates of
return to invest in higher-risk securities
Risk Premium (RP):
 The portion of the expected return that can be
attributed to an investment’s risk beyond a riskless
investment
 The difference between the expected rate of
return on a given risky asset and that on a less
risky asset
20
Risk/Return Relationship
21
Portfolio Returns
Expected return on a portfolio, rˆp
The weighted average expected return on the
stocks held in the portfolio

22
Portfolio Returns
Realized rate of return, r
 The return that is actually earned
 Actual return usually different from expected
return
23
Portfolio Risk
Correlation Coefficient, 
 Measures the degree of relationship between two
variables.
 Perfectly correlated stocks have rates of return
that move in the same direction.
 Negatively correlated stocks have rates of return
that move in opposite directions.
 http://www.youtube.com/watch?v=35NWFr53cgA
24
Portfolio Risk
Risk Reduction
 Combining stocks that are not perfectly correlated
will reduce the portfolio risk through
diversification.
 The riskiness of a portfolio is reduced as the
number of stocks in the portfolio increases.
 The smaller the positive correlation, the lower the
risk.
25
General Results
Portfolio Variance
Number of Securities
Source: Adapted by Edwin J. Elton and Martin J. Gruber, “Risk Production and Portfolio Size: An Analytical Solution,” Journal of
Business, October 1977, 415–437.
26
Firm-Specific Risk versus Market Risk
Firm-Specific Risk:
 That part of a security’s risk associated with
random outcomes generated by events, or
behaviors, specific to the firm.
 Firm-specific risk can be eliminated through
proper diversification.
27
Firm-Specific Risk versus Market Risk
Market Risk:
 That part of a security’s risk that cannot be
eliminated through diversification because it is
associated with economic, or market factors that
systematically affect all firms.
28
Firm-Specific Risk versus Market Risk
Relevant Risk:
 The risk of a security that cannot be diversified
away, or its market risk.
 This reflects a security’s contribution to a
portfolio’s total risk.
29
The Concept of Beta
Beta Coefficient, :
 A measure of the extent to which the returns on a
given stock move with the stock market
  = 0.5: Stock is only half as volatile, or risky, as the
average stock.
  = 1.0: Stock has the same risk as the average risk.
  = 2.0: Stock is twice as risky as the average stock.
 Covariance of itself (A with A) is variance.
30
Portfolio Beta Coefficients
The beta of any set of securities is the
weighted average of the individual securities’
betas
31
Risk Premium for a Stock
32
The Required Rate of Return for a Stock
33
Capital Asset Pricing Model (CAPM)
A model used to determine the required return on an
asset, which is based on the proposition that any
asset’s return should be equal to the risk-free return
plus a risk premium that reflects the asset’s
nondiversifiable risk.
34
Security Market Line (SML):
The line that shows the relationship between
risk as measured by beta and the required
rate of return for individual securities.
35
Security Market Line (SML):
36
The Impact of Inflation
rRF is the price of money to a riskless
borrower.
The nominal rate consists of:
 a real (inflation-free) rate of return, and
 an inflation premium (IP).
An increase in expected inflation would
increase the risk-free rate.
37
Changes in Risk Aversion
The slope of the SML reflects the extent to
which investors are averse to risk.
An increase in risk aversion increases the risk
premium and increases the slope.
38
Changes in a Stock’s Beta Coefficient
The Beta risk of a stock is affected by:
 composition of its assets
 use of debt financing
 increased competition
 expiration of patents
Any change in the required return (from
change in beta or in expected inflation)
affects the stock price.
39
Stock Market Equilibrium
The condition under which the expected
return on a security, r, is just equal to its
required return, r̂
Actual market price equals its intrinsic value
as estimated by the marginal investor,
leading to price stability
40
Changes in Equilibrium Stock Prices
Stock prices are not constant due to changes
in:
 Risk-free rate, rRF,
 Market risk premium, rM – rRF,
 Stock X’s beta coefficient, x,
 Stock X’s expected growth rate, gX, and
 Changes in expected dividends, D0.
41
Physical Assets Versus Securities
Riskiness of corporate assets is only relevant
in terms of its effect on the stock’s risk.
42
Word of Caution
CAPM
 Based on expected conditions
 Only have historical data
 As conditions change, future volatility may differ
from past volatility
 Estimates are subject to error
43
Different Types of Risk
Systemic Risks
 Interest rate
 Inflation
 Maturity
 Liquidity
 Exchange rate
 Political
44
Different Types of Risk
Unsystemic Risks
 Business
 Financial
 Default
Combined Risks
 Total
 Corporate
45