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Summary - Fundamentals of Corporate Finance
Finance (Đại học Kinh tế Quốc dân)
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Topic 1: Overview of Financial Management
Corporate finance answers 3 main questions:
-What long-term investments (Capital Budgeting)
-Where to get long-term financing (Capital Stru cture)
-How to manage everyday financial activities: collecting
and paying (Working Capital Management)
Financial leverage: degree to which a firm is utilizing
borrowed money. Higher FL  higher risk of bankruptcy.
Goal of FIN mgmt is to maximize the current market value
per share of existing stock, i.e. maximize firm’s value
(shareholder wealth maximization).
Agency problem: Conflict of interest between principal &
agent. Results in direct & indirect agency costs.
Indirect: Lost opportunities that would ↑ firm’s value in
LR if accepted | Direct: Corporate expenditures that
benefit management (e.g. large offices, high pay),
Monitoring cost (e.g. audits)
Whether managers act in shareholders’ best interest
depends on 1) compensation plans tied to share value, 2)
direct intervention by shareholders, 3) threat of firing, 4)
threat of takeover, 5) awareness of good corp governance.
Roles in Organizations
Treasurer: cash mgmt, credit mgmt, capital expenditures
(budgeting), financial planning, |Controller: taxes, cost
acct’g, financial acct’g & data processing. Acct’g, Tax Dept.
Financial Markets
Primary: original sale of securities by govts & corporations
(market for new issues) | Secondary: securities bought &
sold after original sale (means of transferring ownership)
Topic 2: Financial Statement Analysis
Mkt value of shareholders’ equity (mkt capitalization) =
share price x no. of o/s shares = MV of firm – MV of debt
Enterprise value = Market value of equity + debt - cash
Operating cash flow = EBIT + depreciation – taxes
Net capital spending = Ending net fixed assets – beginning
net fixed assets + depreciation
Net working capital = CA – CL
Cash flow to creditors = interest paid – net new
borrowing (∆ in long-term debt)
Cash flow to stockholders = dividends paid – net new
equity raised (∆ in common stock and paid-in surplus)
CFFA (Free cash flows) refer to the cash flow in excess of
that required to fund profitable capital projects.
CFFA (Free cash flows) = OCF – net capital spending –
∆NWC = Cashflow to creditors + cashflow to stockholders
Common-size balance sheets (income statements):
compute all accounts as a % of total assets (% of sales).
Liquidity ratios measure firm’s ability to pay SR bills.
Current ratio = CA/CL
Quick ratio = (CA-inventory)/CL
Cash ratio = Cash/CL
NWC to total assets = NWC/TA
Interval measure = CA/average daily operating costs
Solvency ratios show how heavily a company is in debt.
Debt ratio = Total liabilities/TA
Debt-equity ratio = Total liabilities/TE = (TA-TE)/TE
Equity multiplier = TA/TE = 1 + debt-equity ratio
Long-term debt ratio = LT debt/(LT debt + total equity)
Times interest earned ratio = EBIT/interest expense
Cash coverage ratio = (EBIT + depreciation)/interest exp
Asset management ratios measure how productively a
firm is using its assets.
Inventory turnover = COGS/average inventory
Days’ sales in inventory = 365/inventory turnover
Receivables turnover = Credit sales/receivables balance
Days’ sales outstanding = Accounts receivable/average
daily sales = 365/receivables turnover
FA turnover = Sales/net fixed assets
TA turnover = Sales/total assets
Profitability ratios measure how successfully a business
earns a return on its investment.
Profit margin = Net income/sales
Basic earning power (BEP) = EBIT/total assets
ROA = Net income/total assets
ROE = Net income/total equity
ROE doesn’t consider risk, nor amt of capital invested. Focuses only
on return. Might encourage managers to make investment
decisions that don’t benefit shareholders.
Market value ratios provide indications on firm’s
prospects and how the market values the firm.
Price-earnings ratio = Market price per share/EPS
EPS = Net income/no. of outstanding shares
Market to book Ratio = Mkt value per share/Book value
per share = Mkt value of equity/Book value of equity
The Du Pont Identity
Difference between ROA and ROE is a reflection of the use
of debt financing/financial leverage
ROE = Profit Margin x Total Asset turnover x Equity
Multiplier = ROA x Equity Multiplier
PM measures firm’s operating efficiency and cost control (How
much net profit is a firm generating per dollar of sales? ) | TATO
measures firm’s asset use efficiency (How many sales dollars has
the firm generated per each dollar of assets?) | Equity multiplier
measures firm’s financial leverage (How many dollars of assets has a
firm acquired per each dollar in shareholders' equity?)
Topic 3: Time value of money
Future Value: amount of money an investment will grow
to over a period of time given interest rate
Compounding: accumulative interest on an investment
over time to earn more interest
FV = PV x (1+r)^t
In future value problems, the compound (interest) rate is
adjusted upward to reflect higher risk and to increase
the future cash flows.
Present Value (discounted cash flow valuation): current
value of future cash flows discounted at discount rate
PV = FV/(1+r)^t
For a given amt to be received at a given time period in
the future, higher interest rate  lower PV of amt.
For a given amt to be received in the future at a given
interest rate, longer time period  lower PV of amt.
Multiple cash flow receipts in the future: Find PV of each
individual cash flow and sum them.
Annuity PV = PMT x (1/r) x (1-[1/(1+r)^t])
PV Annuity due = Annuity PV x (1+r) [Set calc to BGN mode]
Perpetuity PV = Periodic payment amt/r
Implied discount rate i = (FV/PV)^(1/n) – 1
EAR and APR
APR = Stated/quoted interest rate = Period rate x no. of
periods per year. EAR is the interest rate expressed as if it
were compounded once per year
To find EAR:
1) Find FV of principal sum = PV x (1+i)^n
2) EAR = (FV – principal)/Principal
i.e. EAR = [1 + (APR/n)]^n – 1
Capital gain yield = Capital gain/initial price = (P1-P0)/P0 = g
(constant dividend growth)
Approx. real rate of return = nom rate - inflation rate
Exact (1+ real rate) = (1+nom return)/(1+inflation rate)
Probability scenarios
Expected return = sum of (possible returns in each
scenario x probability of scenario occurring)
n
i.e.:
where wi= fraction of portfolio’s
dollar value invested in stock i, and
ri= possible return from stock i
r^ p =∑ wi r^ i
i =1
Variance = sum of (return in each scenario – expected
return)^2 times probability of scenario occurring
Standard deviation = square root of variance
Historical data scenarios
Expected return = arithmetic average return (what is
earned in a typical year)
Estimated variance using historical data = [sum of (actual
return in each historical year – arithmetic average
return)^2]/(n-1)
T
∑ rt
r̄ =
t=1
T
Arithmetic average
return
√
n
∑ ( r̄ t −r̄ Avg )2
t=1
Average annual return
(arithmetic mean)
n−1
Estimated variance
Coefficient of variation measures risk per unit of return.
CV = standard deviation/mean
Topic 5: Risk and Return II
Risk premium: additional return over and above risk-free
rate earned for taking on risk.
Expected portfolio return: compute by relative weights of
assets in the portfolio. (weights always add up to 1)
m
i.e.: r^ p =
∑ w j r^ j
j=1
Investment risk: diversifiable + non-diversifiable risk.
Diversifiable risk = nonsystematic risk = firm-specific risk
Non-diversifiable risk = systematic risk = market risk = β
A well-diversified portfolio (negatively correlated assets)
can eliminate diversifiable risk.
β = Cov(Ri , RM)/market variance
β(market) = 1 and β of a risk-free asset = 0.
But converse is not true; a β of 0 doesn’t always mean an
asset is risk-free. β = 0 simply means ROA equals Rf.
N = 60, I/Y = 5/12, PV
= 24,000, FV = 0
 PMT = -452.91
 Monthly payment
of $452.91 will yield
an EAR of 5.12%
(e.g. Housing loans,
biz term loans)
N = 60, PMT = -500, PV
= 24,000, FV = 0
 I/Y = 0.7629
 EAR = (1+0.7629%)12
-1 = 9.55%
(e.g. Hire purchase, car
loans)
N = 60, PMT = -400, PV
= 18,000, FV = 0
 I/Y = 0.9963
 EAR = (1+0.9963%)12
-1 = 12.63%
(e.g. Mortgage loans)
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1.
Find the monthly PMT
2.
Now n = 28 (60-32) & find new PV (loan amt o/s)
3.
To find proportion of principal and interest of 33rd
payment, PV32 x (5%/12) = interest portion.
Principal portion = original PMT – interest portion.
Topic 4: Risk and Return I
Intrinsic value: estimate of an asset’s worth based on PV
of expected future cash flows discounted at required ROR.
Market price: based on perceived information as seen by
the marginal investor (can be theoretically incorrect).
Total Percentage return = dividend yield + cap gain yield
Dividend yield = Dividend/initial share price = D1/P0
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β < 1 means asset has less systematic risk than market
(return < Rf  diversification instrument) and vice versa.
Higher β  higher systematic risk
Higher S.D  higher TOTAL risk
Risk premium on an asset is proportional to its β, i.e.
higher β means higher risk premium and thus higher
required returns on investment.
Impact of inflation on β: increase in inflation rate
increases required rate of return for a given value of β,
upward shift of entire security market line.
Impact of risk aversion: increase in inflation rate increases
required rate of return for a given value of β, inward skew
of security market line (pivot left from Rf y-intercept)
CAPM: Ri = Rf + βi(RM – Rf)
where Ri = required return on investment, Rf = risk-free rate, (RM –
Rf) = market risk premium
CAPM is an equation describing the SML. It depends on 1)
pure time value of money, 2) reward for bearing
systematic risk, and 3) amount of systematic risk.
SML plots return against risk. For underpriced asset,
expected return would be above the SML (req rr)j; for
overpriced asset, expected return would be below the
SML.
Reward-to-risk ratio:
Expected return on asset−risk free rat
Beta of asset
At equilibrium, if all securities are correctly priced, they
will have the same reward-to-risk ratio, and NPV = 0.
Topic 6: Bond Valuation
Coupon: a bond’s periodic interest payment. Coupon amt
= (Coupon rate x par value)/no. of payments per year.
Coupon rate: annual coupon divided by par value of bond
Coupon rate of debenture > secured debt, subordinated debenture >
senior debt, bond w/o sinking fund > bond with sinking fund, noncallable bond > callable bond.
Par: face value of the bond (or principal amt) assigned by
the issuer, this amt will be repaid at the end of the term
(it is generally $1,000 unless otherwise stated)
Maturity: specific date on when the principal amt is paid
Term: the time remaining until the payment date
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Callability: a feature whereby the issuer can redeem the
bond before it matures. From the corporate perspective,
callable bonds may have value over non-callable bonds as
corporation has the option to call the bond if the I/R falls.
Seniority: preference in position over other lenders, and
debts are sometimes labeled as senior or junior to
indicate seniority  some debts are subordinated
Debenture: a bond backed by issuer’s general credit and
ability to repay and not by an asset or collateral
Basis points: a measure of differences between yields or
I/R (1% = 100 basis points)
Convertibility: Option of exchanging a bond for a specific
amt of stock. Must occur at specific times, specific price
under specified conditions (detailed in bond indenture)
Protective covenants: the part of the indenture that limits
certain actions a company might otherwise wish to take
during the loan term (protect lender’s interests) Sinking
fund: provision to pay off a loan over its life rather than all
at maturity (similar to amortization)
bonds: disaster bonds, income bonds, convertible bonds,
put bonds (opposite of callable bonds). | Taxable Bonds:
Valuation of Bond
Bond value = PV of coupons + PV of par = PV annuity + PV
lump sum
PV of par value
Constant dividend (zero growth dividend; g=0)
Firm will pay a constant dividend forever  perpetuity.
Bond Value = C
PV annuity
factor
[ ]
1
1(1+k d )N
kd
Interest rate risk
The longer the bonds and the lower the coupon rates, the
more sensitive to i/r changes (higher interest rate risk)
Bond ratings
Bond ratings are an assessment of the creditworthiness of
the corporate issuer. They do not address I/R risk.
Investment-grade bonds are rated at least BBB or Baa.
Grade below BBB or Baa are low-grade or “junk” bonds.
Interest rate risk
The longer the bonds and the lower the coupon rates, the
more sensitive to i/r changes (higher interest rate risk)
Topic 7: Stock Valuation
Price of stock is the PV of all expected future dividends.
^ =
¿
t
D
F
(1+k d ) N
F = face value, kd = Req
rate of return on debt
PV of the coupons
Valuation of Bond at t=0
FV = par value (usu 1,000) | PMT = periodic coupon
payment | I/YR = discount rate | N = no. of periods
Valuation of Bond (finding price x years later)
same as above, except N = no. of periods left to maturity
Overall ROR = (Annual coupon + Bond price ∆)/Beg. price
Yield to Maturity (YTM)
The rate earned if bond is held to maturity. It is the I/R
required in the market on a bond (the rate which
discounts all future cash flows to their present value).
YTM includes not only the interest payments you will
receive all the way to maturity, but also takes into acct
any difference between the current par value of the bond
and the actual trading price of the bond at that time.
D
P
¿
P0 =
+
D
t+2
t+3
D∞
t +1
+
+
+. . .+
( 1+ r )∞
( 1+r )t + 1 ( 1+r )t +2 ( 1+r )t + 3
s
s
s
s
D1
re
where re= cost of equity-required
return of stockholders (usually
estimated using CAPM)
Constant dividend growth (stable growth)
Firm will increase the dividend by a constant percent
every period (firm assumed to grow at the rate equal to
economy’s LT nominal growth rate (inflation + real growth
in GDP).
D1 = D0 (1+g)1
D (1+g ) D1
D2 = D1(1+g)1= D0(1+g)2
P0 = 0
=
1
t
r e -g
r e -g
Dt=Dt-1(1+g) =D0(1+g)
Requires re > g
 If re < g  negative stock price
 If rs = g  stock price is infinite
Supernormal growth
Dividend growth is not consistent initially, but settles
down to constant growth eventually.
1) Compute dividends for each year until growth levels off.
2) Find expected future price when growth levels off.
3) Find PV of expected future cash flows.
To find YTM: Key in FV, PMT, N and PV (opposite sign!)
YTM = I/Y x no. of annual payments (e.g. quarterly = I/Y
x4)
I/R increase  PV decrease, and vice versa.
So as YTM increase, bond prices decrease, and vice versa.
Bonds of similar risk (and maturity) will be priced to yield
about the same return (YTM), regardless of coupon rate.
Current yield
Annual interest paid by a bond, expressed as a percentage
of its current market price. (-) does not take into account
any capital gain or loss associated with the principal to be
paid at maturity.
e.g. a $1,000 bond selling for $850 & paying an 8%
coupon rate has a current yield of $80/$850 = 9.41%
Discount/Premium
If discount rate rises above coupon rate, bond’s value falls
below par  bond sells at a discount.
If discount rate falls below coupon rate, bond’s value rises
above par  bond sells at a premium.
Bond selling at… satisfies this condition
Discount: coupon rate < current yield<YTM
Premium: coupon rate>current yield>YTM
Par value: coupon rate=current yield=YTM
e.g. if YTM < coupon rate, a bond will sell at a premium, &
increase in the market I/R will decrease this premium.
Other bond types
T-Bills: pure discount bonds with original maturity of 1
year or less | T-Notes: coupon debt with original maturity
between 1 and 10 years | T-Bonds: coupon debt with
original maturity greater than 10 years | Zero-Coupon
Bonds: make no periodic interest payments (coupon rate
= 0%). Entire YTM comes from the difference between the
purchase price & par value [1+YTMn= (Face
Value/Price)^(1/n)]| | Floating Rate Bonds (Floaters):
Coupon rate floats depending on some index value e.g.
adjustable rate mortgages and inflation-linked treasuries.
Less price risk. Coupons cannot go above a specified
“ceiling” or below a specified “floor”. | Other types of
Market equilibrium
Stock prices stable, no tendency to buy or sell.
Expected returns must equal required returns.
i.e. rE = (D1/P0) + g = Rf + βi(RM – Rf)
If expected return (calculated from dividends and price) is
greater than required return (from CAPM) then P0 is low
and people will buy. Thus P0 will go up and expected
return will fall until it equals req. return
Corporate Value Model (free cash flow method)

Find the market value (MV) of the firm, by finding
the PV of the firm’s future CFFAs.

Subtract MV of firm’s debt and preferred stock
[Vp=D/rp] to get MV of common stock

Divide market value of common stock by the
number of shares outstanding to get intrinsic stock
price (value) per share.
Topic 8: Capital Budgeting I
Capital budgeting refers to the process of deciding how to
allocate the firm’s scarce capital resources (land, labor,
capital) to its various investment alternatives. A capital
budget outlines the planned expenditure on fixed assets.
Good decision criteria takes into account TVM, adjusts for
risk and provides information whether we are creating
value for the firm.
NPV: The difference between the intrinsic value of a
project and its cost. If NPV > 0, means PV of cash inflows >
PV of cash outflows, project is expected to add value to
the firm and will therefore increase shareholders’ wealth.
Use NPV if there is a conflict between NPV and any other
rule. May have to estimate required return from CAPM.
n
∑
NPV =
t =1
¿
CF t
( 1+ k ) t
−CF 0
Accept project if NPV > 0.
¿
Payback period: The number of years to recover the initial
(nominal cost). Estimate future cash flows, add cash flows
to the initial investment until recovered. Divide the
remaining value of the investment by the last cash flow to
get fraction. Accept project if payback period < cutoff. (+)
Quick and easy to calculate and understand, adjusts for
uncertainty of later cash flows. (-) Biased towards
liquidity, ignores TVM, requires arbitrary cutoff, ignores
cash flows beyond cutoff, biased against long-term
projects e.g. R&D.
Discounted payback period: How long it takes to recover
the initial cost on a discounted basis. Divide the remaining
value of the investment by the last discounted cash flow
to get fraction. Accept project if discounted payback
period < cutoff. (+) Includes TVM, easy to understand,
does not accept estimated negative NPV investments. (-)
Same as payback period.
Average Acct’g Return: Average net income/Average book
value. Average book value depends on how asset is
depreciated. Accept project if AAR > preset rate. (+) Easy
to calculate, needed information usually available. (-) Not
a true rate of return, ignores TVM, uses an arbitrary
benchmark cutoff rate, based on accounting net income &
book values, not cash flows and intrinsic/market values.
Internal rate of return (IRR): The discount rate that makes
NPV = 0. Accept project if IRR > required return. (+) Best
alternative to NPV, intuitively appealing, based entirely on
estimated cash flows and independent of interest rates
found elsewhere. (-) More than 1 IRR solution for nonconventional cash flows, may not evaluate mutually
exclusive projects correctly. IRR assumes CFs are
reinvested as IRR, which is not as realistic as being
reinvested at company’s WACC.
NPV vs IRR generally lead to identical decisions if 1)
project cash flows are conventional (i.e. first CF –ve,
subsequent CFs +ve), & 2) projects are not mutually excl.
(i.e. CF of one is impacted by the acceptance of the other.)
I/YR = 0
CF0 = -165,000
CF1 = 63,120
CF2 = 70,800
CF3 = 91,080
<CPT><IRR>
Modified IRR (MIRR): The discount rate that causes the
PV of a project’s terminal value to equal the PV of costs.
TV is found by compounding inflows at WACC. Used when
there are non-conventional cash flows. Accept project if
MIRR > required return. (+) Correctly assumes
reinvestment at opportunity cost = WACC, avoids the
problem of multiple IRRs. (-) Not truly an internal rate of
return, no real need to consider reinvestment of CFs.
Profitability Index: Total PV of future CFs/Initial
investment. Measures benefit per unit cost based on
TVM. Accept project if PI > 1. (+) Useful when limited
capital, closely related to NPV and easy to understand. (-)
May lead to incorrect decisions in comparing mutually
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exclusive projects. (Total PV of future CFs = NPV of
project, rem to add back initial investment amount!)
equity generally don’t vary with sales as they are
conscious capital structure decisions by management.
Topic 9: Capital Budgeting II
Costs and benefits associated with a capital budgeting
project are measured in terms of cash flow rather than
earnings. CF must be incremental (firm’s CF with project firm’s CF without project), measured on an after-tax basis.
Stand-alone principle: Analyze each accepted project in
isolation from the other activities of the firm; “mini-firms”
with own assets, revenues and cost (firm = portfolio).
Determining if additional fixed assets are needed:
Calculate Capacity Sales (max. sales that can be supported
by current level of assets) = Current Sales/Current %
Operating Capacity. If Planned sales < Capacity sales, no
additional FA is required.
Types of CF
Sunk cost – costs that have been accrued in the past
(SHOULD BE EXCLUDED).
Opportunity cost – costs of lost options (RELEVANT)
Side effects – Externalities eg cannibalization (RELEVANT)
Changes in NWC – Year on year basis, ADD BACK NWC AT
PROJECT END. (RELEVANT)
AFN/EFN Equation method
AFN = (A*/S0)∆S – (L*/S0)∆S – M(S1)(RR)
Financial statement method: ∆N/P + ∆LT-Debt (no
interest exp, diff dividend payout, diff capital structure)
FA Requirement: Target ratio (%) = FA/Capacity sales
∆FA = Target ratio*∆Sales (additional sales)
Assumptions of AFN equation:

Firm operating at full capacity

Constant profit margin

Constant dividend payout ratio/RR
Recovery of NWC assumptions: Proj NOT sold at end of life, cash
portion of CA is retrieved, AR fully collected, all AP paid, remaining
inventory sold at cost.
Financing costs – Dividends, interest expense (IGNORE)
Taxes – depreciation reduces taxes (RELEVANT)
R&D/Marketing costs – extensive R&D effort results in a
new product (SHOULD BE EXCLUDED)
WACC = req. rate of return on debt * (1-Tax rate) * (TL/TA)
+ (req. rate of return on equity)*(TE/TA)  TA = TL + TE;
Tax rate = Marginal corporate tax rate; rE (from CAPM)
If excess capacity, sales will not change but assets will be
lower, turnovers better, less new debt, lower interest,
higher profits, EPS, ROE, improved TIE and debt ratio.
Since no FA is needed, AFN – projected increase in FA.
Pro forma Statements and CF
Recall: OCF = EBIT + depreciation – taxes
If there’s no interest expense, then
Net operating profit after tax (NOPAT) = EBIT – taxes, thus
OCF = NOPAT + depreciation
Additional capital spending and changes in WC = Net CF
= OCF - NCS - changes in NWC = CFFA
DETAILED EXAMPLE: UNEQUAL LIFE PROJECTS & EAA
Depreciation and Net Salvage Value (SV)
Depreciation tax shield = D x T (Deprec exp x Tax rate)
Computing straight line depreciation:
D = (initial cost – SV)/no. of yrs (take SV into acct)
D = initial cost/no. of yrs (straight line FULL depreciation)
Internal growth rate: how much the firm can grow assets
using RE/ internally generated funds as the only source of
financing.
Accum. Depreciation = D x no. of years in use
Book value (B) = initial cost – accum. Depreciation
Internal Growth Rate =
If salvage value (S) ≠ book value (B)  tax effect.
After-tax salvage value = S – T(S - B) if S>B (Gain on sale)
= S + T|S-B| if S<B (Loss on sale)
Net capital spending = Ending net fixed assets – beginning
net fixed assets + depreciation
Methods to Computing OCF
1. Bottom-Up Approach
oWorks only when there is no interest expense
oOCF = NI + depreciation
oWhere NI = sales – costs – depreciation – taxes
oTaxes = Tax rate x (sales – costs – depreciation)
2. Top-Down Approach
oSame result as bottom-up approach if no interest exp
oOCF = Sales – costs – taxes
oDon’t subtract non-cash deductions/interest expense
3. Tax Shield Approach
oOCF = (Sales –Costs)(1-T) + Depreciation*T
oCosts here don’t include depreciation
Mutually Exclusive Projects with Unequal Lives (EAA)
PV = NPV of project, I/YR = required return, N = project
life, FV = 0. <CPT><PMT> to find an equivalent annuity
(replacement chains) to the lump-sum NPV.
Rule: Select highest EAA (lowest if comparing costs)
Impact of inflation (Downward bias on PV)
Need to adjust revenues (e.g. 10% annually) and costs
(60% of revenue), but NOT depreciation.
DETAILED EXAMPLE: REPLACEMENT PROBLEM
If TA < TL + OE then it can be resolved by repaying ST debt
(decrease notes payable), repaying LT debt, buying back
stock (decrease owner’s equity), paying more in dividends
(reduce addition to RE) + or increasing cash account. (Plug
variables determine where the extra funds will go or the
loss in funds will be raised.  TA = TL + OE)
ROA×b
1-ROA×b
where b = retention ratio
Sustainable growth rate: how much the firm can grow by
using internally generated funds and issuing debt (AFN) to
maintain a constant debt-equity ratio. (>internal growth)
OCF
Machine A
Initial cost
Operating cost
after tax
Depreciation
tax shield
∆ in NWC
Salvage value,
S – T(S-B)
Net Cash Flow
T=0
-5m
T = 1-4
0
-500k(1-0.4)
= -300k
920k(0.4) =
368k
0
-5m
68k
T=5
-300k
368k
0
400k
468k
 NPVA = -4,475,531.16, NPVB = -5,676,367.70
 EAAA = $1,150,625.30, EAAB = $1,025,574
 Choose Machine B, as it incurs lower costs
Topic 10: Financial Planning and Forecasting
Purpose: Assess if firm’s anticipated performance is in line
with general targets/investor’s expectations, estimate
effects of proposed operating changes, anticipate future
financing needs, estimate future CFFA, set appropriate
targets for compensation plans.
Elements of Financial Planning
Capital budgeting decisions: investment in new assets
Capital structure decisions: degree of financial leverage
NWC management decisions: liquidity requirements
Dividend policy decisions: cash paid to shareholders
Financial Statements
 TA = TL + TE  Balance Sheet
 NI = Rev – COGS – Exp – Taxes  Income Statement
 NI = Addition to RE + Dividends
 Dividend payout ratio = Dividends/NI
 Retention ratio = (NI-Dividends)/NI = RE/NI
 Dividend payout ratio + Retention ratio = 1
Percentage of Sales approach
Pro Forma Income Statement: If profit margin (NI/Sales)
is assumed to be constant, costs will vary directly with
sales. Dividends do not vary directly with sales.
Pro Forma Balance Sheet: Initially assume all assets
(including fixed assets if firm is operating at full capacity)
and A/P vary directly with sales. Notes payable, LT debt &
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Sustainable Growth Rate =
ROE×b
1-ROE×b
where b =
retention ratio
AFN = (A*/S0)∆S – M(S1)(RR) (L*=0; non-spontaneous)
If >sustainable growth rate, projected D/E ratio increases.
If current D/E ratio > projected, not sustainable.
Determinants of growth
Using Dupont Identity ROE = PM * TATO * EM
 Profit margin: operating efficiency
 Total asset turnover: asset use efficiency
 Financial leverage: choice of debt ratio
 Dividend policy: choice of how much to pay to
shareholders vs. reinvesting in the firm
Topic 11: Working Capital Management
Gross working capital = total current assets
Net working capital = CA – CL
NOWC = CA – non-interest bearing CL = Operating CA –
Operating CL = (Cash + Inv. + A/R) – (Accruals + A/P)
Sources and Uses of Cash
Sources: Increasing LT debt, equity or CL, Decreasing CA
other than cash or FA. | Uses: Decreasing LT debt, equity
or CL, Increasing CA other than cash or FA
Operating Cycle
The operating cycle is the time period from inventory
purchase until the receipt of cash.
Operating Cycle = Inventory period + A/R period
Inventory period is the time required to purchase and sell
inventory. A/R period (days’ sales outstanding) is the time
taken to collect on credit sales.
Inventory period = (Average inventory*365)/COGS =
365/inventory turnover
A/R period = Average receivables/(Credit Sales/365) =
AR/average daily sales = 365/receivables turnover
Cash Cycle
The cash cycle is the time period from when cash is paid
out for purchases to when cash is received from sales.
Cash Cycle = Operating cycle – A/P period = Inventory
period + A/R period – A/P period
lOMoARcPSD|10593153
A/P period is the time between purchase of inventory and
payment for the inventory.
A/P period: Payables turnover = Total purchases from
suppliers/Average payable = (COGS + End inventory – Beg.
inventory)/Average payable
AP Period = 365/payables turnover = Average payable/
(COGS/365)
Minimizing the cash cycle minimizes the amt of external
financing the firm has to raise to fund current operations.
Carrying vs. Shortage Costs
Managing short-term assets involves trade-off between
carrying cost and shortage cost.
Carrying cost is the cost to store and finance the assets. It
increases with increased levels of CA.
Shortage cost is the cost to replenish assets (e.g. trading
and order costs, costs related to safety reserves, i.e. lost
sales and customers and production shortages). It
decreases with increased levels of CA.
Motives for carrying cash
Txns | Precaution | Compensating balances | Speculation
Ways to minimize cash holdings
Lockbox | Insist on wire transfers from customers | Use a
remote disbursement acct | Increase forecast accuracy |
Hold marketable securities | Negotiate a line of credit
365/20 = 18.25 periods per year
EAR = (1.01010)18.25 – 1 = 20.13%
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N=60/365, I/Y=9%, FV=15,000  find PV.
Reducing DSO without reducing sales will increase SR
cash holdings. In LR, company invests cash in productive
assets or pays shareholders, increasing firm’s value.
Evaluating a Credit Policy
NPV of credit policy = PV of cash inflow – PV of cost of
switching (incremental)
PV of cash inflow = (P – V)(Q1 – Q0)/r  perpetuity
Cost of switching = cash given up now + cost of producing
extra units = P(Q0) + V(Q1 – Q0)
where P = sales price, V = variable cost, Q1 = new sales qty upon
switching, Qo = current sales qty, r = req monthly return (in d.p.)
DETAILED EXAMPLE: EVALUATING A CREDIT POLICY
DETAILED EXAMPLE: LOCKBOX
Float
The difference between cash as shown on firm’s books
and on its bank books.
Disbursement float (always +ve)
Generated when a firm writes checks.
= Available balance at bank - book bal. after disbursement
Collection float (always -ve)
Checks received increase book balance before bank
credits the account.
= Available balance at bank - book bal. after receiving
Net float = Disbursement float + Collection float =
Available bank balance – Book balance
Measuring Float
Size of float = Dollar amt x Time delay
Delay= mailing time + processing delay + availability delay
Goal of Float Management is to reduce collection delay.
To increase overall float, stretch out A/P as long as
possible (negotiate longer terms with suppliers). Turn A/R
as quickly as possible (make it easy for customers to pay
e.g. lockbox, prepaid envelopes, discounts).
DETAILED EXAMPLE: MEASURING FLOAT
Cash Surplus and Deficit
Cash surplus: exists when seasonal demand for assets is
low  buy marketable securities with seasonal surpluses
Cash deficit: exists when seasonal demand for assets is
high  convert marketable securities back to cash and/or
borrow from banks when deficits occur
Temporary vs. Permanent Assets
Temp current assets: Additional CA carried during peak
periods (seasonal). Level of CA decreases as sales occur.
Perm current assets: Minimum level of CA carried by firm
at all times. Considered perm because level is constant.
Choosing the Best Policy
(1) Cash reserves. (+) Firm less likely to face financial
distress & better able to handle emergencies. (-) cash &
marketable securities earn a lower return. | (2) Maturity
hedging: Try to match financing maturities with asset
maturities. Finance temp assets with ST debt, perm assets
& fixed assets with LT debt & equity | (3) Interest rates.
When ST rates < LT rates, it may be cheaper to finance
with ST debt. However, rates can increase quickly  may
become unable to refinance ST loans.
Characteristics of ST securities
Maturity | Default risk | Marketability | Taxability
ST Borrowing
1) Bank loans: Promissory note, line/letter of credit,
2) Commercial Paper, 3) Trade credit & Accruals
Cost of float is the opportunity cost of not being able to
use the money, i.e. cost of float = daily receipt x delay.
Credit Management
Trade-off between increased sales and cost of credit.
A/R = credit sales per day x length of collection period
Cash Budget
Purpose: Forecast cash inflows, outflows and ending cash
balances. Used to plan loans needed/funds available to
invest. Components: Start with Cash inflows (collections
from sales, FA disposal, interest earned, other income).
Less: cash paid for purchases, other expenses (e.g. wages,
rent). Bad debt expenses reduce collections from sales.
TOS: If TOS are A/B, net C  A% discount if pay in B days.
From operations
DETAILED EXAMPLE: CASH DISCOUNT
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Period rate = 1/99 = 1.01010%
Period = 30 – 10 = 20 days of credit received
DETAILED EXAMPLE: COMPENSATING BALANCE
Effective Interest Rate of a compensating balance
Amt that needs to be borrowed = Required amt/(1 –
compensating balance requirement %)
Interest paid = Amt borrowed x (1 + quoted interest rate)
Effective interest rate = Interest paid/Required amt
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Topic 12: Options
A call option is one that confers the right (but not the
obligation) to BUY a given asset on (or before) a given
date for a predetermined price (known as the exercise or
strike price). A put option is one that confers the right
(but not the obligation) to SELL a given asset on (or
before) a given date at a predetermined price (known as
the exercise or strike price).
American: Exercise any time
European: Exercise at expiration
General strategy: Buy call option if expect asset price to
increase. Buy put option if expect asset price to decrease.
Exercise (strike) price: price at which the option holder
can purchase or sell the stock (or other underlying asset)
Expiration/maturity date: the final date at which the
option can be used. Prices are higher for options with the
same strike price but longer expiration.
Intrinsic value: difference between exercise price of
option and spot price of the asset (Call: S – E, Put: E – S). It
is the value of the option if it were to expire today.
Time value: option price - intrinsic value
Comparison: Calls vs. Puts
Call option with strikes less than the current price are
worth more than the corresponding puts. Call options
with strikes greater than the current price are worth less
than the corresponding puts.
Call options have unlimited profit potential, while put
options have limited profit potential since the underlying
asset’s price cannot be less than zero.
Exercise Price vs. Spot Price
Call option
In-the-Money: E<S
At-the-Money: E=S
Out-of-the-Money: E>S
Put option
In-the-Money: S<E
At-the-Money: S=E
Out-of-the-Money: S>E
Comparing the Strategies
 Stock + Put
oIf S<E, exercise put and receive E
oIf S≥E, let put expire and have S
 Call + Treasury bills with PV = E
oPV(E) will be worth E at expiration of the option
oIf S<E, let call expire and have investment E
oIf S≥E, exercise call using the investment and have S
Put-Call Parity
 Payoff from 1st Strategy = Payoff from 2nd Strategy
 Thus, they must cost the same, i.e. Price of underlying
stock + Price of Put = Price of Call + PV of Exercise Price
(zero coupon bond)
 If prices are not equal, arbitrage will be possible.
Call Option Value Bounds
Upper bound: Call price must be ≤ stock price.
Lower bound: Call price must be ≥ (S – E) or 0, whichever
is greater.
If either bound is violated  arbitrage opportunity.
Value of call sure to finish in the money = S – PV(E)
Determinants of option values
1. Stock price
Stock price ↑, call price ↑, put price ↓
2. Exercise price
Exercise price ↑, call price ↓, put price ↑
3. Time to expiration
Time to expiration ↑, both call and put prices ↑
4. Risk-free rate
Risk free rate ↑, call price ↑ and put price ↓
5. Volatility
Higher TOTAL variance in underlying asset returns,
both call and put prices ↑
APPENDIX: NPV CROSSOVER RATES (Mutually Exclusive)
Why NPV cross: (1) Size (scale) diff: NPV different at
discount rate = and (2) Timing diff: project with faster
payback has more CF in early years for reinvestment.
IRR(A) > IRR(B) but which investment has a higher NPV
depends on required rate of return.
Year
Investment A
Investment B
0
-$400
-$500
1
$250
$320
2
$280
$340
lOMoARcPSD|10593153
(B has larger cash flows in the later years.)
1) Find NPV of switching from A to B: NPV(B-A) = -100 +
70/(1+IRR) + 60/(1+IRR)2
2) Calculate return on this investment by setting NPV = 0
& solving for IRR: = -100 + 70/(1+IRR) + 60/(1+IRR)2 = 0.
 CF0 = -100, CF1 = 70, CF2 = 60  <CPT><IRR>
SPACE FOR EXTRA NOTES
e.g 15 year bond mature in 10 years – N=10
To find discount rate, P/V negative*
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