discounting and compounding
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Christopher B. Stone µ01
Present value of future cash flow
n
r ! 1
FV
PVr = discount raten = number of periods
Discounting: calculation of present valuesDiscounting: calculation of present values
Compounding: calculation of future valuesCompounding: calculation of future values
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Christopher B. Stone µ01
Internal rate of return
IRR is that unique discount
rate which, when applied toa series of future cashflows, yields a net present
value of 0.
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Financial management rate of return
Serie A Serie B Serie
F (100.00)$ (100.00)$ (50.00)$
F1 -$ 7.18$ (42.82)$F2 -$ 7.18$ 7.18$
F3 -$ 7.18$ 7.18$
F4 -$ 7.18$ 7.18$
F5 141.42 117.18 107.18$
7.18% 8.86% 8.12%
Only Series A is a ³pure´ IRR
Series B and Series C have money extracted from the system
Series C has money invested in the system after t0
The IRR model assumes1) That money invested in the system is held in an accountbearing interest at the IRR before being invested;2) That money extracted from the system is re-invested in an
account yielding the IRR.
IRR FMRR
IRR Safe rate
IRR Re-investment rate
Negative cash f low s after t0, before they are
invested, are held in an account that produces
interest at
Money extracted from the system is re-
invested at
FMRR bifurcates negative and positive cash flowsFMRR bifurcates negative and positive cash flows
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Financial management rate of return
PV FV
0 0
10 .1.1 .1.1.1
F uture valued at re-investment rate
PV¶ed at safe rate
FMRR > reFMRR > re- -investment rate for worthwhile investmentsinvestment rate for worthwhile investments
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Hurdle rates
The earnings you foregoby deploying capital in adifferent way
The rate you must get on an
investment for the deal tomake sense
I f hurdle rate < I RR, NPV is positiveI f hurdle rate < I RR, NPV is positive
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Sensitivity analysis
If you discount your cash flo s @ the HRand get a + V the V represents your profit over the life of the deal.
If HR<IRR+ V
V @ HR is the positivecushion you have
nr 1
FV V
Annuitize this figurecalculate mT to get et Uniform Series US
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Recourse debt
Creditor can sue debtor if not re paid
Might be secured might not
Most corporate debt is recourseException: real estate
Recourse
Borro er has no personal liability
Must be secured other ise it's nothing
You can still sue for fraudulent conveyances etc.
on recourse
Debt
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Compounded interest
At YR1 I o e 1The 1 does not accrue interest if unpaid
Simple
At YR1 I o e 1The 1 interest itself accrues interest
Compound
Interest
I borro 100 @ 1
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Capital asset pricing model
f mf e R R R k !
Cost of
capital Risk-freereturn
USG securities
Average rate of returnon common stocks
(S&P 00)
Co-variance
of returns againstthe portfolio
(departure from the average)< , security is safer than S&P 00 average
> , security is riskier than S&P 00 average
Cost of equity capital = return expected on firm¶s common stock Cost of equity capital = return expected on firm¶s common stock
Cost of capital = Risk-free return + compensation for additional risk beyond a USG bondCost of capital = Risk free return + ( x market risk premium)Cost of capital = Risk free return + ( x margin by which stock market exceeds risk-free return
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Methods of inventory valuation
o er of cost or r et Cost
I OFirst oo s into in entor
re first oo s o t
Cost Y
LI Ost oo s into in entor
re first oo s o t
n in in entor l tion etho s
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Christopher B. Stone µ01
Depreciation methods
Str i ht line
S o the e rs
1 0 etho o le e linin l n e
e linin l n e
eler te
epre i tion etho s
= Cost-salvage valueUseful life
= Cost-salvage value * remaining years of useful lifen(n+ )
Keyed off the remaining balance in each year AFT R depreciationDoes N T use salvage value
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Christopher B. Stone µ01
Liquidity ratios
Currentratio
=Current assets
Current liabilities
Quickratio
= Current assets - inventoryCurrent liabilities
Cash flowliquidity
ratio=
Cash flow from operations*Current liabilities
*From the cash flow statement
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Leverage ratios
Debtratio
=LiabilitiesAssets
Debt equityratio
=LiabilitiesNet worth
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Financial leverage index
Financialleverage
index
=Return on equity
Adjusted return on assets
= Net earnings* equity**[ arnings + interest ( -tax rate)] assets
* Note this does not include pfd div** r market cap
Is a company trading positively on its leverageI.e. is it bringing in capital at less than the return
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Activity ratios
Accountsreceivableturnover
=Net sales*
Accounts receivable
*From the income statement
Inventoryturnover
=C GS*
Inventory
Accountspayableturnover
=Total expenses*Accounts payable
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Operating cycle
Capital
infusion$
Sale
InventoryAccounts
receivable
Avg. amount of time inventory is outstanding+
Avg. amount of time receivables are outstanding
Operatingcycle
=
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Capital
infusion$
Sale
Cash conversion cycle
Avg. amount of time inventory is outstanding+
Avg. amount of time receivables are outstanding-
(A
vg. amount of time payables are outstanding)
Cashconversion
cycle=
Accountspayable
(Payment)
Accounts
receivable
Inventory
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Profitability ratios
Gross profit
margin =
Gross profitGross sales
This is very much driven by variable costs cost of goods sold. Overhead is OT included.
Measures profitability
A business can be profitable and still trade negatively on its leverage A business can be profitable and still trade negatively on its leverage
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P ratio
P ratio =Stock price per share
arnings per share
Growth stockHigh E ratio
Value stockLo E ratio
Return ontotal assets
=arnings + interest
Assets