Christopher B. Stone ‘01
Present value of future cash flow
FV
PV 
n
1  r 
r = discount rate
n = number of periods
Discounting: calculation of present values
Compounding: calculation of future values
Christopher B. Stone ‘01
Annuities
n
n
In advance
PmT
In arrears
CF0
n
n
n
PmT
PmT
PmT
PmT
PmT
PmT
PmT
PmT
PmT
CFt
Christopher B. Stone ‘01
Internal rate of return
IRR is that unique discount
rate which, when applied to
a series of future cash
flows, yields a net present
value of 0.
Christopher B. Stone ‘01
Financial management rate of return
CF0
CF1
CF2
CF3
CF4
CF5
IRR
Series A
$ (100.00)
$
$
$
$
141.42
7.18%
Series B
$ (100.00)
$
7.18
$
7.18
$
7.18
$
7.18
117.18
8.86%
Series C
$ (50.00)
$ (42.82)
$
7.18
$
7.18
$
7.18
$ 107.18
8.12%
Only Series A is a “pure” 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 assumes
1) That money invested in the system is held in an account
bearing 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
Negative cash flow s after t0, before they are
invested, are held in an account that produces IRR
interest at
Safe rate
Money extracted from the system is reinvested at
Re-investment rate
IRR
FMRR bifurcates negative and positive cash flows
Christopher B. Stone ‘01
Financial management rate of return
PV’ed at safe rate
(50)
(50)
PV
FV
(7.18)
(7.18)
(7.18)
(7.18)
(107.18)
Future valued at re-investment rate
FMRR > re-investment rate for worthwhile investments
Christopher B. Stone ‘01
Hurdle rates
The earnings you forego
by deploying capital in a
different way
The rate you must get on an
investment for the deal to
make sense
If hurdle rate < IRR, NPV is positive
Christopher B. Stone ‘01
Sensitivity analysis
If HR<IRR,
+ NPV
If you discount your cash flows @ the HR
and get a + NPV, the NPV represents your
profit over the life of the deal.
NPV @ HR is the positive
cushion you have
FV
PV 
n
1  r 
Annuitize this figure
(calculate PmT) to get Net Uniform Series (NUS)
Christopher B. Stone ‘01
Recourse debt
Debt
Recourse
Non-recourse
Creditor can sue debtor if not re-paid
Borrower has no personal liability
Might be secured, might not
Must be secured, otherwise, it's nothing
Most corporate debt is recourse
Exception: real estate
You can still sue for fraudulent conveyances, etc.
Christopher B. Stone ‘01
Compounded interest
Interest
I borrow $100 @ 12%
Simple
At YR1, I owe $12
The $12 does not accrue interest if unpaid
Compound
At YR1, I owe $12
The $12 interest itself accrues interest
Christopher B. Stone ‘01
Capital asset pricing model
Cost of capital = Risk-free return + compensation for additional risk beyond a USG bond
Cost of capital = Risk free return + (β x market risk premium)
Cost of capital = Risk free return + (β x margin by which stock market exceeds risk-free return
ke  Rf  β(Rm  Rf )
Cost of
capital
Risk-free
return
USG securities
Co-variance
of returns against
the portfolio
(departure from the average)
Average rate of return
on common stocks
(S&P 500)
B < 1, security is safer than S&P 500 average
B > 1, security is riskier than S&P 500 average
Cost of equity capital = return expected on firm’s common stock
Christopher B. Stone ‘01
Lease financing
Lease financing
Operating lease
Run-of-the-mill "lease"
Lessee incurs a tax-deductible
periodic expense
Lessor enjoys the tax shield
of depreciation
Capitalized lease
Long-term financing
Is like long-term debt
Title is usually transferred
to lessee at the end of the lease term
for a nominal amount
Are reflected in company's
financial statements
Christopher B. Stone ‘01
Income statement
Total revenues
Less Cost of goods sold
Less Fixed costs / purchases
Less Change in inventory
Beginning inventory
Ending inventory
EBITDA
Less depreciation
EBIT
Less interest
EBT
Less taxes
Earnings for com m on & preferred
Less preferred dividends
Earnings for com m on & preferred
Less sinking fund
Unrestricted earnings
Christopher B. Stone ‘01
Methods of inventory valuation
Ending inventory valuation methods
FIFO
First goods into inventory
are first goods out
Lower of cost or market
Cost
LIFO
Last goods into inventory
are first goods out
Cost ONLY
Christopher B. Stone ‘01
Benefits of FIFO and LIFO
Technique
Econom y
Inflationary
FIFO
Value closing inventory
at end-of-year (current) prices
Method
LIFO
Value closing inventory
at beginning of year prices
Increases value of closing inventory
Decreases value of closing inventory
LESS change in inventory
Higher EBITDA
MORE change in inventory
Low er EBITDA
Decreases value of closing inventory Increases value of closing inventory
Deflationary
MORE change in inventory
Low er EBITDA
LESS change in inventory
Higher EBITDA
Must use the same method for financial & tax accounting
Christopher B. Stone ‘01
FIFO and LIFO calculations
ITEM
Gross revenues
Less COGS
Purchases
Change in inventory
Opening inventory
Closing inventory
Gross incom e
Facts
Sales
Qty
Price
Purchases
Qty
Price
Opening inventory
Qty
Price
Closing inventory
Qty
Price
Market price @ end of year
Year 1
FIFO
LCM
Cost
200
200 $
$
150
100 $
$
100
100 $
$
50
$
$
100
100 $
$
50
100 $
$
50
100 $
$
LIFO
Cost
200
$
100
$
100
$
$
100
$
100
$
100
$
Year 2
FIFO
LCM
Cost
80
80 $
$
50
100 $
$
50
50 $
$
50 $
$
50
100 $
$
50
50 $
$
30
(20) $
$
LIFO
Cost
80
$
50
$
50
$
$
100
$
100
$
30
$
Year 3
FIFO
LCM
Cost
200
200 $
$
50
50 $
$
50
50 $
$
$
$
50
50 $
$
50
50 $
$
150
150 $
$
LIFO
Cost
200
$
50
$
50
$
$
100
$
100
$
150
$
$
10
20 $
10
20 $
10
20 $
10
8 $
10
8 $
10
8 $
10
20 $
10
20 $
10
20
$
10
10 $
10
10 $
10
10 $
10
5 $
10
5 $
10
5 $
10
5 $
10
5 $
10
5
$
10
10 $
10
10 $
10
10 $
10
10 $
10
5 $
10
10 $
10
5 $
10
5 $
10
10
$
10
10 $
10
5 $
10
10 $
10
5 $
10
5 $
10
10 $
10
5 $
10
5 $
10
10
$
5
$
5
Under FIFO-LCM, opening inventories in the next year should be valued at COST
$
10
Christopher B. Stone ‘01
Depreciation methods
Depreciation methods
Straight line
Accelerated
Sum of the years
Declining balance
= Cost-salvage value
Useful life
150% method
Double declining balance
= Cost-salvage value * remaining years of useful life
n(n+1)
2
Keyed off the remaining balance in each year AFTER depreciation
Does NOT use salvage value
Christopher B. Stone ‘01
Straight line & sum of the years depreciation
Year
Depreciation Expense
0
1
2
3
4
$
$
$
$
Facts
Cost
$
Salvage Value $
Useful Life
Year
1
2
3
4
Facts
Cost
Salvage Value
Useful Life
Straight-line
2,500
2,500
2,500
2,500
12,000
2,000
4
Calculation (sum of the years)
Rem aining years Denom inator Coefficient
4
10
0.4
3
10
0.3
2
10
0.2
1
10
0.1
$
$
12,000
2,000
4
$
$
$
$
Base
10,000
10,000
10,000
10,000
Depreciation
Expense
$
4,000
$
3,000
$
2,000
$
1,000
Sum of the years
Christopher B. Stone ‘01
Declining balance depreciation
Year
%
0
1
2
3
4
Facts
Useful life (yrs)
Cost
Salvage value
150%
150%
150%
150%
150% m ethod
Coefficient
Calculations
Useful
Depreciation Rem aining
Coefficient
life (yrs)
expense
balance
$ 12,000.00
4
0.375 $
4,500.00 $ 7,500.00
4
0.375 $
2,812.50 $ 4,687.50
4
0.375 $
1,757.81 $ 2,929.69
4
0.375 $
929.69 $ 2,000.00
%
200%
200%
200%
200%
Double declining balance m ethod
Coefficient
Calculations
Useful
Depreciation Rem aining
Coefficient
life (yrs)
expense
balance
$
12,000
4
0.5 $
6,000 $
6,000
4
0.5 $
3,000 $
3,000
4
0.5 $
1,000 $
2,000
4
0.5 $
$
2,000
4
$ 12,000
$ 2,000
$12,000 x .375 = $4,500
Christopher B. Stone ‘01
Depreciation graphs
Methods of depreciation
$14,000
Value of asset
$12,000
$10,000
Straight line
$8,000
Sum of the years
$6,000
Declining balance @ 150%
$4,000
Double declining balance
$2,000
$0
1
2
Year
3
4
Christopher B. Stone ‘01
Capitalization vs. expenses
Expenditures
Expenses
Capitalization
Repairs
Recurring events
that produce
long-lived assets
Create an asset that
produces revenue
beyond 1 year
Repair + upgrade
Upgrade is capitalized
Exception: recurring events
can be expensed
Christopher B. Stone ‘01
Merger accounting
Methods of accounting for business combinations
Pooling
Based on BOOK (historical) values
Purchase
Based on fair market value (FMV)
Results in higher net income
on future balance sheets
1) Book value < FMV
2) Goodwill must be amortized
MUST be used if and only if
all 12 conditions are met
Defeat hostile takeovers by ensuring the combination doesn’t qualify for pooling
Christopher B. Stone ‘01
Pooling method
X Corp
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Plant
$ 400,000
Equity
Common
$ 300,000
R/E
$ 150,000
Y Corp
Assets
Liabiliites
Inventory $ 50,000 Debt
$
Plant
$ 150,000
Equity
Common
$ 100,000
R/E
$ 100,000
Total
Total
$ 700,000 Total
Facts
FMV of Y's
Inventory
Plant
$ 700,000
$ 60,000
$ 180,000
$ 200,000 Total
$ 200,000
(Notice that FMV's are irrelevant to the pooling method)
Earnings
X
Y
$ 15,000
$ 20,000
Consideration for X's acquisition of Y
X common $ 250,000
X Corp (after acquisition)
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Investment $ 200,000
Plant
$ 400,000
Equity
Common
$ 400,000
R/E
$ 250,000
Total
$ 900,000 Total
$ 900,000
or
X Corp (after acquisition)
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Inventory $ 50,000
Plant (Y)
$ 150,000
Equity
Plant
$ 400,000 Common
$ 400,000
R/E
$ 250,000
X Corp (consolidated)
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Inventory $ 50,000
Plant
$ 550,000
Equity
Common
$ 400,000
R/E
$ 250,000
Total
Total
$ 900,000 Total
$ 900,000
$ 900,000 Total
$ 900,000
Pooling: Uses book value, A inherits T’s retained earnings
Christopher B. Stone ‘01
Purchase method
X Corp
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Plant
$ 400,000
Equity
Common
$ 300,000
R/E
$ 150,000
Y Corp
Assets
Liabiliites
Inventory $ 50,000 Debt
$
Plant
$ 150,000
Equity
Common
$ 100,000
R/E
$ 100,000
Total
Total
$ 700,000 Total
Facts
FMV of Y's
Inventory
Plant
$ 700,000
$ 60,000
$ 180,000
$ 200,000 Total
$ 200,000
(Purchase method uses FMV)
Earnings
X
Y
$ 15,000
$ 20,000
Consideration for X's acquisition of Y
X common $ 250,000
X Corp (after acquisition)
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Investment $ 250,000
Plant
$ 400,000
Equity
Common
$ 550,000
R/E
$ 150,000
Total
$ 950,000 Total
$ 950,000
or
X Corp (after acquisition)
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Inventory $ 60,000
Plant (Y) $ 180,000
Equity
Plant
$ 400,000 Common
$ 550,000
Goodw ill $ 10,000 R/E
$ 150,000
X Corp (consolidated)
Assets
Liabiliites
Cash
$ 300,000 Debt
$ 250,000
Inventory $ 60,000
Plant
$ 580,000
Equity
Goodw ill
$ 10,000 Common
$ 550,000
R/E
$ 150,000
Total
Total
$ 950,000 Total
$ 950,000
$ 950,000 Total
$ 950,000
Purchase: Uses FMV, A doesn’t inherit T’s retained earnings
Christopher B. Stone ‘01
Goodwill
Goodwill
Reputation, talented mgmt., good relationships with suppliers, etc.
Cannot be sold apart from identifiable assets
Enterprise can record goodwill ONLY when it purchases an entire business
Amortizable under a 40-yr period (usually - shorter in high-tech)
Valuing goodwill
Residual method
Purchase price
Less FMV of assets
Excess earnings method
Item
Average earnings over X years
Less expected return on identifiable assets
Excess earnings
Amount @ 10% interest that w ill produce
$50,000 in excess earnings each year
(I.e., goodw ill)
Facts
Identifiable assets (book value? FMV?)
Return on assets
Amount
$ 150,000
$ 100,000
$ 50,000
$ 500,000
$ 1,000,000
10%
Christopher B. Stone ‘01
Stock and dividend issuance
Scenario 1 (par stock issued)
Assets
Liabiliites
$
10,000
Cash
c/s
Paid-in capital
Total
$
10,000 Total
Equity
$
$
$
100
9,900
10,000
Facts
1) Board authorizes and issues 100 shares at @1 par value, selling for $100 per share
2) Board authorizes and issues 100 shares of "no-par stock" for $100/share
3) As in #1; earnings for the year are $5,000
4) As in #3; Board declares dividend of $1,000
Scenario 3 (earnings of $5,000 reported)
Assets
Liabiliites
$
10,000
$
5,000
Equity
c/s
$
Paid-in capital
$
Retained earnings $
Cash
Cash
Total
Cash
Cash
Painting
Total
Cash
Cash
$
15,000 Total
$
Scenario 5 (Board buys a Van Gogh)
Assets
Liabiliites
$
10,000
$
2,000
$
2,000
Equity
c/s
$
Paid-in capital
$
Retained earnings $
$
14,000 Total
$
c/s
Total
$
10,000 Total
Equity
$
$
10,000
10,000
5) As in #4; Board buys a Van Gogh for $2,000
6) Painting is distributed as dividend ("deemed sale")
7) Covertible debt to stock
Scenario 4 (div of $1,000)
Assets
$
$
Cash
Cash
Equity
c/s
$
Paid-in capital
$
Retained earnings $
100
9,900
5,000
15,000
Liabiliites
10,000
4,000
Total
$
14,000 Total
$
100
9,900
4,000
14,000
Scenario 6a (Van Gogh distributed as div - "deem ed sale")
Assets
Liabiliites
$
10,000
$
2,000
$
4,000
Equity
c/s
$
100
Paid-in capital
$
9,900
Retained earnings $
6,000
Cash
Cash
Deemed cash
100
9,900
4,000
14,000
Total
$
16,000 Total
$
16,000
Scenario 6b (Van Gogh distributed as div - "deem ed sale")
Assets
Liabiliites
$
10,000
$
2,000
Equity
c/s
$
100
Paid-in capital
$
9,900
Retained earnings $
2,000
Total
Cash
Cash
$
12,000 Total
$
Scenario 8: convertible debt (before)
Assets
Liabiliites
$
100,000 Debt
$
c/s
Total
$
100,000 Total
Equity
$
$
12,000
50,000
Cash
Cash
c/s
Total
Com pany has 100 outstanding shares of $5 par value com m on
Assets
Liabiliites
$
900 Debt
$
300
Cash
Cash
Equity
c/s
$
Paid-in capital
$
Retained earnings $
Total
$
900 Total
$
1,200 Debt
Liabiliites
$
$
100,000 Total
Equity
$
$
Buys back treasury shares for $150
Assets
Liabiliites
$
750 Debt
$
Equity
c/s
$
Paid-in capital
$
Retained earnings $
Treasury shares
$
100
200
300
600
Total
-
Cash
Initial condition
Assets
$
Scenario 8: convertible debt (after)
Assets
Liabiliites
$
100,000 Debt
$
50,000
100,000
Cash
Scenario 2 (no-par stock issued)
Assets
Liabiliites
$
10,000
Cash
$
750 Total
$
-
100,000
100,000
300
100
200
300
(150)
750
Com pany declares a stock dividend of 10 shares @ $6/share
Assets
Liabiliites
$
1,200 Debt
$
-
Christopher B. Stone ‘01
Liquidity ratios
Current
ratio
=
Current assets
Current liabilities
Quick
ratio
=
Current assets - inventory
Current liabilities
Cash flow
liquidity
ratio
Cash flow from operations*
=
Current liabilities
*From the cash flow statement
Christopher B. Stone ‘01
Leverage ratios
Debt
ratio
Debt/equity
ratio
=
=
Liabilities
Assets
Liabilities
Net worth
Christopher B. Stone ‘01
Financial leverage index
Is a company trading positively on its leverage?
I.e., is it bringing in capital at less than the return?
Financial
leverage
index
=
Return on equity
=
Adjusted return on assets
Net earnings* / equity**
[Earnings + interest (1-tax rate)] / assets
* Note this does not include pfd div
**Or market cap
Christopher B. Stone ‘01
Activity ratios
Accounts
Net sales*
receivable =
Accounts receivable
turnover
Accounts
payable
turnover
=
Inventory
turnover
COGS*
=
Inventory
Total expenses*
Accounts payable
*From the income statement
Christopher B. Stone ‘01
Operating cycle
Capital
infusion
$
Accounts
receivable
Inventory
Sale
Operating
cycle
=
Avg. amount of time inventory is outstanding
+
Avg. amount of time receivables are outstanding
Christopher B. Stone ‘01
Cash conversion cycle
Capital
infusion
$
Accounts
payable
Accounts
receivable
Inventory
(Payment)
Sale
Cash
conversion
cycle
=
Avg. amount of time inventory is outstanding
+
Avg. amount of time receivables are outstanding
(Avg. amount of time payables are outstanding)
Christopher B. Stone ‘01
Profitability ratios
Gross profit
margin
=
Gross profit
Gross sales
This is very much driven by variable costs / cost of goods sold. Overhead is NOT included.
Measures profitability
A business can be profitable and still trade negatively on its leverage
Christopher B. Stone ‘01
P/E ratio
P/E ratio
=
Stock price per share
Earnings per share
Growth stock
High P/E ratio
Return on
total assets
=
Value stock
Low P/E ratio
Earnings + interest
Assets