Week 1 Hirshleifer model (chapter 1 and 2)
Assumptions
A certain world is assumed: the individual knows all the decisions alternatives and
the corresponding outcomes.
There is a one-period model where only two moments are important: the start of
the period (now, t=0) and the end of the period (later, t=1)
The individual has a current income of CF 0 and a future income of CF 1.
Each participant can borrow or lend unlimitedly against the risk-free market interest
rate r f .
Formulas
PVA T A −T
[1−( 1+ R ) ]
R
C 0 max C1
OG=C 0+
(1+ r)
OG OH
(1+r )
OG OA + AG
OA CF 1
CF 0 +
(1+ r)
AG(NPV ) OF
−EA+
(1+ r)
OF = revenue investment
-EA = initial investment
C1 CF 1 +OF ± ( borrowed∨lended )∗¿
(1+r )
C0 CF 0 −EA ± ( borrowed∨lended )∗¿
(1+r )
OH OG (1+ r)
OH C 0 ( 1+r )+C 1
Amount borrowed ∨lended CF 0 −C0 −EA
+ Lended out
- Borrowed
NPV −EA+ EG
BH AG∗( 1+r )
IRR OF
−EA+ =0
( 1+ IRR )
PV 0 CF T
T
(1+r T )
T
PV 0 ( series ) CF T
∑ ( 1+ r )T
t =1 T
Enterprise value Market value of equity + interest bearing debt – cash
Market-to-book ratio Market value of equity
Book value of equity
, Net debt Total debt – excess cash – short term investments
Earnings Per Share (EPS) Net income
Shares outstanding
Debt-to-enterprise ratio Net debt
enterprise value
P/E Share price Market cap .
=
EPS net income
Networking capital Current assets – current liabilities
Market value of equity Number of shares * price
Debt ratio All debt
Book value of equity
Retained earnings net income−dividends
Change in shareholder’s retained earnings+ net sales of share
equity
Change in shareholder’s Net income−dividends+ sales of shares−repurchases of shares
equity
Gross margin Gross profit
Sales
Operating margin operating income
sales
Net profit margin Net income
Sales
Current ratio current assets
current liabilities
Quick ratio cash∧short term investments+ accounts receivables
current liabilities
Cash ratio cash
current liabilities
Accounts receivable days accounts receivable
average daily sales
Accounts payabale days accounts payable
average daily cost of sales
Inventory days inventory
average daily cost of sales
Inventory turnover annual cost of sales
inventory
Return on equity net income
book value of equity
Return on assets Net income +interest expense
book value of assets
Return on invested capital EBIT (1−taxrate)
book value of equity +net debt
Debt equity ratio total debt
total equity
Assumptions
A certain world is assumed: the individual knows all the decisions alternatives and
the corresponding outcomes.
There is a one-period model where only two moments are important: the start of
the period (now, t=0) and the end of the period (later, t=1)
The individual has a current income of CF 0 and a future income of CF 1.
Each participant can borrow or lend unlimitedly against the risk-free market interest
rate r f .
Formulas
PVA T A −T
[1−( 1+ R ) ]
R
C 0 max C1
OG=C 0+
(1+ r)
OG OH
(1+r )
OG OA + AG
OA CF 1
CF 0 +
(1+ r)
AG(NPV ) OF
−EA+
(1+ r)
OF = revenue investment
-EA = initial investment
C1 CF 1 +OF ± ( borrowed∨lended )∗¿
(1+r )
C0 CF 0 −EA ± ( borrowed∨lended )∗¿
(1+r )
OH OG (1+ r)
OH C 0 ( 1+r )+C 1
Amount borrowed ∨lended CF 0 −C0 −EA
+ Lended out
- Borrowed
NPV −EA+ EG
BH AG∗( 1+r )
IRR OF
−EA+ =0
( 1+ IRR )
PV 0 CF T
T
(1+r T )
T
PV 0 ( series ) CF T
∑ ( 1+ r )T
t =1 T
Enterprise value Market value of equity + interest bearing debt – cash
Market-to-book ratio Market value of equity
Book value of equity
, Net debt Total debt – excess cash – short term investments
Earnings Per Share (EPS) Net income
Shares outstanding
Debt-to-enterprise ratio Net debt
enterprise value
P/E Share price Market cap .
=
EPS net income
Networking capital Current assets – current liabilities
Market value of equity Number of shares * price
Debt ratio All debt
Book value of equity
Retained earnings net income−dividends
Change in shareholder’s retained earnings+ net sales of share
equity
Change in shareholder’s Net income−dividends+ sales of shares−repurchases of shares
equity
Gross margin Gross profit
Sales
Operating margin operating income
sales
Net profit margin Net income
Sales
Current ratio current assets
current liabilities
Quick ratio cash∧short term investments+ accounts receivables
current liabilities
Cash ratio cash
current liabilities
Accounts receivable days accounts receivable
average daily sales
Accounts payabale days accounts payable
average daily cost of sales
Inventory days inventory
average daily cost of sales
Inventory turnover annual cost of sales
inventory
Return on equity net income
book value of equity
Return on assets Net income +interest expense
book value of assets
Return on invested capital EBIT (1−taxrate)
book value of equity +net debt
Debt equity ratio total debt
total equity
