### Formula Sheet: 1) Present Value Factors 2) Other Formulas 3

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Formula Sheet:
1) Present Value Factors
Cash Flow
Present Value Factor
T-period annuity
immediate
t = 1, 2, …, T
T-period annuity due
t = 0, 1, …, T-1
Perpetuity
t = 1, 2, 3, …
Growing T-period
annuity immediate
t = 1, 2, …, T
Growing T-period
annuity due
t = 0, 1, …, T-1
Growing perpetuity
t = 1, 2, 3, …
2) Other Formulas
•
•
•
•
•
•
•
•
•
•
•
•
�1 −
1
1
�� �
(1+)
�1 −
1
1+
� �  �
(1+)
�1 −
(1+)
1
�� �
(1+) −
�1 −
1

(1+) 1+
�� �
(1+) −
1
−
EAR = (1 +  ) − 1
EAR =   − 1
Duration
Modified Duration = Volatility (%) =
Dividend Growth Model: 0 =
0 =
1
ROE =

+
EPS
1
−
1+YTM
Book equity per share

Payout ratio =

Plowback ratio = 1 −

g = Plowback ratio × ROE
CAPM:  =  + ( −  )
Sharpe Ratio =
−

Portfolio Variance = 12 12 + 22 22 + 21 2 12 = 12 12 + 22 22 + 21 2 12 1 2
3) Formulas for project cash flows
•
Project cash flow = Project operating cash flow – Project capital spending – Change in net working
capital
• Calculating operating cash flow (OCF):
 The bottom-up approach:
Project net income = EBIT – taxes
OCF = Net income + depreciation = EBIT – taxes + depreciation
 The top-down approach:
OCF = Revenue – costs and expenses – taxes
 The tax shield approach:
OCF = (Sales – costs) × (1 – t) + depreciation × t
• Net working capital = Inventory + Accounts receivable – Accounts payable
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