1. BA 640 Formula Chapter 6 Risk and Return
1) Rate of return = Amount received - Amount invested
Amount invested
n
k = ∑ k i Pi
ˆ
2) Expected rate of return Pi = Probability , ki = Rate of return
i =1
Calculator 1) Selecting Mode LR : MODE 5
2) Clear Data : CST EXE AC
3) Insert return before : -22 ALFHA Nj 0.1 MAR …… SHIFT 1 EXE
; DT x
∑ (k )P
n 2
= −k
ˆ
σ = Variance = σ
2
3) Risk or Standard deviation i i
i =1
Calculator 1) Insert return before : -22 ALFHA Nj 0.1 MAR …… SHIFT 2 EXE
; DT xσ n
CV = Risk / Return = σ/x
4) Coefficient of variation
5) Beta coefficient ( β ) Calculator insert Mkt. before : 25.7 ALFHA CFj 40 MAR …… SHIFT 8 EXE
β
, DT
6) Correlation ( r ) Calculator insert Mkt. before : 25.7 ALFHA CFj 40 MAR …… SHIFT 9 EXE
( -1 < r < 1 ) , DT r
∑ (k )P
n 2
n
= − kp
ˆ
∑ wi kˆi σp
ˆ
7) Expected return on a portfolio k p = , Risk on a portfolio pi i
i =1
i =1
8) Security Market Line (SML) : ki = kRF + (RPM)bi
Required return = Risk-free return + Premium for risk
Required return on stock i = Risk-free rate of return + (Market risk premium)(Stock i ‘ s beta)
Chapter 9 Bonds and Their Valuation
CF
CF CF
+ + .....+ n
1 2
(1+ k) (1+ k) (1+ k)n
1) PV = Calculator 1) Selecting Mode FIN : MODE 4
1 2
SHIFT AC EXE AC
2) Clear Data :
3) PV = 10 n 10 i% 100 PMT 1000 FV COMP PV EXE
2) Yield to maturity (YTM) or kd = 10 n -887 PV 90 PMT 1000 FV COMP i% EXE
Chapter 10 Stock and Their Valuation
D1 D2 D3 D∞
P=
+ + +. . . +
ˆ
(1+ ks )1 (1+ ks )2 (1+ ks )3 (1+ ks )∞
1) Stock Value = PV of Dividends 0
ˆ D (1 + g ) = D1
P0 = 0 D1
3) k s = +g
ˆ
ks − g ks − g
2) If g is constant, then
P0
= Actual dividend yield + Actual capital gains yield
3) k s
D D ps
V ps = k ps =
ps
or
4)
V ps
k ps
kS = kRF + (kM - kRF) bFirm
5) Use the SML to calculate kS ;
1) After-tax component cost of debt = kd ( 1-T )
Chapter 11 The cost of Capital
D
=
ps
2) The cost of preferred stock k
;
ps
Pn

2. WACC = wdkd (1-T) + wpskps + wceks
3) Weighted Average Cost of Capital (WACC) ;
ˆ
ks = k s = kRF + RP = D1 / P0 + expected g
4)
5) ks = Bond yield + Risk premium
6) g = (Retention rate)(ROE) = (1.0 – Payout rate)(ROE) = b(ROE)
Chapter 13 The Basics of Capital Budgeting : Evaluating Cash Flows
1) Payback period = Year before full recovery + Unrecovered cost at start of year
Cash flow during year
2) Net Present Value (NPV) : Sum of PVs of inflows and Outflows = PV inflow – PV outflow
n n
CFt
CF t
∑ NPV = ∑
= − CF0
NPV
(1 + k )t (1 + k )t
or
t=0 t =1
Calculator -100 CFj 10 CFj 60 CFj 80 10 i% COMP NPV EXE
n
CF t
∑ (1 +
IRR = =0
)t
3) Internal Rate of Return (IRR) : NPV =0 ;
IRR
t=0
Calculator -100 CFj 10 CFj 60 CFj 80 10 i% COMP IRR EXE
TV
4) Modify Internal rate of return (MIRR) : PV costs = PV terminal value : PV costs =
(1 + MIRR ) n
Chapter 8 Time Value of Money
FVn = PV (1 + i )
n
⎛1⎞
n FV
⎜ ⎟
n
or PV = = FV
1)
(1 + i )n n
⎝1+ i⎠
mn
⎛ ⎞
mn
⎛ ⎞
i i
= PV ⎜ 1 + Nom ⎟ = ⎜ 1 + Nom ⎟ − 1 .0
FV or Effective annual rate
2) n
⎝ m⎠
⎝ m⎠
Chapter 14 Cash Flow Estimate and Risk Analysis
1) Net Proceeds from sales (NP) = MV + Tax ; MV = Market value
= MV + Tax rate ( MV-BV) ; BV = Book value
2) Net operating working capital (NOWC) = All current assets that _ All current liabilities that
do not pay interest do not pay interest
= Operating current assets – operating current liabilities
3) Operating capital = (Net operating working capital) – (Net plant and equipment)
4) NOPAT = Net operating profit after taxes = EBIT(1-Tax rate)
5) Operating cash flow (OCF) = NOPAT + Depreciation = EBIT(1-Tax) + Depreciation
= (Sales – CGS – Operating Expense – depreciation)(1-Tax) + Depreciation
= (Sales – CGS – Operating Expense)(1-Tax) + (Depreciation x Tax)
6) Free cash flow (FCF) = Operating cash flow - Gross investment in operating capital
= NOPAT – Net investment in operating capital
7) Free cash flow (FCF) = EBIT(1-Tax) + Depreciation + ∆NWC + ∆CAPEX
8) EBIT = Sales – CGS – Operating Expense – depreciation
= Sales – Variable Cost – Fixed Cost