# Chapter 15_ Raising Capital

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```					                       Chapter 12 & 13, Risk and Return

•   Risk Premium = Average Return - T-Bill Rate.

•   for historic returns, Var® = [(R1-R)2 +…+ (RT-R)2]
T-1

•   for historic returns, SD® = Var®

s
•   For expected returns,   E(R) =        (pi x ri)
i =1

s
•   For expected variance, Var(R) =  [pi x (ri - r )2] where SD® = Var(R)
i =1

•   The CAPM formula:        E(Ri ) = Rf + [E(RM ) - Rf ] x Bi
Chapter 9, Net Present Value and Other Criteria

•   NPV =     Ct_
(1+r)t

•   IRR formula:  Ct             =0
(1+IRR)t

•   PI =  PV of future cashflows
Initial Cost

•   Payback period: the length of time it takes the firm to recover the
project’s initial investment.

Average net income
•        AAR =     ------------------------------
Average book value
Chapter 6, Annuities and Perpetuities -- Basic Formulas

• Annuity Present Value

PV = C x {1 - [1/(1 + r)t]}/r

•   Annuity Future Value

FVt = C x {[(1 + r)t - 1]/r}

• Annuity Due Value
Annuity due value = Ordinary Annuity value X (1+r)

• Perpetuity Present Value

PV = C/r

• The formulas above are the basis of many of the calculations in Corporate
Finance. It will be worthwhile to keep them in mind!
Chapter 10, Making Capital Investment Decisions
•   The Tax-Shield Approach

OCF        =          (S - C - D) + D - (S - C - D) x Tc

=          (S - C) x ( 1 - Tc) + (D x Tc)

=            (S - C) x (1 - Tc) + depreciation tax shield
•   The Bottom-Up Approach

OCF        =          (S - C - D) + D - (S - C - D) x Tc
=          (S - C - D) x (1 - Tc) + D
=             Net income + depreciation
•   The Top-Down Approach
OCF     =             (S - C - D) + D - (S - C - D) x Tc
=             (S - C) - (S - C - D) x Tc
=             Sales - costs - taxes

•   The after-tax salvage value is: market value - (market value - book value) x (Tc)

•   Equivalent Annual Cost: EAC = Present Value of Total Cash Flows / PVAF
PVAF is the Present Value Annuity Factor
Review of Cash Flow (from Chapter 2)
1.Cash flow from assets or Total Cash Flow

Cash flow from assets = Operating cash flow
– Net capital spending
– Additions to net working capital (NWC)
where:
Operating cash flow = Earnings before interest and taxes (EBIT)
+ Depreciation – Taxes

Net capital spending = Ending net fixed assets – Beginning net fixed assets
+ Depreciation

Change in NWC = Ending NWC – Beginning NWC

   Half-year (50%) rule:
In the year of acquisition, 1/2 of net acquisitions is added to the UCC balance and used
to calculate CCA.
The remaining 1/2 is added the following year.
Chapter 11, Project Analysis and Evaluation

•   TC = total variable costs + fixed costs

•   Summary of Break-Even Measures:
where:   FC = total fixed costs
P = Price per unit
v = variable cost per unit
I. The Accounting Break-Even Point
Q = (FC + D)/(P - v)

II. The Cash Break-Even Point
Q = FC/(P - v)

III. The Financial Break-Even Point
Q = (FC + OCF*)/(P - v)

•   Degree of Operating Leverage,        DOL = 1 + FC / OCF
Chapter 15, Raising Capital

•   The number of new shares to be issued =(Funds to be raised)/Subscription price

•   The new share price = (New firm value)/(Total number of shares outstanding).

•   The value of the right must =          Old share price - new share price.

•   Another formula for the Value of a Right:        R 0= (M0 - S) / (N+1)

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