Corporate Finance Thimmesch Fall 2016

Formula Sheet

A. PV=FV/(1+r)^n

B. FV=PV(1+r)^n

1. irf ↑, FV ↓

2. n ↑ i ↑

C. Compounding

1. V = P(1+r)^n

D. Rule of 72

1. 72/Interest Rate

E. Valuing Annuities (and bonds)

1. PV= 1r-1r(1+r)n

2. Irf ↑, PV ↓

F. Sum of discounted present values (interest payments) + Value of principal repayment n years

1. PV= 1r+1r(1+r)n

2. Market price (bond) < Face Value (Par Value) = Discount; Premium
G. Valuing Perpetuities
1. PV of Perpetuity=PMT Discount Rate=Pr
2. i ↑, Price/Value ↓
H. Common Stock/Valuing Perpetuities with Growth
1. PV of Growth Annuity= Initial Payment Discount Rate-Growth Rate or Pr-g
2. P = earnings, r = capitalization rate, g = growth rate
I. Valuing a Perpetuity with Initial Growth
Year Dividend x Discount Factor at 10% = Present Value
1
$1.00
.9091
$.9091
2
$1.04
.8264
$.8595
3
$1.0816
.7513
$.8126
4
$1.1249
.6830
$.7683
5
$1.17
.6209
$.7264
Subtotal
$4.0759
6
Perpetuity of $1.17 / .10 = $11.70 x .5645 =
$6.6046
Total Present Value
$10.6805
J. NPV
1. NPV of Project = PV of Funds to be Received - PV of Funds Invested
K. Effective Annual Rate
1. EAR or r=(1+APR or in)n-1
L. Internal Rate of Return
1. When discount rate that NPV = 0
M. Cost of Capital
1. Cost of Capital (CAPM)=Expected Return on Equity=Risk Free Rate of Return+Beta(Expected Market Rate of Return-Risk Rate of Return
2. re= rf+β(mr-rf)
3. risk ↑, expected return ↓
N. WACC
WACC= Value of DebtValue of Firm×Interest Rate+Value of EquityValue of Firm×Capitalization Rate
O. Expected Value
1. EV = the mean of probable values for each firm = risk = variance
2. Calculate this risk by finding the variance (deviation from the mean in each case)
P. Value Additivity
1. PVA+B = PVA + PVB
Q. Tax Shield
where r=interest rate on debt; d=Amount of Debt
R. Present value of the Tax Shield =
S. Formula for Cost to an Existing Investor from Issuance of Cheap Stock (Dilution)
L=
1. L = Shareholders loss through dilution
2. m = Market price of a share before issuance
3. a = Shareholders share ownership at the time new shares are issued
4. x = Shares outstanding before dilutive issuance
5. d = Number of shares issued in dilutive distribution
6. p = Proceeds from sale of new shares
T. Yield to Maturity
1. c(1 + r)-1 + c(1 + r)-2 + . . . + c(1 + r)-Y + B(1 + r)-Y = P
a) where
(1) c = annual coupon payment (in dollars, not a percent)
(2) Y = number of years to maturity
(3) B = par value
(4) P = purchase price
II. Dividend Discount Model
1. Formulas
a. Predicting Dividends
i. Constant Growth Stock
Dn = Dn-1 (1+g)n
Dn = Future Div. amount in year n.
g = growth rate = ROE x Payout Ratio
Payout Ratio = Dividends per share / Earnings per Share
(ROE) Return on Equity = Earnings per share / BV per share
b. Dividend Discount Model
i. General Formula
Dt = Expected Dividends in year t.
k = discount rate
t = Terminal Year
ii. Zero Growth Stock (i.e. dividend payments won’t change over time).
Where D = Expected Dividends
iii. Getting Discount Rate (k):
Reverse engineer from comparable companies (k= D/V)
Risk free rate of return + risk premium.
After tax cost of debt = (interest rate) (1- corp. tax rate)
WACC = (Value of debt x int. – tax rate) + (Value of Equity x cap. rate)
Value of Firm Value of Firm
Chapter 2: Financial Statements and Accounting Principles
I. Introduction
A. Accounting and financial statements are used to determine the value of companies.
B. The accounting profession has provided sets of general principles (standards, rather than rules) that in some cases allow several approaches to accounting for transactions.
C. The general accounting principles have been generated by a series of organizations over time.
I. Rule Making Bodies
A. American Institute of Certified Public Accountants (AICPA)
1. Principal professional organization for accountants
2. From 1939 to 1959 this group issued bulletins addressing specific problems.
3. Issued rules for companies to put together their financial statements
4. Had an accounting principles board - APB
5. Issued opinions on how to issue statements
6. Accountants trade organization - not independent of accountants
B. Financial Accounting Standards Board (FASB)
1. Representatives of the accounting profession, business, education and government
2. Independent of accountants - various stakeholders involved
3. Issue statements creating principles by which companies put together financial documents
4. SFAS #________
5. More like standards than rules.
C. Generally Accepted Accounting Principles (GAAP)
1. Standards of the profession
D. SEC
1.

f external transactions with third parties

D. Cash

1. Recognize transaction when actual money is received

E. Accrual

1. Make contract for sale of car, but has not transpired yet (will occur at a future time). Do not have money, but do have obligation from other party that you are going to receive money. Count receipt of that money as an asset of that firm even though you do not have it yet.

IV. Accounting Principles

A. Value

1. Intro

a) Stream of monetary benefits that a particular asset can provide – worth value of stream of benefits that asset (i.e. land) provides

2. Examples

a) Shares (dividends)

b) Bonds (coupon payments)

B. Flexibility

1. No one set of rules, different firms can use different methods that work for them

C. Standardization

1. We prefer standardization so that companies can be compared

2. Accounting Organizations (FASB) seek some standardization while allowing flexibility

D. Historical Cost Principle

1. Assets reported in terms of historical cost in arms-length transaction

E. Reliability Principle

1. Intro

a) Value of assets should be verifiable.

b) Can be shown to a regulator and show value assigned to a particular asset

c) Sometimes difficult/costly to show what accounts for value of a particular asset

2. Example

a) Intro

(1) If you have 1 million widgets and can sell them for $2 apiece, but some have defects and will be returned, how to account for them?

b) Sampling

(1) See what percentage are defective and show value of saleable inventory

F. Cost-Effective Principle

1. Accounting reports should be cost effective and need only report material information – information of a magnitude that it might influence a decision.

G. Economic Entity Principle

1. Intro

a) If parent owns at least 50% of a subsidiary, typically financial statements of subsidiary are included in statements of parent

2. Goal

a) To maintain single set of statements where parent actually controls the subsidiary