Exam Notes for Introduction to Finance

01 FINANCIAL STATEMENTS, TAXES & CASH FLOW

1. Balance sheet
 A snapshot of the firm’s assets & liabilities at a given point in time (i.e. “as of …”)
 Assets
 LHS / Upper portion: Shows how the firm uses its capital (investments)
 In decreasing order of liquidity
 Liquid assets: Cash
 Fixed assets: Tangible (e.g. property) & intangible (e.g. branding, copyright)
 Liabilities & owners’ (shareholders / stockholders / investors) equity
 RHS / Lower portion: Summarises the sources of capital / how the firm raises the
money it needs
 In ascending order of when due to be paid
 Owners’ equity: Paid in dividend form  An accounting measure of the firm’s net
worth
 Balance sheet identity
 Assets = Liabilities + Shareholders’ equity
 Net working capital (NWC) = Current assets – Current liabilities
 Usually positive for a healthy firm
 Liquidity
 Speed & ease of conversion to cash w/o significant loss of value
 Valuable in avoiding financial distress

2. Market value vs Book value
 Book value: Balance sheet value of the assets, liabilities & equity
 Market value: True value (the price at which the assets, liabilities & equity can actually be
bought / sold)
 More relevant for decision-making

3. Income statement
 Measures performance over a specified period of time (period, quarter, year)
 End result  Net income (“bottom line”)
 Net income = Revenues – Expenses
 Retained earnings = Net income – Dividends

4. Financial statements
 Generally Accepted Accounting Principles (GAAP) matching principle
 Only recognise revenue when it is fully earned (record as it happens)
 Match expenses required to generate revenue for the period of recognition
 Non-cash items
 Expenses charged against revenue that do not affect cash flow (e.g. depreciation)
 Time & costs
 Fixed & variable costs
 Not obvious on income statement
 Earnings management
 Smoothing earnings: To minimise fluctuation  Stable income
 GAAP leaves “wiggle room” (by manipulating depreciation relative to earnings)

5. Marginal tax rates vs Average tax rates
 Marginal tax rates = % tax paid on the next dollar earned
 More relevant for decision-making
 Average tax rates = Total tax bill ÷ Taxable income

,6. Cash flow
 Cash flow from assets (CFFA)
 CFFA = Operating cash flow (OCF) – Net capital spending (NCS) – Changes in NWC
 OCF = Earnings before interest & taxes (EBIT) + Depreciation – Taxes
 NCS = Ending net fixed assets – Beginning net fixed assets + Depreciation
 CFFA = Cash flow to creditors (bondholders) (CFCR) + Cash flow to stockholders
(owners) (CFSH)
 CFCR = Interest paid – Net new borrowing
 CFSH = Dividends paid – Net new equity raised


02 TIME VALUE OF MONEY

7. Definitions
 Time value of money: The difference in value between money today & money in the future
 Present value (PV)
 The current value of future cash flows discounted at the appropriate discount rate
 Value at t=0 on a time line
 Future value (FV)
 The amount an investment is worth after ≥ 1 period(s)
 “Later” money on a time line
 Interest rate (r)
 Its terminology depends on usage
 Risk free interest rate, Rf: The interest rate at which money can be borrowed / lent
w/o risk over a given period of time

8. Present value & future value: General formula
 FV = PV (1 + r)t
 r = period interest rate
 t = number of periods
 (1 + r)t = future value interest rate factor
 Finding the PV of a future cash flow is “discounting”, which is the reverse of “compounding”

9. Future value (FV)
 Effects of compounding
 Simple interest: Interest earned only on original principal
 Compound interest: Interest earned on principal & on interest received
 “Interest on interest”: Interest earned on reinvestment of previous interest
payments
 Compounding frequency
r nt
 FV = PV (1 + )
n
 n = number of times the interest is compounded in a year
 t = number of years
 Where the interest is compounded “continuously”
 Let n  ∞
lim
𝑛→∞ FV = PV x ert

10. Present value (PV)
 Worth less than FV due to:
 Opportunity cost (the loss of other alternatives when 1 alternative is chosen)
 Risk & uncertainty

, 11. Discount rate
 Implied rate of interest
1
FV t
 r=( ) –1
PV

12. Number of periods
FV
( ¿)
 t = ln PV ¿
ln(1+r )

13. Relationships
 For a given interest rate: The longer the time period, the higher the FV; the lower the PV
 For a given time period: The higher the interest rate, the higher the FV; the lower the PV
 For a given interest rate & PV, the more frequent the interest is compounded, the higher the
amount of interest & FV
 For a given interest rate & FV, the more frequent the value (or cash flows) is discounted, the
lower the amount of PV


03 DISCOUNTED CASH FLOW VALUATION

14. Annuity
 A finite set of equal sequential cash flows
 Ordinary annuity: 1st payment occurs at the end of the period
1
1− t
 PV = PMT [ (1+r ) ]
r
t
(1+r ) −1
 FV = PMT [ ]
r
 Annuity due: 1st payment occurs at the beginning of the period (1 st payment begins
immediately)
t
(1+r ) −1
 FV = PMT [ ] (1 + r)
r
1
1− t
 PV = PMT [ (1+r ) ] (1+ r)
r

15. Perpetuity
 A perpetual annuity: An infinite set of equal sequential cash flows
 1st cash flow occurs 1 period from now
PMT
 PV =
r
 PMT = payment

16. Interest rates
 Effective annual rate (EAR)
 The interest rate expressed as if it were compounded once per year
 To compare 2 alternative investments w/ different compounding periods
 Annual percentage rate (APR)
 The annual rate quoted by law
 APR = Periodic rate x Number of periods per year
 Relationship between EAR & APR