Final cheat sheet for finance PDF

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Final Cheat Sheet for Finance...

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WACC: Required return that pays all interest and principal and compensates shareholders

Market yield (i) =

Cost of equity 1st METHOD: Dividend Models

n=8

Re

Constant dividend:

= Div/

P0

2

Cost of preference shares:

P0

= required rate of return

R =¿ / P 0

= current preference share price

= current share price WACC =

Re

Dividend growth:

¿1

=(

/

P0

)+

g g = constant growth rate of dividend

¿1

= dividend received next period

However, only applies when paying dividends, assumes constant rate, does not consider risk nd

2 METHOD: Security Market Line Expected return depends on:

Re

=

Rf

+

β ( Rm−R f ) Rf = Risk free rate of interest Rm−R f = Market risk premium β = Systematic risk of asset

Cost of debt if perpetual: D = market value of debt INT = interest paid on debt

[

−n

1−(1+i) i

]

d=¿ ∫ ¿ D R¿

−n

then times by no. outstanding which is issue cost/current bond trading $ What is $ of bond issued 2 years ago, has 8 years to maturity, coupons are paid half-yearly and PMT was made today, rate is 5% p.a. and current market yield is 6% p.a. with a FV of $200,000 FV = $200,000

×

5,000 N.B Coupon rate % needed

5% 2

( ) ( )

D E P +R e + Rp ( ) V V V

= market return on debt finance = market return on equity = market return on preference shares = market value of debt = market value of ordinary shares (no.

×

current market $)

= market value of preference shares

=

×

6.25 = 625000

Market value 7.5% 7.9% 8.5% 10.8%

Market rate 12m 9m 5m 66m 92m

×

5%/6.25 = 8%

Weight × Required Rate of Return or Market Rate = Totals for WACC

Capital Structure

EPS = Profit after tax/# of shares ROE = PAT/shareholder funds (no.

×

$)

To calculate the break-even point 1. Point where EPS is the same as EBIT 2. Or, EPS =

( EBIT −1 ) ×(1−t c ) No . of shares

Then to calculate the break-even point: EPS (Current) = EPS (Proposed)

(EBIT – I ) × ( 1 – t c ) No . of shares option1 (EBIT – I )× (1 – t c ) No . of shares option2

=

WAAC = 7.5(1-0.3)(12/92) + 7.9(1-0.3)(9/92) + 8.5(5/92) + 10.8(66/92) = 9.44%

Where I = INTerest Solve algebraically Capital structure example Lucy has $8 million of debt, interest rate of 5% pa., tax rate of 30% Plans a $4 million debt issue to repurchase equity Current share price is $40 and there are 400,000 shares issued EBIT is expected to be $2,500,000

WAAC Example 2 Book value of Long-Term Debt ($4m), Preference Shares ($1m), Ordinary Shares ($2m)

EBIT INT

Current 2,500,00 400,000

Planned 2,500,00 600,000 (5% × + E) 1,900,000 570,000 1,330,000 300,000 4.43 11.08%

The long term debt is perpetual and carries a fixed rate of 8.5% pa. It is advised that the current replacement cost for this type of debt is 7.25% pa 8.5%/7.25% =4689655 Market value = 4m Current market require rate of return = 7.5%

Pre-tax profit 2,100,000 Tax 630,000 Net income 1,470,000 # of shares 400,000 EPS 3.68 The company has 1,000 ordinary shares on issue and ROE 9.2% each share pays a constant dividend of 0.40 per year (likely to stay this way indefinitely). The current market price of a share in $4.00 However, only allows changes in EBIT, does not consider implicit costs of different debt levels, MV = 1m × $4 (market price) = $4000000 additional information must be used Current market require rate of return = 0.4/4 = 10%

×

Preference shares have a $10 FV, paying an annual dividend of 5%. The last sale of one of the company’s

Modigliani and Miller

Suggest overall cost of capital is constant regardless E.g. Apples in France cost EURO2 per kg and AUD3, of debt, value is determined by real assets, especially the exchange rate is 0.61 as interest payments are tax deductable Price in France = 0.61, 3 = EUR1.83 There is a profit opportunity so the price Optimal capital structure of apples and/or exchange rate When WACC is minimised and firm’s value is should change maximised Value = Value if all equity is financed + PV of tax Relative PPP shield – PV costs of financial distress Change in exchange rate is determined by the difference in the inflation rates in the two countries

Foreign Exchange

Break-even analysis Used to measure impact of different capital structures and results on EPS

= company tax rate

WAAC Example 1 Source Bonds Permanent debt Pref shares Ordinary shares Total market V

+ FV (1+i)

PMT = $200,000

issued

MV = 1m/10

However, only if project is identical to the firm, not appropriate for firms with divisions

Cost of debt if it matures:

PV = PMT

Rd Re Rp D E P tc

However, requires market risk premium and beta, relies on past for future Cost of debt

Rd ( 1−tc)

preference shares on the market was at a price of $6.25 Current market RRR = $10

p Div = current fixed dividend per share

Div = constant dividend payment

Re P0

×

6% 2

D

FOREX: Price of one country’s currency expressed in E.g. AUD1 = SGD1.2, inflation rate is 3% in Australia and 7% in Singapore terms of another country’s currency Meaning prices in Singapore relative to Participants: dealers, overseas banks, clients, Australia are increasing at 7-3 = 4% brokers, RBA Therefore the price of the SGD should Purpose: export/imports, borrowing/lending/, fall by 4% relative to AUD buying/selling assets, speculation and arbitrage Predicted exchange rate AUD1= 1.2 Therefore AUD1.04=1.25 Terminology Cross-rate: exchange rate between 2 currencies Interest Rate Parity excluding USD (two used to determine third) Eurocurrency: money deposited in a financial centre Exchange rate should appreciate/depreciate as to equalise effective realised interest rates between outside of the country whose currency is involved countries LIBOR: the interest rate that international banks charge for loans of Eurodollars overnight in the E.g. If Aus rates 8% pa and US rates were 5%, a London market Spot trade: agreement to exchange currency ‘on-the- devaluation of the A against US is expected. If you borrow US 1 million at 5% and covert to A1 million, spot’, actually settled in 2 business days and invest at 8% Forward trade: agreement to exchange currency at At the end of the year you have some time in the future A$1,080,000 Appreciate: value of the currency rises (takes more And repay $1,050,000 foreign currency to buy the appreciating currency) Make a profit of A$30,000 Depreciation: the value of a currency falls This is not sustainable as the exchange rate would move Currency codes SGD = Singapore dollar; GDP = Great Britain Pound; CHF = Swiss Francs; JPY = Japanese Yen; HKD = Hong Foreign Exchange Risk Importers face risk of depreciation of AUD (need to Kong Dollar; SEK = Swedish Kronor increase amount of AUD for given amount of USD) The Foreign Exchange Quote Exports face risk of appreciation of AUD AUD/USD = 1.0564/1.0567 AUD = Commodity Currency E.g. Importer of USA-grown oranges orders 10,000kg US = Terms currency from their supplier at US$2 per kg. The order is First price = buy price placed today but payment is made in 60 days. The Second price = Sell price selling price is AUD$3 per kg. The exchange rate is A$1 = US$0.9 and this rate can be locked-in today. Facts: SD is most traded, AUD is 5th most, turnover What is the profit? 192 billion USD per day, UK/US did most trading Cost in $US is 10,000 x 2 = 20,000 Cost in $A is 20,000/0.9 = 22,222 Conversions Therefore profit is (10,000 x 3) – 22,222 Assume you want to get a NZD to a SEK, if AUD/SEK = = 7,778 6.8962 and AUD/NZ = 1.2524 What if $A dropped to US$0.80 6.8962 1.2524 = 5.5064 Cost in $US =is 20,000/0.8 = 25,000 (therefore $1NZD = 5.5064 Kronor) Therefore profit is 30,000 – 25,000 = 5,000 Predicting exchange rates Fundamental analysis e.g. interest rates, inflation Capital Budgeting: selecting projects that Technical analysis i.e. graph of historical market maximise shareholder wealth

÷

Purchasing power parity Absolute PPP Same price for product regardless of where (gold)

FIRST METHOD: Accounting Rate of Return

Average net profit (Initial Cost+Salavage)/2

A firm can acquire a machine for $18,000 and this will result in a net increase in cash flows by $5,600 per year for 5 years. At the end of 5 years, the machine has no value. Assume straight line depreciation of $3,600 a year Accounting profit is 5,600 – 3,600 = 2,000 per year Average book value is (18,000 + 0)/2 = 9,000 ARR is 2000/9000 = 22% SECOND METHOD: Payback Period (length)

Investment cost Yearly cash flows If unequal flows; work out the year it’s paid in, then difference divided by next payment THIRD METHOD: Discounted payback Cash flows are converted to PV first to remove TVM problem FOURTH METHOD: Net Present Value

−Original+

Cash flow Cash flo + ( 1+% ) ( 1+% )

FIFTH METHOD: Internal Rate of Return IRR is the rate of return that gives a 0 NPV Accept projects with a IRR > discount rate Reject projects with IRR < required return Profitability Index PI = (NPV + Initial Cost)/Initial Cost Indifferent if PI = 1 Accept if PI > 1 Reject if PI < 1 Shows relative profitability of project or PV of benefits per dollar of cost Capital Budgeting 2 (estimating project cash flows, financing costs, tax and depreciation) Cash flows at the start (at the beginning/initial) Purchase of equipment Proceeds from sale of old machine Investment in working capital Market value of assets owned that are to be used in the project

Depreciation tax savings = Depreciation x 0.3 After-tax cash outflow = 950,000 (1 – Total -57,950 Total 14,350 x Total 0.3) = 665,000 Net after-tax cash flow = Pre-tax cash flow (1 – 0.3) + 11.050 x Fixed cash costs will remain at $350,000 pa. Depreciation x 0.3 1−( 1.15 ) ‘Savings’ is as good as a cash inflow $350,000 of stock is required at the beginning of the 0.15 We have ‘tax affected’ cash flows year and this cost is reflected in operating cost Cash flow at start of -350,000 Straight line depreciation Cash flow at tend of +350,000 Risk and Return: (portfolios, market efficiency, Constant % written off each year, cannot go below 0 The required rate of return is 8% security market line and beta) WDV = Initial Cost – Accumulated Depreciation Discount rate for NPV ATO sets the asset’s effective life Efficient Markets Hypothesis is that no one can Start Over the life End consistently make abnormal profits Cash flow at the end Purchase of Sales Sale of plant One-off cash flows to restore to previous situation plant 665,000 200,000 Measuring return E.g. Investment in working capital and salvage value -1,500,000 Less costs P/L on sale Percentage return of assets (can be tax implications) Inventory 350,000 90,000 One period % return = -350,000 Tax saving Recovery of Salvage value of assets 30,000 inventory Tax effect on asset sale if the salvage value and book 350,000 value is different Total Total Total 345,000 If SV > BV, the difference is taxable profit 640,000 -1,850,000 Many investments have periodic cash flows, to 1−(1.08 If SV < BV, the difference is a loss −10 adjust for this: Both situations, tax-related cash flows occur 0.08 where t t t −1 t t −1 What costs are inflows/outflows? D t =¿ the dividend Capital Budgeting Example 2 Sale of old machine Inflow; Start Cost of new machine $65,000 (Outflow; Start) BV of old machine No Time value of money Tax depreciation on new machine $8,000 Purchase price of new Outflow; Start −n or P = D/r (where r is the PV = FV Company tax rate 30% Installation cost Outflow; Start Selling expense for new Outflow; Over Life Increased sales from new machine $3,000 (Inflow; rate of return on investment) Over Life less tax = 3000(1 – 0.3) = 2,100) Market research No Decreased cash operating costs $14,500 (Inflow; Sale of new product Inflow; Over Life Average return on investment Over Life less tax = 14,500(1 – 0.3) = 10,150) Depreciation expense No Life of new machine 6 years R=( Expense that remains No 1 + 2 +…+ n )/n Salvage value of new machine $8,500 (Inflow; Year 6) Increase tax saving Inflow; Over Life r = return for the period n = number of observations Reduced sales in existing Outflow; Over Life N.B Check if this is an inflow or outflow on sale products 6,500 – (8,000 x 6) = 17,000 i.e. WDV Variability (or risk) of returns Increase in sale from new Inflow; Over Life 17,000 – (8,500 x 0.3) = 2,550 A risk-free asset has a standard deviation equal to 0 Decrease cash operating cost Inflow; Over Life

[

End of period value – Start of pe Start of period value

[

(1.08)

R =( P −P

Salvage value of new machine today $7,500 (Inflow; Now) N.B Check if this is a profit or loss Capital Budgeting Example 1 6,000 is WDV (from below) New machine costs $1,500,000 and will be sold in 10 6,000 – (7,500 x 0.3) = -450 years for an estimated salvage value of $200,000. The tax allowable depreciation life is 15 years at 30% Current BV of old machine $6,000 Depreciation of old machine $1,000 (1,000 x 0.3 = Cash flow at start -1,500,000 300) Depreciation expense = 1,500,000 Remaining life of old machine 6 years 15 =

÷

100,000 Tax savings = 100,000 x 30% = $30,000 per year Cash flow in year 10 (when sold) of -200,000 Company taxes (30%) Book value in year 10 is 1,500,000 – (10 x 100,000) = All operating revenue and operating costs are 500,000 taxable 100,000 is accumulated depreciation Purchases of assets are not deductible at the time of Tax affect = (500,000 – 200, 000) x 30% = 90, 000 purchase (but depreciation is allowed as a tax 500,000 – 200, 000 is BV – SV deduction) Annual cash operating costs are $500,000 and expected cash sales are $950,000 Cash flow during the life After-tax cash inflow = 500,000 (1 – 0.3) Tax (outflow) = 350,000 After-tax cash flow = Pre-tax cash flow (1 – 0.3)

Start New machine -65,000 Sale of old machine +7,500 Tax expense -450

Over Life Increased sales 3,000 Cost savings 145,000 Net cash flow before tax 17,500 Tax -5,250 Dep tax saving 2,100

End Sale of new machine 8,500 Tax saving 2,550

r

S=

´ 2 +…+¿ (Rn− R) ´ 2 /n−1 (R1−R) √¿ ´R = average return R=¿ actual return for observation

Also found by square root of the variance Standard deviation example Example: the yearly share prices are 2006, $10; 2007, $16; 2008, $12; 2009, $18 Average yearly return for 2007 = (16 – 10)/10 = 60% Avg yearly return for 2008 = -25% Avg yearly return for 2009 = 50%

´R

Future variability (incorporates probabilities)

√ ∑ P ×[ R −E ( R ) ]

σ= Ri Pi

= (60 + -25 + 50)/3 = 28.33%

2

i

i

= return for state i = probability of state i

E.g. investment has 50% chance of 12%, 30% chance of 15%, 20% chance of -5% E(R) = 0.5(12) + 0.3(15) + 0.2(-5) = 9.5% Standard deviation = 2 2

0.5 ( 12−9.5) +0.3 ( 15 −9.5) +0.2( ¿ √¿

r

Standard deviation

Average or S=

Expected Return Example E.g. investor believes returns depend on the state of the economy Probability Return Strong 0.25 20% Weak 0.15 - 20% No changes 0.60 10% E(R) = 0.25(0.20) + 0.25(-0.20) + 0.60(0.10) = 0.08 = 8%

+D )/ P

(1+r )

r

Expected return

(1.15) Expected return = ∑ P × R i i Pi = probability of state i Ri = return for state i

= 7.36%

Systematic and unsystematic surprises Systematic affects large number of assets and is attributable to market factors which are unavoidable Unsystematic affects a single asset/small group and can be eliminated by forming a diversified portfolio (e.g. only one country) Portfolios (collection of assets) Expected rate of return for portfolio is: Weighted average of expected rates of return for each individual asset in the portfolio

r ¿

∑ W × E (Ri)

= p i Wi = % invested in asset i E(Ri) = expected return of asset

E(

Covariance and correlation Covariance is degree of association between two Correlation standardises from – 1 and + 1, moving together is 1 Many investments diversify portfolios and reduce risk (but minimum/systematic cannot be eliminated)

√(60−28.33 ) +(−25 −28.33) + Beta and systematic risk 2

2

Risk premium the excess after comparing returns to risk-free asset (cash)

Beta is a measure of systematic risk, measure relative to an average asset

β β

= 1 for the average asset (same as market) > 1 are more affected by market-wide

events

β

< 1 there is less systematic risk then the

market Beta Example Security

Amount Beta Weight invested ANZ 5,000 0.75 25% ASX 7,000 1.10 35% COH 8,000 1.36 40% Total invested is 20,000 Beta = 0.25(0.75) + 0.35(1.10) + 0.4(1.36) = 1.12 THE RELEVANT PORTION OF AN ASSET’S RISK TO AN INVESTOR IS NON-DIVERSIFIABLE RISK Capital Asset Pricing Model Linear relationship between expected return and systematic risk

R + β(R m− R f )

E(R) = f Rf = risk free rate Rm = expected return market B = beta of security All assets must lie on this line

Time Value of Money Simple interest

FV =PV +∫ ¿ or PV 1+i× n ¿ ∫ ¿ PV × i × n PV =FV /(1+i × n)

(

Compounded interest n

FV =PV (1+i) FV −n PV = or FV (1+i) n (1+i) Effective annual rates (EAR) To convert a nominal rate to an effective rate m ; m = no.

EAR=(1+i ) −1

compounding periods Annuities

FV =PMT

[

n

(1+i) −1 i

PMT = annuity payment n = number of payments i = per period interest rate

]

−n

PV =PMT 1−(1+i) i

[

Perpetuities

PV =PMT /i PMT (1− ( 1+i )−n)/i

] simplified

Valuation of debt Valuing short-term debt (bills) PV = FV/(1 + rt) r = interest rate (market rate, or YTM) t = time to mature Valuing long term debt (bonds) −n PV = PMT

[

1−(1+i) i

(1+i)−n

]

+ FV...