Formulas International Finance - Master PDF

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FORMULAS - INTERNTIONAL FINANCE (MASTER)

Table of Contents FORMULAS - INTERNTIONAL FINANCE (MASTER).....................................................................1 2ND ,3RD . AND 4TH CHAPTER................................................................................................................2 Exchange rates.......................................................................................................................................................2 Purchasing Power Parity........................................................................................................................................3 Fisher Effect...........................................................................................................................................................4 Interest Rate Parity................................................................................................................................................5 Forward Rate and Future Spot Rate......................................................................................................................5

7TH, 8TH AND 9TH CHAPTER..................................................................................................................6 Transaction costs...................................................................................................................................................6 Forward rate quotations........................................................................................................................................6

SESSION 3B – CFA MATERIAL..............................................................................................................6 Value of the Portfolio.............................................................................................................................................6

SESSION 3C – CFA MATERIAL..............................................................................................................6 SESSION 5A – 14TH CHAPTER - THE COST OF CAPITAL FOR FOREIGN INVESTMENTS...........................7 Capital Asset Pricing Model - CAPM......................................................................................................................7 WACC - Weighted Average Cost of Capital............................................................................................................7 DISCOUNT RATES FOR FOREIGN INVESTMENTS....................................................................................................7

SESSION 5B – 15TH CHAPTER - INTERNATIONAL PORTFOLIO INVESTMENT.........................................8 FOREIGN MARKET BETAS.......................................................................................................................................8 Bond return formula..............................................................................................................................................8 Stock return formula.............................................................................................................................................9

SESSION 5C – CHAPTER 17 - CAPITAL BUDGETING FOR THE MULTINATIONAL CORPORATION............9 INCREMENTAL CASH FLOWS.................................................................................................................................9

SESSION 6D – CASH FLOW ESTIMATION + PROJECT ANALYSIS...........................................................10 OBERATING CASH FLOW......................................................................................................................................10 PROJECT CASH FLOWS.........................................................................................................................................10 AAR......................................................................................................................................................................10 PRO FORMA INCOME STATEMENT......................................................................................................................11 CHANGES IN NWC...............................................................................................................................................11 OPERATING CASH FLOW......................................................................................................................................12 TOTAL CAHSFLOW FROM ASSETS........................................................................................................................12

1 Anna Lilja Johansen

FIRST SESSION

2ND ,3RD . AND 4TH CHAPTER Exchange rates Quoted in direct terms: you need ISK 115 to buy USD 1, i.e.

Quoted in indirect terms: for ISK 1 you get USD 0.0087, i.e.

Calculating the change in the value of a currency (relative to another currency)

Make sure that S1 and S0 are quoted equally and that you interpret this “return" correctly!

2 Anna Lilja Johansen

Purchasing Power Parity

where: • • • • •

St is the future spot rate S0 is the current spot rate ih is the home inflation rate if is the foreign inflation rate t is the time period

Purchasing Power Parity •

If purchasing power parity is expected to hold, then the best prediction for the one-period spot rate should be written as

•

Less precise: S t−S 0 =i h−i f S0

Purchasing Power Parity • Adjusting the quoted or nominal exchange rate for the inflation rate(s) yield the real exchange rate

•

Real exchange rates should stay the same, if the nominal rates adjust to the inflation differential (i.e. PPP holds). This means that domestic and foreign firms are unaffected by inflation. 3 Anna Lilja Johansen

Fisher Effect • 1 + rnominal = (1 + rreal )(1 + i ) • Less precise: rnominal = rreal + i • Without government intervention: differences in (nominal) interest rates result from differences in inflation:

• This implies that countries with higher inflation rates have higher interest rates.

International Fisher Effect •

The spot rates adjust to the interest rate differential countries. • In this sense, the international Fisher effect combines purchasing power parity and the Fisher effect:

between two

• The nominal interest rate differential should reflect the inflation rate differential. • Expected rates of return are equal in the absence of government intervention.

International Fisher Effect •

Simplified (if rf is relatively small): S 1− S 0 =r h−r f S0

•

Implications: • Currency with lower interest rate is expected to appreciate relative to the one with a higher rate. • Financial market arbitrage: insures interest rate differential is an unbiased predictor of change in future spot rate.

4 Anna Lilja Johansen

Interest Rate Parity The forward exchange rate (F) differs from the spot exchange rate (S) at equilibrium by an amount equal to the interest differential between two countries. The forward premium or discount equals the interest rate differential:

In equilibrium, returns on currencies will be the same, i.e. no profit will be realized and interest parity exists:

Forward Rate and Future Spot Rate Unbiased forward rate • If the forward rate F0,t is unbiased, then it should reflect the expected future spot rate E(St ). • Stated as:

5 Anna Lilja Johansen

7TH, 8TH AND 9TH CHAPTER Transaction costs • • • •

Bid-ask spread Bid: price at which the bank will buy the currency Ask: price at which the bank will sell the currency (offer price) Percent spread (PS) formula:

Forward rate quotations •

Outright rate: quoted to commercial customers.

•

Swap rate: quoted in the inter-bank market as a discount or

SESSION 3B – CFA MATERIAL Value of the Portfolio Current value = S0 * FX0 Future value = ST * FXT

SESSION 3C – CFA MATERIAL Terminology • Vt = value of foreign assets to be hedged at time t • Vt* = value of foreign assets measured in domestic currency • St = spot exchange rate • Ft = futures exchange rate • R = rate of return on portfolio measured in foreign currency • R* = rate of return measured in domestic currency • s = percentage movement in the exchange rate

6 Anna Lilja Johansen

SECOND SESSION

SESSION 5A – 14TH CHAPTER - THE COST OF CAPITAL FOR FOREIGN INVESTMENTS COST OF EQUITY CAPITAL Capital Asset Pricing Model - CAPM rE = rf + βi ( E(rm) - rf ) where rE = the equity required rate E(rm) = the market rate of return rf = the risk free rate of return βi= Cov(rm, ri)/ m2 where

WACC FOR FOREIGN PROJECTS WACC - Weighted Average Cost of Capital

(WACC = r0)

r0 = (E/V) rE + (D/V) rD (1 - t) where E/V = the parent’s equity ratio D/V = the parent’s debt ratio rD (1 - t) = the after-tax debt cost rE = the equity cost of capital r0 is used as the discount rate in the calculation of Net Present Value. Two Caveats: a. Weights must be a proportion using market, not book value. b. When calculating WACC, weights must be marginal, i.e. they must reflect the firm’s future debt structure.

DISCOUNT RATES FOR FOREIGN INVESTMENTS Relevant Market Risk Premium a. Should use the U.S. portfolio b. Can adjust foreign market risk premium by calculating: MRPFOREIGN = MRPHOME * (FOREIGN / HOME) 7 Anna Lilja Johansen

SESSION 5B – 15TH CHAPTER - INTERNATIONAL PORTFOLIO INVESTMENT THE BENEFITS OF INTERNATIONAL EQUITY INVESTING Correlations and the Gains From Diversification FOREIGN MARKET BETAS 1. Calculation of foreign market betas Foreign market beta

Correlation Std dev with U.S. x for. mkt. market Std dev U.S. mkt. 4. Calculation of Expected Return: =

rp = a rUS + ( 1 - a) rRW where

rp = portfolio expected return rUS = expected U.S. market return rRW = expected global return (rest of the world)

5. Calculation of Expected Portfolio Risk = (P ) 2 1/2 2 2 2 P = [a US + (1-a) RW + 2a(1-a) USRW ρUS,RW]

where

ρUS,RW = 2 US = 2 RW =

the cross-market correlation U.S. return variance Rest of world return variance

MEASURING TOTAL RETURNS FROM PORTFOLIO INVESTING Bond return formula (Exact): 1 + rh

where 8 Anna Lilja Johansen

rh B(t)

=[1 +B(1) - B(0) + C ](1+s) B(0)

= dollar return = foreign currency bond price at time t

C = coupon income s = depreciation/appreciation of foreign currency Stock return formula: 1 + rh =[ 1+ P(1) - P(0) + D ](1+s) P(0) where

rh P(t) D

= dollar return = foreign currency stock price at time t = foreign currency annual dividend

SESSION 5C – CHAPTER 17 - CAPITAL BUDGETING FOR THE MULTINATIONAL CORPORATION BASICS OF CAPITAL BUDGETING 2. NPV Formula: n

N P V

= - I

0

+

å t =1

X t (1 + k )

where I0 = initial cash outlay Xt = net cash flow at time t k = cost of capital n = investment horizon

Getting the base case correct INCREMENTAL CASH FLOWS Rule of thumb: Incremental cash flows

9 Anna Lilja Johansen

Global = corporate cash flow with project

-

Global flow without project

t

SESSION 6D – CASH FLOW ESTIMATION + PROJECT ANALYSIS OBERATING CASH FLOW

 OCF = EBIT + Depreciation - Taxes PROJECT CASH FLOWS T2.5 Example: Using Pro Formas for Project Evaluation (continued)  Project Cash Flows

0 OCF

$12,280

Chg. NWC

-10,000

Cap. Sp.

-21,000

Total

-31,000

1 $12,280

2 $12,280

10,000

$12,280

$12,280

 PCF = OCF ± NWC – Capital Spending AAR AAR

=

(Average Net Income) / (Average Book Value)

10 Anna Lilja Johansen

3

$22,280

PRO FORMA INCOME STATEMENT

T2.12 Example: Fairways Pro Forma Income Statement

Year 1

Revenues

2

$60,000

Variable costs

3

4

5

$62,250 $64,500 $66,750

6

$69,000 $71,250

3,000

3,150

3,308

3,473

3,647

3,829

Fixed costs

53,000

53,000

53,000

53,000

53,000

53,000

Depreciation

2,700

4,590

3,213

2,249

1,574

1,102

$1,300

$1,510

$4,979

$8,028

Taxes(20%)

260

302

996

1,606

Net income

$1,040

$1,208

$3,983

$6,422

EBIT

$10,779 $13,319 2,156

2,664

$8,623 $10,655

Slide19

CHANGES IN NWC

T2.13 Example: Fairways Projected Changes in NWC

n Projected increases in net working capital

Year

Net working capital

Change in NWC

0

$ 3,000

$ 3,000

1

3,150

150

2

3,308

158

3

3,473

165

4

3,647

174

5

3,829

182

6

4,020

- 3,829 Slide20

11 Anna Lilja Johansen

OPERATING CASH FLOW

T2.14 Example: Fairways Cash Flows

n Operating cash flows:

Year 0

EBIT $

+ Depreciation

0

$

Operating = cash flow

– Taxes

0

$

0

$

0

1

1,300

2,700

260

3,740

2

1,510

4,590

302

5,798

3

4,979

3,213

996

7,196

4

8,028

2,249

1,606

8,671

5

10,779

1,574

2,156

10,197

6

13,319

1,102

2,664

11,757 Slide21

TOTAL CAHSFLOW FROM ASSETS

T2.14 Example: Fairways Cash Flows (concluded) n Total cash flow from assets:

Year 0

OCF $

– Chg. in NWC

–

Cap. Sp.

=

Cash flow

0

$ 3,000

$18,000

– $21,000

1

3,740

150

0

3,590

2

5,798

158

0

5,640

3

7,196

165

0

7,031

4

8,671

174

0

8,497

5

10,197

182

0

10,015

6

11,757

-3829

-1,954.40*

17,540.40

* Note: MV-(MV-BV)*T=$1,800-($1,800-$2,572)*0.2=$1,954.40 Slide 22

12 Anna Lilja Johansen...