International Corporate Finance (ICF)

InternationalInternationalCorporate Finance (ICF)Corporate Finance (ICF)

Jim Cook

Cook-Hauptman Associates, Inc. (USA)

Day 1 in the pm # 2 / 25International Corporate Finance

AgendaAgenda Thursday – (Sessions am: 8:30-12:00, am: 1:30-5:00)

am: Structures, Statements, Value, Analysis, Currency pm: Time & Currency Discounting/Trading of Money

Friday – (Sessions am: 8:30-12:00, am: 1:30-5:00) am: Workshop on Evaluating Financials. Discussion of the RMB pm: Internal Operations: Cash Management & Project Evaluation

Saturday – (Sessions am: 8:30-12:00, am: 1:30-5:00) am: Workshop on Financial Projections and Raising Capital pm: External Operations: Markets’ instruments and practices

Sunday – (Sessions am: 8:30-12:00, am: 1:30-5:00) am: Workshop on Mini-Cases: Process, Discrete, Software, eBay pm: Reviewing important points. Final Exam.

On the Internet at: http://cha4mot.com/ICF0411


Future Value and CompoundingFuture Value and Compounding

Future Value: If you save 10,000 RMB today, how many RMB will you have in 2 or 3 years?

Year 0 1 2

Value 10000 11881

3

10900 12950

Future Value = ( Present Value ) * ( 1 + interest ) periods

RMB

That depends on the interest rate; for a 9% rate:


Present Value and DiscountingPresent Value and Discounting

Present Value: If you can get 10,000 RMB in 3 years, how many RMB should you get today?

Year 0 1 2

Value 7722 9174

3

8418 10000

Present Value = ( Future Value ) / ( 1 + interest ) periods

RMB


The Time-Value-of-MoneyThe Time-Value-of-Money Time-Value-of-Money Relationship:

Vt+T = Vt * (1 + r ) T

V(t+T) = V(t) * (1 + r) T (general form)

V(T) = V * (1 + r) T (t is presumed to be 0)

FV = PV * (1 + r) T

where all of the above are equivalent and: r is the interest rate per period (assumed constant) T is the duration of the investment (illiquidity) in periods Vt is the value at period t (when t=0, its called the present value or PV) Vt+T is the value at period t+T (future value) or FV

Note: “t” is usually 0, and so is usually left out along with it’s “+”. Only in continuous compounding can “t” be a part of a period.


How Long is the Wait?How Long is the Wait?

Problem: If we deposit 5000 RMB in an account paying 10% per annum, when will it double?

Solve for T : Vt+T = Vt * ( 1 + r ) T

10000 RMB = 5000 RMB * (1.10 ) T

(1.10 ) T = 2 = 10

log(2) = 10T * log(1.1)

T = log(2) / log( 1.10 )

= 7.27 years


Problem: Assume a college education will cost 600,000 RMB when your child enters college in 15 years. If you have 200,000 RMB to invest today, what rate of interest must you earn on your investment to pay for your child’s education?

Solve for r : Vt+T = Vt * (1 + r ) T

600000 = 200000 * (1 + r ) 15

(1 + r ) 15 = 600000/200000 = 3

(1 + r ) = 3 (1/15) = 3 .06666 = 10 .06666 * log103

log10(1 + r) = .06666 * log10 3 = .0318

(1 + r ) = 10 .0318 = 1.076

r = (1+r) – 1 = 1.076 – 1 = 7.6%

What Rate Is Enough?What Rate Is Enough?


Inflation/Deflation DiscountingInflation/Deflation Discounting

Problem: You want to invest some money now to buy a building in 5 years, but buildings are experiencing 4% inflation and all you can get is 7% on your money. If the building costs 1M RMB now, how much should you set aside to fully finance the purchase?

Solve for PV : FV = PV * (1 + r ) T

r is not 3%, but 2.8846% or –1 + ( 1.07 / 1.04 )

1000000 * (1 + .04) 5 = PV * (1 + .07)

5

PV = 1,000,000 * (1.04 ) 5 / (1.07)

5

PV = 1,216,652/1.40255 = 867,457


Non-annual CompoundingNon-annual Compounding Problem: How do the previous answers

change if the Compounding is quarterly?

FVYr = PV * ( 1 + r / 4 ) 4 * Yr

FV2 = 10000 * (1+.09/4) 4

*

2 = 11948 not 11881 RMB

FV3 = 10000 * (1+.09/4) 4

*

3 = 13060 not 12950 RMB

PV = 10000 / (1+.09/4) 4

*

3 = 7657 not 7722 RMB

10 = 5 x (1+.1/4) 4

*

Yr Yr = log2/(4*log1.025) = 7.02 not 7.27 Yrs

(1 + r / 4 ) = 3 4

*

Yr = 10(1/(4*15))*log3) = 1.01848 r = 7.4% not 7.6 %

10 6 = PV * ((1+.07/4)

4 *

5 / (1.04)

5) PV = 85996 not 86261


Normalizing Compounded Interest RatesNormalizing Compounded Interest Rates

Stated (nominal) Annual Interest Rate (AIR)Bank, “Annual Interest Rate is X% at m*X/12% every m months”The stated rate was X%, but the EAR is (1+m*X/12)^12/m - 1“The simple treatment; off a little bit from the compounded”

Effective Annual Interest Rate (EAR): EAR = (1 + AIR / m )

m – 1 (This should be the rate for internal decisions)

Example: Bank says, “AIR is 8.00%, compounded quarterly” It means, “Effective Annual Interest Rate is 8.24%” Advertisement says, “EAR is 8.24%, compounded quarterly” It means, “Quarterly compounding rate is 2.00%”

Continuous Compounded Interest Rate

FV = PV * e r

*

T

V(0+T) = V(0) * e r * T (where: e= 2.71828…)


Perspective & Transition to NPVPerspective & Transition to NPV The preceding must be learned COLD to be an MBA

Interest & Inflation/Deflation Rates are not constant (in reality), but are hard to assign otherwise in the future, except through options like forward contracts

These time-based computations should be thought of as time series, and when you see “time series analysis” you should feel “right at home”

Sometimes a constant amount is contributed or distributed over each period; let’s do these cases next

The following formulae should be applied after you decompose a situation into the appropriate cases.


Simple Future Cash Flows ISimple Future Cash Flows I Perpetuity (constant payout forever)

PV = C/(1+r)1+C/(1+r)2 … C/(1+r)∞ = C * Σ 1 / (1+r) t = C/r

Note: Take the case (as a rough approximation) where you want to guess the value of some instrument that is earning cash at the moment. You might wonder, “if it continues to earn at this rate, what is it’s value now?” It should be clear from the formula above that it is C/r where C (which stands for “Coupon”) or the value in a fixed period and r (which stands for “rate”) or the percent yield for the same period. As an mind exercise, “Why does the average P/E of the stock market move in the opposite direction of the prime interest rate?” “How much?”


Simple Future Cash Flows IISimple Future Cash Flows II

Growing Perpetuity (growing payout forever)

PV = C0 * Σ [ ( 1 + g ) t

-

1 / ( 1 + r )

t ] = C0 / ( r – g )

Annuity (annual fixed payout for fixed duration)

PV = C * [ [ Σ 1 / (1 + r ) t ] - [ Σ 1 / (1 + r )

T +

t ] ]

= C * [ (1 / r ) - 1 / (r * (1+ r ) T

) ] = C / r * [ 1 - 1/ (1+r) T

]

FV = C / r * [ (1+r) T – 1 ]

“Annuity” (constant payout / period for fixed duration)

PV = n * ( C / r ) * [ 1 - 1 / (1 + r / n ) n

* T

] note: n = year / period


Decomposing Simple Cash FlowsDecomposing Simple Cash Flows Pure Discount Bonds (face amount paid upon maturity) PV = Face / ( 1 + r )

T where T = periods until maturity

Level Coupon Bonds (periodic payments plus maturity)

PV = n * C / r * [ 1 - 1 / (1 + r / n ) n

* T

] + Face / (1 + r ) T

note: n is times paid per year (could even be ½, if paid every other year) C is the regular coupon payment and r is the discount rate

Bond Yield to Maturity (given the market price, what’s the yield)

note: you have to solve the above equation for r which is difficult for r>2and impossible, in the general case, for r>6

Procedure: Set up a NPV in a spreadsheet and when NPV = 0 the discountrate is the Bond Yield to Maturity.


Net Present Value (NPV)Net Present Value (NPV) Some tips for computing NPV:

Only add (subtract) cash flows from the same time period Specify a cash flow for each time period (even when it is $0) Use a spread sheet; saves a lot of time and effort

A Common International Discount Rate LIBR: London InterBank Rate (used for loans between banks)

The general formula for calculating NPV:NPV = - C0 + C1/(1+r) + C2/(1+r)2 + ... + CT/(1+r)T

This is nothing more than the sum for each number of periods: 1 + 2 + 3 … T minus the initial value (C0 is the price paid at time T=0).


Foreign Exchange MarketsForeign Exchange Markets

Exchange Rate - Amount of one currency needed to purchase one unit of another.

Spot Rate of Exchange - Exchange rate for an immediate transaction.

Forward Exchange Rate - Exchange rate for a forward transaction.


Forward Premiums & DiscountsForward Premiums & Discounts

Example - The yen spot price is 111.300 yen per dollar and the 3 month forward rate is 112.645 yen per dollar, what is the premium and discount relationship?

Premium = ( year / period ) * ( Forward – Spot ) / Spot = - Discount

Premium = 4 * ( 112.645 – 111.300 ) / 111.300 = .048

Answer - The dollar is selling at a 4.8% premium, relative to the yen. The yen is selling at a 4.8% discount, relative to the dollar.

What would you guess: The dollar’s getting stronger or weaker relative to the yen? Why?


Interest Rate Parity Theory

The ratio between the risk free interest rates in two different countries is equal to the ratio between the forward (future) and spot (today’s) exchange rates.

Note: r = “rational” prime interest rate in country of subscript for period given by the forward duration where annual is EAR computed.

Interest Rate Parity TheoryInterest Rate Parity Theory

=r+1

r+1

domestic

foreign

mesticforeign/do

mesticforeign/do

S

f


Exchange Rate ExampleExchange Rate Example

Value of US bond = $1,000,000 * 1.05 = $1,050,000

Value of Japan bond = $1,000,000 * 112.645 = 112,645,000 yen exchange

112,645,000 yen * 1.0025 = 112,927,000 yen bond pmt

112,927,000 yen / 107.495 = $1,050,500 exchange

Example - You have the opportunity to invest $1,000,000 for one year. All other things being equal, you have the opportunity to obtain a 1 year Japanese bond (in yen) @ 0.25 % or a 1 year US bond (in dollars) @ 5%. The spot rate is 112.645 yen:$1 The 1 year forward rate is 107.495 yen:$1

Which bond will you prefer, why? With and without transaction costs?


Expectations Theory of Exchange Rates

Expectations Theory of Exchange Rates

The expected spot exchange rate equals the forward rate

mesticforeign/do

mesticforeign/do

S

f

mesticforeign/do

mesticforeign/do )

S

E(s


Purchasing Price Parity EquilibriumPurchasing Price Parity Equilibrium

Purchasing Power Parity Equilibrium

The expected change in the spot rate equals the expected difference in inflation between the two countries.

=i+1

i+1

domestic

foreign

mesticforeign/do

mesticforeign/do )

S

E(s


Exchange Rate RelationshipsExchange Rate Relationships

Example - If inflation in the US is forecasted at 2.0% this year and Japan is forecasted to fall 2.5%, what do we know about the expected spot rate? Given a spot rate of 112.645 yen : $1

foreign/$

foreign/$

$

foreign )=

i+1

i+1

S

E(s

112.645

E(s )=

.02+1

.025-1 foreign/$Es = 107.68


International Fisher EffectInternational Fisher Effect

International Fisher Effect

The expected difference in inflation rates equals the difference in current interest rates.

Also called common real interest rates.

=i+1

i+1

domestic

foreign

domestic

foreign

r+1

r+1


Universality of Real InterestUniversality of Real Interest

Example - The real interest rate in each country is about the same.

.028 =.975

1.0025=

i+1

r+1)(

foreign

foreignrealr

.029 =1.02

1.05=

i+1

r+1)(

$

$realr

+ 1

+ 1

Why aren’t they identical? Is this an arbitrage opportunity?


Concluding RemarksConcluding Remarks

Questions and Answers

Thank you, again.

You can find a copy of this lecture (130 KB) on the Internet at:

http://cha4mot.com/ICF0411

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International Corporate Finance (ICF)