International Finance Faculty: Professor Bernard Dumas

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 International FinanceFaculty Professor
Bernard Dumas
Fall 2008

• Capital Budgeting and exchange rates
• Valuation with an exchange rate forecast vs.
  valuation after hedging

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Purpose of this lecture and the next

• Develop proper method such that
• In any given situation (list below),
• The way the cash flows (numerator) are calculated
• Is congruent with the discount rate being used
  (denominator)

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Issues in project valuation

• One issue already handled in previous courses
• Equity vs. debt / tax aspect
• FCF (at zero debt) discounted at WACC
• Or Adjusted Present Value method FCF (at zero
  debt) discounted at zero-debt cost of capital,
  plus PV of tax savings due to debt
• ?Physical investment decision not completely
  independent of liabilities side

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New issues in project valuation that come up
particularly in the international context

• This lecture Currencies and currency risks
• Next lecture
• Parent-subsidiary relationship
• when subjected to different tax rates
• when there are minority shareholders
• Can there be conflict between the two points of
  view?
• Different costs of capital in different
  countries, because of segmentation exploit cost
  of capital advantage
• Blocking of funds

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Capital budgeting and exchange rates

• We now investigate the influence of exchange
  rates and their variations,
• assuming that other imperfections are absent.
• Consider a world without taxes and with a unified
  capital market, where exchange rates fluctuate
  randomly.
• It is frequently the case that
• the cash flows generated by a project depend on
  the values taken by the various exchange rates
  during the project's life.
• This link may be especially strong when the
  project involves producing a good in one country
  and selling it (perhaps after assembly or
  conditioning) in another country
• but many other circumstances can also have this
  effect
• Exposure effect (see earlier lecture)
• How should this fact be taken into account when
  making the decision to undertake or not to
  undertake the project?

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Overview

• Cash flow forecasts in general
• Approaches to currency risk
• Cash flow forecasts based on an exchange rate
  forecast (PPP, UIRP?)
• Present valuation of cash flows derived from an
  exchange rate forecast
• Cash flow forecasts after hedging
• Present valuation of cash flows after hedging
• Approximate equivalence

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Cash flow forecasts in general(just a reminder)
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Cash flow forecasts in general

• Start with a forecast of sales (main value
  driver).
• Note may depend on exchange rate
• Based on that, use the accounting model of fixed
  and variable costs to forecasts costs of
  production
• Note may depend on exchange rate
• Note fixed does not mean fixed over time. It
  means the same no matter whether sales turn out
  to be higher or smaller than expected. In that
  sense, fixed costs have lower risk
• The result is operating income before interest,
  depreciation and taxes (EBITDA)
• Subtract taxes, taking into account tax saving
  from depreciation
• (Do not subtract interest or take it into account
  in taxes we want the cash flows at zero debt)
• Forecast from sales the need for working capital
  by means of turnover ratios
• Subtract increase in net working capital
• Subtract capital expenditures (these influence
  depreciation)
• This is Free Cash Flow at zero debt
• Do this under several scenarios, take the
  expected value
• Note the expected value is probability weighted
  but it does not account for the pricing of risk
  in the financial market this will be reflected
  as a risk premium in the discount rate

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Approaches to currency risk
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Currency unit

• Some people ask in which currency unit should I
  do my calculations of cash flow forecasts?
• General principle which should serve to avoid
  many pitfalls
• A MINIMAL REQUIREMENT FOR A RATIONAL DECISION
  MAKING PROCESS IS THAT IT LEAD TO THE SAME FINAL
  DECISION, IRRESPECTIVE OF THE MEASUREMENT UNIT
  USED IN THE CALCULATIONS.
• This principle is not based on any economic
  assumptions (such as market integration,
  uncovered interest rate parity etc..)
• This means that the currency of accounting is
  irrelevant if one does things properly, one
  should reach the same decision
• whether one computes euro flows and discounts
  them with an appropriate euro discount rate,
• or computes cash flows in LCs and discounts them
  with an appropriate LC discount rate.
• By the same token, it is immaterial whether
  constant (i.e., deflated or real) or current
  euros are used, provided the corresponding
  discount rate is also used.

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Currency of accounting

• Nevertheless, it is often more convenient
• to measure some cash flow components in one
  particular currency,
• and other cash flow components in some other
  currency.
• It all depends on the information that is
  provided initially.
• We are going to illustrate that idea

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Value-additivity principle

• Take three securities with cash flows A, B and C
  trading in the same financial market
• Suppose that the cash flows paid by security C
  are going to be exactly equal (at all times, in
  all states of nature) to the cash flows paid by A
  plus the cash flows paid by B (i.e., XC XA
  XB),
• Then the market value of C is equal to the market
  value of A plus the market value of B (i.e., VC
  VA VB)
• Note it is not obvious that this holds in
  practice (in the case RD/STT, we had A B and
  yet VA was not equal to VB).
• But should hold by virtue of absence of arbitrage
• The principle has two important practical
  implications
• Already exploited Each project may be valued on
  its own merits,
• To be further exploited Divide and conquer
  technique
• a project's cash flow stream may be broken down,
  for the convenience of the analyst, into
  component cash flow streams,
• whose present values may be obtained separately
  and then added together.
• Often the parts differ in terms of risk level or
  currency composition or any other characteristic.

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Two approaches to valuation

• Add and discount
• Form a forecast of the exchange rates (PPP,
  UIRP?)
• Based on it, forecast (i.e., calculate expected
  value of) the entire Free Cash Flow
• Find some discount rate appropriate to the whole
  expected cash flow, to obtain the entire present
  value
• Discount and add
• Forecast pieces of the free cash flow, where the
  different pieces are denominated in different
  currencies
• Discount each one at a discount rate appropriate
  to each
• Convert all pieces at time-0 spot rate into a
  common currency and add together to get the
  entire present value

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Cash flow forecasts based on an exchange rate
forecast (PPP, UIRP?)

• Present valuation of cash flows derived from an
  exchange rate forecast

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Forecast, add and discount

• Consider, for instance, a project costing 100LC
  today and returning, with certainty, in six
  months an entire FCF equal to
• 50 LC 10 SLC/ in units of LC
• or equivalently
• 50 LC /SLC/ 10 in units of
• The reason the information is in this form is,
  perhaps, that the project will operate in the
  local country but that there will be some export
  sales to Europe.

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Forecast, add and discount

• The current spot exchange rate is 8.3LC/
• Suppose your forecast of the exchange rate is
  8.47 LC/
• Then your expected cash flow is50 LC 10
  8.47 LC/ 134.7 LC
• Then you try to guess a discount rate and your
  guess is 13.91 per year. The present value
  is134.7/(113.91/2) 125.94 LC

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Forecast, add and discount

• This method has two drawbacks
• One has to forecast the exchange rate, which is
  a difficult exercise
• One has to discount a risky cash flow, whose
  appropriate discount rate is harder to obtain
  than are certainty discount rates
• Too often, the exchange risk ends up being
  improperly priced
• For instance, if use PPP forecast, the
  calculation is based on the idea that there is no
  risk of PPP deviations (or that that risk is
  diversifiable against the market so that it
  receives a zero price)

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Cash flow forecasts after hedging

• Present valuation of cash flows after hedging
• Approximate equivalence

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Discounting separately

• It is far better to evaluate the present values
  of the two component cash flows separately.
• The information from the foreign-exchange market
  is readily available
• today's spot exchange rate 1 8.3 LC
• today's 6 mo. LC interest rate 13 1/4 p.a.
• to day's 6 mo. interest rate 10 p.a.
• The Net Present Value of the project is
• or, equivalently
• Either way you look at it, the project is
  acceptable
• This example illustrates that
• It is easier to discount separately each currency
  component
• Foreign-exchange market provides pricing of
  exchange risk

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Or evaluate on a hedged basis

• The info on spot Xrate and interest rates implies
  to day's 6 mo. forward exchange rate is 1
  8.43 LC).
• One can also value hedged cash flows and get the
  same results
• or
• Takeaway If we find that more convenient, we can
  always calculate the present value of cash flows
  after hedging,
• since hedging has no impact on present value
  (Value-additivity principle) except perhaps for
  tax effects
• This does not require that we actually implement
  the hedge. This is only a pricing exercise.
• This does not require an assumption that the
  forward rate is a forecast of the future pot rate

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Equivalence and invariance

• Note an element of the previous calculation
• Valuation on a hedged basis is equivalent to
  replacing forecast exchange rate with the forward
  exchange rate
• Big advantage it does not matter what your
  forecast of the exchange rate was
• You know that you can use riskless rate for
  discounting

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Generali-zation of the ideaAB
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The role of exposure

• Suppose project information is given in a
  different form
• Suppose, for instance, that we know
• that there are only two possible values for the
  spot exchange rate in six months
• and that some project will return the following
• cash flow measured in dollars
•  either 15.39 if, in six months, 1
  9.27 LC
• or 16.59 if, in six months, 1
  7.59 LC
• Should decompose A rapid exposure analysis or
  decomposition shows that this cash flow is
  equivalent to 50 LC 10, so that we can
  evaluate this project as we did above.

/LC
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The case of cash flows that are subject to other
risks as well

• In the last examples, cash flow risk was only
  exchange rate risk
• Consider instead
• 50LC interpreted as the cash flows absolute
  exposure (not percentage exposure ?) to LC
• But cash flow is also subject to other risks than
  exchange risk

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The case of cash flows that are subject to other
risks as well

• Deal with exchange risk first by adding hedging
  and get expected value of cash flow after
  hedging
• Again, this is equal to forecasting cash flows
  using the forward rate AS IF it were a forecast
  of the future spot rate.
• Note this is not the same as taking E(CFtLC) and
  translating it at forward rate by simple
  multiplication
• Then the expected cash flow after hedging must be
  discounted at a required of return after hedging.
  The present value is
• The discount rate, kH, is the required euro
  expected rate of return on a comparable equity
  share that has been hedged against /LC risk (see
  earlier lecture)

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Takeaways

• I have not used any forecast of the exchange rate
• Instead, I have priced the currency risk
• from the information provided to me by the
  forward exchange market
• by looking at the project as if hedged
• This assumes that the hedge is available
• And that the forward market and the shareholders
  market are integrated with each other
• Recall the concept of required rate of return
  after hedging
• If assumptions are violated, must use XR forecast
  but then it is not clear how to price the
  corresponding risk.