International Finance: Putting Theory Into Practice

710 CHAPTER 19. SETTING THE COST OF INTERNATIONAL CAPITAL

we want to value as that for the traded assets. To implement this procedure, we
need a theory, like the Capital Asset Pricing Model, to tell us what types of risk are
relevant, how these risks should be measured, and what return is expected in the
home-country capital market in light of the project’s risks. Since we use the home-
country capital market as the yardstick, the discount rate is the required return in
home currency—and if the cost of capital is expressed in home currency, we have
to translate the expected cash flows and their risks from foreign currency into home
currency before we discount.

For such a translation, we need expected values for the future spot rates for
various maturities. In fact, we need also the covariance. IfC ̃∗denotes the cash flow
infcandC ̃∗S ̃the cash flow inhc, then

E(C ̃∗S ̃) = E(C ̃∗)×E(S ̃) + cov(C ̃∗,S ̃). (19.2)

You may have noticed the covariance effect in the Freedonian Crown exposure ex-
ample in Chapter 13, which we reproduce here:

Example 19.1
A British company is considering a project in Freedonia. Assume that the Freedonian
crown (fdk) cash flow can take on either of two equally probable values,fdk150 orfdk
100, depending on whether the Freedonian economy is booming or in a funk. Let there also
be two, equally probable time-T spot rates,gbp/fdk1.2 and 0.8. Thus, measured ingbp,
there are four possible cash flows: 150×1.2 =gbp180, 150×0.8 =gbp120, 100×1.2
=gbp120, and 100×0.8 =gbp80. These numbers are shown in Table 19.1. In each
cell, we also show the joint probability of each particular combination. When thefdkis
expensive, a recession is more probable than a boom because an expensive currency means
that Freedonia is not very competitive. The inverse happens when the crown is trading
at a low level; then it is more likely that the economy will be booming. These effects are
reflected in the probabilities shown in each of the four cells in Table 19.1.

Table 19.1:Cash flows for the Freedonian project

State of the economy

Boom:C∗=150 Slump:C∗=100 Prob(S) E(C ̃|S)

ST=1.2 p= 0.15;C=180 p=0.35;C=120 0.50 138

ST=0.8 p= 0.35;C=120 p= 0.15;C= 80 0.50 108

Prob(C∗) p= 0.50 p= 0.50

The expectations of the exchange rate and thefdkcash flows are easily calculated as

E(S ̃) = (0. 50 × 1 .2) + (0. 50 × 0 .8) = 1. 00 , (19.3)

E(C ̃∗) = (0. 50 ×150) + (0. 50 ×100) = 125. (19.4)

But the expected cash flow is not 1. 00 ×125 = 125:

E(S ̃C ̃∗) = (0. 15 ×180) + (0. 35 ×120) + (0. 35 ×120) + (0. 15 ×80) = 123. (19.5)