Okay. We’re done with all the formulas in this chapter,
now let’s put all of them back together, don’t worry it sounds a lot scarier than, you know,
it’s going be a lot easier than it sounds, that’s what I’m trying to say, so let’s do
an International Capital Budgeting example, it means nothing but calculating the net present
value for an international company that’s evaluating its overseas investment opportunity. As always, we want to be calculating the projects
net present value, if the net present value we find is about zero dollars, we’re going
to recommend to accept this investment opportunity, otherwise, if the net present value is below
zero dollars, we would recommend to reject this investment opportunity. There are two different ways we could solve
an NPV problem like that, two approaches to overseas project equation. This, so called, home currency approach and
this, so called, foreign approach, the home currency approach, first estimates the cash
flows for year, zero, one, two, and so on in the foreign currency and then the idea
is we want to convert those foreign currency cash flows into the home currency, into the
dollars, right? As quickly as we can. So, we would — to do that, we would need
to know which exchange rate to use for each year’s cash flow, so we estimate future exchange
rates, which formula from this chapter can be used for that? We can use the uncovered interest rate parity
formula, so we’re going to review it in our next example. Once we have the exchange rate for year one,
year two in the future, year three in the future, and so on, we can then convert our
foreign currency cash flows into the domestic currency cash flows, into the dollars, that’s
step number three, and then in the last step, we just discount the dollar cash flows using
the domestic required return to find the net present value in dollars. The foreign currency approach has everything,
kind of, backwards, pretty much, we basically keep everything in the foreign currency until
the very end. So, we estimate our cash flows in the foreign
currency this is, you know, the same step one across the two approaches, then we discount
them; so, we essentially, we’re essentially, you know, finding the NPV in the foreign currency,
whether they’re in dollars. What do we use for the discount rate, for
that NPV calculation? We use the International Fisher Effect to
convert the domestic required return to foreign required return and then we do the discount
and to find the NPV, which should be the NPV, the nominated in the foreign currency, whether
they’re in dollars. So, it’s like you’re finding the NPV in the
foreign currency and only in the last step we convert the foreign currency NPV into dollars
using today’s spot exchange rate. So, it’s like in the whole currency approach,
the first thing we want to do is convert all cash flows for project into dollars. With the foreign currency approach, we want
to convert everything into dollars last, and we are calculating the NPV in the foreign
currency as kind of the step one. Okay. So, it turns out that it actually doesn’t
matter which one of two approaches you decide to use to find the net present value for your
overseas project because both will give you the same exact net present value. Let’s look at the following example; a U.S.
cell phone company is considering selling its cell phones in Germany the initial cost
of this cell phone project in Germany would be ten million Euro’s, notice how it’s denominated
in Euro’s, rather in dollars and that’s kind of the whole point of this overseas project
everything starts with a foreign currency, expected revenues from this project, it’s
actually more like profits that would be a more correct word to use, off the tax profits. We learned that in chapter ten in this class,
so expected after tax profits are two million Euros’ in one year, three million Euros’ in
two years, five million Euro’s in three years, and ten million Euro’s in four years. The risk-free rate in the U.S.A. is 5% and
it’s 8% in Germany, the current spot exchange rate is .67 Euros’ per dollar, which is the
same thing a \$1.50 per one Euro. The required rate of return on similar investments
in the U.S.A. is 10% calculate the net present value of this cell phone project in Germany. Okay. Let’s start with the home currency approach
first. Step one says, estimate cash flows in foreign
currency. We already have them, they’re given, year
zero cash flow is negative 10 million Euro’s, year one, two million Euro’s, year two, three
million Euro’s, year three, five million Euro’s, and year four, ten million Euro’s, they’re
given so we don’t need to calculate anything for step one. Step two, we kind of, the goal is to convert
all the future cash flows back into dollars, so for that, we need to know what exchange
rate we will use for each year. So, in step two, we estimate future exchange
rate for each year using the uncovered interest rate parity formula. The formula says the expected exchange rate
for any year in the future equals today’s spot exchange rate, multiplied by open parenthesis,
1 plus, the difference between the foreign risk-free rate, and the U.S. risk free rate,
closed parenthesis, raised to the power of T, T indicating the number of years in the
future for which we are trying to estimate this spot exchange rate. So next year’s expected exchange rate equals
today’s spot rate, which is .67 Euro’s per dollar, multiplied by, open parenthesis, 1
plus foreign countries risk free rate, which is Germany’s 8% rate or .08 in decimals, minus
the U.S. risk free rate or .5% or in decimals .05 we don’t use any power, although we could
put 1 at the end of, you know, closed bracket. The answer is .69 Euros’ per \$1, so that’s
the expected exchange rate in one year. The only thing that we change in the calculations
of the expected exchange rates for years two, three, and four, is the power at the end of
the parenthesis, power is two, three, and four and the answers we get are .71 Euro’s
per dollar .73 Euro’s per dollar .75 Euro’s per \$1, the numbers will be kind of continuously
increasing, right? And by the way, this means that the dollar
is expected to get stronger because each dollar can give us more and more and more Euro’s,
but that’s not the question that we are answering, so let’s move on. Now that we have the exchange rates estimated
for each future year of this four-year project in Germany, we can then proceed to step number
three, convert future cash flows from Euro into dollars. So, we have all cash flows in Euro’s, we convert
them into dollars using the proper exchange rate for that year. So, for example, to convert the initial investment,
ten million Euro’s into dollars, we take ten million Euro’s and divide by .67 Euro’s per
dollar, which was given as today’s exchange rate, or the current spot exchange rate, this
gives us negative 15 million dollars. The same way we convert our next year’s cash
flows from Euro’s into dollars using the exchange rate we found in step number two for, you
know, is the estimated exchange rate for that time, so we take two million Euro’s divide
by .69 Euro’s per dollar, from the previous step, which gives 2.9 million dollars and
then the same way we divide three million Euro’s from year two, five million Euro’s
from year three, and ten million Euro’s from year four, by their own exchange rates that
we estimated in the previous step for years two, three, and four to give us the estimated
projects cash flows for this year’s expressed in dollars. So, the second year’s cash flow in dollars
is 4.2 million dollars, the third year’s cash flow in dollars is 6.9 million dollars and
the fourth, the final year’s cash flow is 13.3 million dollars, okay? We are done with step three, what’s now left
is combining all these cash flows from this project into one, sort of, summarizing dollar
amount, which is the net present value, the profitability of this four-year project. So, step two; discount the dollar cash flows
using the domestic, the U.S. required return. The required return on similar investments
in the U.S.A. is 10% is given to us, so we take minus 15 million dollars from year 0
and we add all future dollar cash flows, discount it back to year 0 using the 10% given discount
rate. So, for example, from year one we add 2.9
million dollars, divided by 1 plus .1 for year two, we have 4.2-million-dollar cash
flow, divided by 1 plus .1 squared, and then for the third year’s discounted dollar cash
flow it uses the third power in the denominator and the last year’s discounted cash flow uses
the fourth power in the denominator. Of course, this is something you can do in
just one step in the financial calculator, either way, you get 5.41 million dollars and
your conclusion for this project would be to accept it because it’s worth it. Let’s do it in the financial calculator, let
me bring it up, let me clear everything, second plus minus answer, off and back on. So, cash flow keys, in the financial calculator,
start with pressing the cash flow, the CF button, what’s cash flow in year 0? It’s minus 15 million dollars, so let’s, you
know, drop the six zeros for the millions and do it, you know, in millions, right? So, 15, negative, enter, now it’s saved. I press the down arrow key, the display shows
cash flow 01, what’s flow number one in the future? That’s 2.9 million, I put 2.9, I save it by
pressing enter, I press the down arrow key, but before I enter my second year’s cash flow,
the display wants me to give information on the frequency of the first year’s cash flow,
F01. The default is one and we’re going to keep
it at the default well at 1 because we would only need to change it to something else,
like two, for example, if we have 2.9 repeated again, consecutively, two consecutive years
back to back, but that’s not the case in our entire problem. So, all the frequencies for each of our future
cash flow will actually be left at the default value of one. So, I can press enter and then the down arrow
key again or I could just press the down arrow key without pressing enter, it would, you
know, not make any difference. Cash flow number two in the future, 4.2, 4.2
enter, down and down arrow key again. Cash flow number three in the future, 6.9,
6.9 enter, enter, down, down in the fourth future cash flow, 13.3. 13.3 enter down, down, that’s it, there is
no more cash flow number five. Now I just need to compute the net present
value based on all these cash flows I have just entered using 10% for discount rate,
10% is given. So, I press the NPV button, I is the interest
rate that I need to enter, so I put 10, enter, down, compute. 5.38, so I think the reason I’m a little bit
off from what I said earlier, which is 5.41 million is because there must be some rounding
error that happened when we were actually finding all these dollar cash flows, because
we already were rounding them too much, they’re like remember in millions of dollars, so they
are like six more digits after the million value, right? So, they’re probably already rounded in the
previous steps and that’s why I got a slightly different number, but 5.41 million, that I
had explained earlier, is more accurate because it’s actually based on unrounded numbers. Okay. So, 5.41 million, if you don’t round any of
your intermediate steps and that implies that the project is worth it.