# (15 of 18) Ch.21 – Overseas project’s Net Present Value calculation using Home currency approach

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.