Problem $1(10$ points$)$

Global Trade Inc. is considering a foreign investment with a useful life of $6$ years through its

subsidiary in Spain to manufacture car parts and initial investment amount is $17,000,000.$ From

this investment, the subsidiary expects $300,000$ units of sales in the first year, which is expected

to grow $10\%$ for year $2$ and $3,5\%$ in year $4,4\%$ in year $5$ and remain the same in year $6.$

Additionally, the subsidiary expects to sell those parts for $25$ during the first three years of the

project and for $30$ in the following years. Variable manufacturing cost is $10$ per unit during

the first three years of the project and for $12$ in the following years.

The subsidiary will have $2,000,000$ fixed costs each year, total depreciation expense of the

project will be $9,000,000$ and company uses straight line depreciation. The company expects to

sell the investment for $8,000,000$ after all taxes at the end of $6$ years.

For working capital, subsidiary will borrow $5,000,000$ from a Spanish bank which is subject to

$8\%$ annual interest and will be transferred to the buyer of the project at the end of $6$ years. The

subsidiary is subject to $21\%$ corporate tax, additionally, the firm will pay $15\%$ withholding tax

for remittances abroad except for capital transfers.

Spot EUR$/$USD exchange rate is $1\mathrm{.}08$ and CFO of Global Trade Inc. expects the exchange rate to

appreciate within the next $3$ years by a normally distributed probability with $5\%$ mean and $2\%$

standard deviation each year, then, each year thereafter depreciate by a normally distributed

probability with $3\%$ mean and $1\%$ standard deviation.

Global Trade Inc. has $$60$ million worth of bonds outstanding with $7\%$ annual coupon rate and

$6\%$ annual yield to maturity.

The company's $40$ million shares of common stock sell for $$1\mathrm{.}25$ per share and have a beta of

$1\mathrm{.}5.$ The risk$-$free rate is $4\%,$ and the market return is $10\%.$ Tax rate is $21\%.$ Question: Ignore CFO$$s exchange rate expectations and assume spot rate will remain the same for

the next $6$ years. Calculate the number of units that the company should sell for the

project to have an IRR equal to company$$s cost of capital.