# Mathematics homework

· All questions must include workings and a reasoned answer, not just the final number.

Task content:

**Read the following context;**

Our company has been mainly producing parts for cars with combustion engines. We are facing a challenging time. Potential shifting trends towards electric automobiles had apparently caused a reduction in our demand, that has been decreasing during the last years. In order to adapt to the future circumstances, the following different scenarios are being considered:

§ Changing the production line to adapt to the electric automobile market.

§ Investing in different projects to adapt to the new situation.

§ Selling the company before facing severe losses.

**Question 1**

We were considering adapting our production line, in order to produce some parts for electric automobiles, this way, and after analyzing the possible market opportunities, we could expect to obtain net revenues of $50,000 per month for at least the next 12 years.

a) What is the maximum that we should invest on this project if we consider a cost of capital of 4%?

b) If we ask for a loan of 5,000,000 at an annual interest rate of 1% compounded quarterly, to be paid in 10 years, how much would you have to pay every quarter to cover the loan?

**Question 2**

There was another option on the table; a potential client has offered the possibility to sign a contract, starting in 4 years, with a duration of 8 years (so it will produce 8 payments), to purchase a specific part that we can produce, but that will require a total reconversion of the whole factory. This contract is signed for annual revenues of $800,000. To do this, we must replace the machinery and the production plant must be reconverted.

a) What is the maximum amount of money we could afford to invest if we want a profitability of at least 5%?

b) If we ask for a loan to be paid back in 5 years in constant equal monthly payments of $40,000, how much will we pay in total for the loan?

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**Question 3**

After these previous calculations, the project still requires a big initial investment, and other options are being considered. Another project, that consists of just readjusting some parts to adapt them to assemble to electric cars, would produce net revenues of $200,000 per year, for 10 years. Assuming that these revenues will grow at a constant 1% per year, and are assessed at a cost of capital of 2,5%:

a) Would it still be profitable if it required an initial investment of $1,500,000?

b) If we take these annual revenues of $200,000 growing at a 1% per year, and we invest them in a bank account that offers an annual rate of 5% for 10 years, how much will we have at the end?

**Question 4**

Finally, there is a last consideration:

a) Selling the company: Considering that our plant produces annual cashflows of $260,000 decreasing at a 0,8% annual, expected to last for many years, for how much should we value the company today if investors are willing to obtain a profitability of 4%?

—- It assesses the following learning outcomes:

· to assess the present value of future cash flows and the future value of regular savings, annually and periodically

· to understand the perpetuity and annuity valuation and their factors – annual and periodical – and with various starting dates with and without growth

· to assess the future revenue generation of a regular savings scheme and the amount needed to be saved over time to meet a future series of payments

· to understand the process of investments appraisal and projects classification

· to determine percentage calculations and discounting