BCO126 MATHEMATICS OF FINANCE Final Task brief & rubrics

Task

General instructions:

1. Log in to your Moodle course and download the Final assignment.

2. Use a blank sheet of paper to hand-write your formulas and your workings to obtain the result for each question.

3. Include each question number and highlight each final result.

Task content:

Part I

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?

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%?

PART II

Question 1

After retirement, you would like to have $16,000 income each year, for at least 30 years. How much should you have saved in your retirement account to receive this income if the annual interest rate is 6 percent per year? (Assume that the payments start one year after your retirement)

Question 2

A real estate property can be rented for 19000€ per year. We assume that it can last for many decades, with growing maintenance costs of 0,75% per year. For how much would you value it today if you want to obtain at least a profitability of 7% ?

Question 3

A friend has taken a $170,000 mortgage out on his house at an interest rate of 6 percent per year. If the mortgage calls for equal payments per semester for 6 years, what is the amount of each payment?

Question 4

If you start making $170 saving contributions per month, starting at the end of this month, and continue them for 11 years, what is the future amount of money that you will receive if the annual interest rate is 3%?

Question 5

Calculate how much you should invest today in a project that will generate cash-flows of 12000€ per year, starting in 5 years, and during the following 15 years, if you want to get a profitability of 5%.

Formalities:

· Font: Arial 12,5 pts.

· Text alignment: Justified.

· The formulas and procedures to obtain the result must be included.

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

Rubrics

Rubrics

Descriptor

9-10

The student constructs a well-reasoned conclusion from accurate calculations that demonstrate an excellent understanding of the concepts.

8-8.9

The student arrives at a good conclusion with mostly accurate calculations, demonstrating a good understanding of the concepts.

7-7.9

The student makes a fair conclusion despite some inaccuracies in the calculations. The student’s understanding of the concepts is fair.

6-6.9

Several inaccuracies and incoherent or incomplete conclusion. The student demonstrates some, but insufficient understanding of the concepts.

3-5.9

Systematic inaccuracies and incoherent/incomplete or missing conclusions. The student demonstrates insufficient understanding of the concepts. They may mention some relevant ideas or concepts, although it is clear that the relationship between them is not understood by the student.

1-2.9

The student demonstrates insufficient understanding of the concepts and does not include any relevant calculations.

0

The student leaves the question blank or cheats.

Points are stated at the end of each question.

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