# Mathematics of finance

Question 1
We want to acquire a new equipment for a price of \$150,000. Considering that the banks are currently offering an average annual rate of 5%, calculate each of the following investment options and explain which is more attractive in order to be able to obtain the \$150,000 that we need, based on those calculations. Please show your workings for each option.
a)  Investing 90,000 in a product that offers an annual interest of 5% compounded quarterly for 10 years to produce \$150,000.
b)  Investing 90,000 in a product that offers annual 6,5% simple interest for 10 years.
c)  Investing 90,000 in a project that will produce annual cashflows of \$15,100 for 10 years.
Best option:

Question 2
From a project we could expect to obtain net revenues of \$650,000 per year for at least the next 10 years, if we adapt our production line, in order to produce some new parts. Considering this situation
a)  What is the maximum that we should invest on this project if we consider a cost of capital of 4%?
b)  If this project required an initial investment of \$4,000,000, what would be its NPV consider a cost of capital of 4%?
c)  What is its payback period given that the initial investment is \$4,000,000?

Question 3
Another project would produce net revenues of \$180,000 per year, for 9 years. These revenues are expected to grow at a constant 0,5% 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 \$1,900,000?
b)  If we invest these annual revenues of \$180,000 growing at a 0,5% per year in a bank account that offers an annual rate of 4% for 9 years, how much will we have at the end?

Question 4
A potential client has offered the possibility to sign a contract that will start in 5 years. This contract is signed for annual revenues of \$600,000.
a)  What is the maximum amount of money we could afford to invest if we want a profitability of at least 5%?

Question 5
Considering that our plant produces annual revenues of \$260,000 decreasing at a 1,2% annual, and it is expected to last for a very long time.
a)  For how would investors buy the plant if they wanted to obtain a profitability of at least a 6%?

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