July: Financial Mathematics
You work in the purchasing department of a large engineering company.
In 1 year's time your company will need 100 tonnes of steel for use in a large construction project and it is your job to buy and sell steel so that you ensure that the company has the steel by the time it is needed. You have a total budget of £5000 and at present 1 tonne of steel costs £50 but in 1 year's time the cost will be either £40 or £60 (you don’t know which).
You could also purchase a “PUT OPTION” which is a contract that allows you the option of buying 10 tonnes of steel at £45 per tonne in 1 year's time. Each PUT OPTION costs you £100 now and you can buy as many options as you like.
You must either purchase the steel now or in 1 year's time and any money you don't spend now will earn 10% interest over the year (so, for example, if you don't spend any money now you will have £5500 in 1 year's time).
Can you find a way to guarantee that in 1 year's time you will have the 100 tonnes of steel you need (it is not acceptable to purchase less than 100 tonnes) AND still have some money left over?
What is the largest amount of money you can have left over?