An investment opportunity requires an initial investment of £12m and will return £10m and £5m after 3 years 6 months and 7 years, respectively.

a. State the equation of value f (i) = 0 for this opportunity and determine all real roots of f (i).

b. An investor is considering funding the investment with a loan and initially using the proceeds to repay the loan before generating a profit. If the prevailing interest rate on the loan is 7% per annum, should the investor use the loan? Explain your reasoning.