Address the questions below
A property development company has just purchased a retail outlet for $4,000,000. A further $900,000 will be spent refurbishing the outlet in six months' time. An agreement has been made with a prospective tenant who will occupy the outlet beginning one year after the purchase date. The tenant will pay rent to the owner for five years and will then immediately purchase the outlet from the property development company for $6,800,000. The initial rent will be $360,000 per annum and this will be increased by the same percentage compound rate at the beginning of each successive year. The rental income is received quarterly in advance. Calculate the compound percentage increase in the annual rent required to earn the company an internal rate of return of 12% per annum effective. [9] An insurance company borrows f50 million at an effective interest rate of 9% per annum. The insurance company uses the money to invest in a capital project that pays f6 million per annum payable half-yearly in arrears for 20 years. The income from the project is used to repay the loan. Once the loan has been repaid, the insurance company can earn interest at an effective interest rate of 7% per annum. (i) Calculate the discounted payback period for this investment. [4] (ii) Calculate the accumulated profit the insurance company will have made at the end of the term of the capital project. [5] [Total 9] A company is considering investing in the following project. The company has to make an initial investment of three payments, each of f85,000. The first is due at the start of the project, the second one year later, and the third payment is due two years after the start of the project. After 10 years it is assumed that a major refurbishment of the infrastructure will be required, costing f125,000. The project is expected to provide no income in the first two years, an income received continuously of f30,000 in the third year, E32,000 in the fourth year, E34,000 in the fifth year and E36,000 in the sixth year. Thereafter the income is expected to increase by 2% per annum (compound) at the start of each year. The income is expected to cease at the end of the 20th year from the start of the project. The cashflow within each year is assumed to be received at a constant rate. (i) Calculate the net present value of the project at a rate of interest of 7% pa effective. [6] (ii) Show that the discounted payback period does not fall within the first 10 years, assuming an effective rate of interest of 7% pa. [5] (iii) Calculate the discounted payback period for the project, assuming an effective rate of interest of 7% pa. [5] [Total 16]You have been asked to advise a sports magazine, as a consultant statistician. You have been asked to investigate the hypothesis that football managers in the Italian "Serie A", are dismissed more quickly than those in the English premier league. Each league has twenty teams, each with one manager. During the season the following events happened (at the end of the months indicated) to the twenty managers who started: Month Italy England 1 One dismissed One died One left of his own accord 5 One left of his own accord One dismissed 6 Two dismissed One left of her own accord 8 One died Two dismissed 11 Two dismissed One dismissed Hence there were thirteen of the original twenty managers still employed by the same club at the end of the season, for each of the two leagues. (i) Calculate the Kaplan-Meier estimate of the distribution function and its approximate variance for each league separately. [10] (ii) Comment on the hypothesis that Italian managers are dismissed more quickly than those in England. [2] [Total 12]
