(i) Describe the essential feature of a proportional hazards model. [2] A study was made of the impact of drinking beer on men aged 60 years and over. A sample of men was followed from their 60th birthdays until they died, or left the study for other reasons. The baseline hazard of death, u, was assumed to be constant, and a proportional hazards model was estimated with a single covariate: the average daily beer intake in standard-sized glasses consumed, x. The equation of the model is: h(t)=exp(x) where h(t) is the hazard of death at age 60 +1. The estimated value of is 0.03, and the estimated value of is 0.2. (ii) Explain how and should be interpreted, in the context of this model. [2] (iii) Calculate the estimated hazard of death of a man aged exactly 62 years who drinks two glasses of beer a day. A man is aged exactly 60 years and drinks three glasses of beer a day. [1] (iv) (a) Calculate the estimated probability that this man will still be alive in 10 years' time. (b) Calculate the expectation of life at age 60 years for this man. [2] Another man is aged exactly 60 years. He drinks beer only in his local bar. He drinks all the beer he buys and is expected to continue drinking the same amount of beer every day until he dies. The owner of the bar is interested in selling as much beer as possible. (v) Determine the average number of glasses of beer a day the owner must sell the man in order to maximise the total amount of beer the man buys over his remaining lifetime [4] The latest balance sheet of Rough Ltd is as follows: Rough Ltd Balance sheet as at 31 March 2008 ASSETS Non-current assets Intangible Property, plant and equipment m m 8 7 15 Current assets Inventory 2 Trade receivables 3 20 Total assets EQUITY AND LIABILITIES Share capital Retained earnings 6 10 Non-current liabilities Secured loans Current liabilities 7 Trade payables Bank 20 Vest Ltd supplies raw materials to Rough Ltd. The finance director of Vest has just discovered that Rough has run into serious problems and is likely to be wound up. This is a matter of major concern because Rough owes Vest 500,000 which is included in the trade payables as at the latest balance sheet date. The finance director of Vest is trying to estimate how much, if anything, the company will receive once Rough has been wound up. The following information has been gathered from various sources: Intangible non-current assets comprise the cost of buying a licence to manufacture a product that has been the cause of Rough's downfall. The product has been linked to a major consumer safety scare. Property, plant and equipment has been offered for sale and is likely to realise 6m. Inventory and trade receivables are likely to realise 50% of their book values. A major quoted company has had a policy of reinvesting earnings and paying very little in the way of dividends for many years. The company now finds itself with a significant cash balance and very few attractive projects in which to invest. The directors are debating the merits of paying a substantial dividend. (i) (ii) Explain why the potential tax implications of receiving a dividend might make this proposal unpopular with this company's shareholders. [8] Explain why it might not be viable for the company to simply retain the funds and to wait until some attractive investment opportunities arose. [8] (iii) Explain why a quoted company might choose to release commercially sensitive information about investments and performance to the financial markets. [4] Problem Consider a model where money enters the utility function because of the transaction services it provides to households. The economy is populated by a continuum of identical infinitely-lived households. The representative households wants to maximize his lifetime utility: U = E = E s'u (Ct, Lt, M) where (0,1) is the discount factor, C is consumption, Le is labor, M. is nominal holdings of money (cash), and P is the price level in the economy. Foor simplicity, assume utility takes the following form: 26 (Ct, Lt, 1/4+) = In C + y ln - Mt Pt ML+x Pt '1+x' where 0,0,0 Notice that y indexes the importance of real money holdings for transactions, while indexes the disutility from working. Utility is then increasing in consumption C. and real cash, but decreasing in labor Lt. The household's budget constraint in every period t is: P+C++ M++ B = R_1 Bt1 + Mt1 + WLt + Te where B+ is a government bond which delivers a riskless gross return Re (hence R+-1B-1 are payments in t from a bond purchased in t -1, including both the principal and the interests). The term + stands for transfers received by the central bank. As in class, we are going to denote gross inflation in period t as The firm's problem is the following. It chooses labor L+ to maximize profits A = PYW.Lt, subject to Y =A+Lo, where a = (0, 1) under flexible prices and perfect competition. Answer to the followings.