Question 1 (25 marks) ANSWER BOTH PARTS OF THIS QUESTION Part 1 (15 marks) Assume a world of certainty in which individuals can lend or borrow unlimited amounts of money at the same riskless rate. Individual X currently ears and consumes 75,000 this period, and will earn and consume 90,000 next period. This pattern of consumption is represented by point E in the diagram below. Individual X also has the opportunity to invest in a capital project. If they decide to invest, their new patter of consumption will be represented by point B. Investment costs 30,000 and yields additional income next period of 45,000. Consumption ('000s) next period B 90 E G D Consumption ('000s) this period 75 150 (a) Explain what individual X must do to position themselves at other points on the line DEF between points E and F, and on the line ABC between points B and C. Calculate the risk-free rate of interest. Hence deduce the NPV of the capital project. Calculate the individual's total present value of consumption if (1) they undertake the project; (ii) if they do not invest in the project. (7 marks) (b) Suppose individual X wishes to consume one-third of their total present value of income this period, and the remainder next period. Calculate the amount consumed by individual X in each period if (1) they do not undertake the project; (ii) they do undertake the project. In each case explain how their desired consumption profile will be financed. (5 marks) Question 1 (25 marks) ANSWER BOTH PARTS OF THIS QUESTION Part 1 (15 marks) Assume a world of certainty in which individuals can lend or borrow unlimited amounts of money at the same riskless rate. Individual X currently ears and consumes 75,000 this period, and will earn and consume 90,000 next period. This pattern of consumption is represented by point E in the diagram below. Individual X also has the opportunity to invest in a capital project. If they decide to invest, their new patter of consumption will be represented by point B. Investment costs 30,000 and yields additional income next period of 45,000. Consumption ('000s) next period B 90 E G D Consumption ('000s) this period 75 150 (a) Explain what individual X must do to position themselves at other points on the line DEF between points E and F, and on the line ABC between points B and C. Calculate the risk-free rate of interest. Hence deduce the NPV of the capital project. Calculate the individual's total present value of consumption if (1) they undertake the project; (ii) if they do not invest in the project. (7 marks) (b) Suppose individual X wishes to consume one-third of their total present value of income this period, and the remainder next period. Calculate the amount consumed by individual X in each period if (1) they do not undertake the project; (ii) they do undertake the project. In each case explain how their desired consumption profile will be financed
