Help me solve the following questions correctly.,,,
3. (4 points) In 9 months, a company will sell one of its equipments, and receive from this sale $5 million. Immediately aer receiving the $5 million, the company wants to invest it into zero-coupon government bonds which at the time of purchase will have a maturity of 6 months. Furthermore, the company wants to lock in the price of these zero-coupon government bonds today using a forward contract. Use the discount factor data in the table to answer the below questions. a. (1 point) What is the 9-month forward price of one zero~coupon bond (with a face value of $1000) today which the company wants to purchase in 9 months? I). (1 point) How many bonds (with a face value of $ 1000) will the company purchase according to the forward contract? 0. (2 points) After 9 months, you observe the discount factors in the right-hand side column of the above table. What is the total payoff of the forward contract for the company? (I.e., what is the company's "prot" by buying the bonds at the previously agreed-upon forward price, and selling them immediately for their actual market price?) H! 1' 3% _ m 1!. m m .1. m .- lHlHH $3 T-Mobile Wi-fi 8:09 AM 80% instructure-uploads.s3.amazonaws.com C 1 of 1 Intermediate Microeconomics Fall 2018 Sections 3 & 4 Problem Set #5 Due Monday, October 22, 2018 at 9:30AM 1. Jake owns a small factory located close to a river that occasionally floods in the Spring with disastrous consequences. He intends to sell the factory and retire next year. His only wealth is the factory so his retirement income will be the proceeds of the sale. If there's no flood, the factory will be worth $500,000. If theres a flood, the factory will only be worth $50,000. He can buy insurance at the rate of $0.10 for each $1.00 worth of insurance coverage. He thinks the probability of a flood is 1/10. Let of denote dollars if there is a flood and cyp denote dollars if theres no flood. Jakes expected utility function is U(CF, CNF) = 0.1 ,CF +0.9.CNF (a) What is his bundle (CF, CNF) if he buys no insurance? (b) To buy $x of insurance, he pays $0. Ix in insurance premiums whether there is a flood or not, but he collects S.x in benefits if there is a flood. If he's bought Six of insurance, what is op and cyp in terms of x? Combine the equation for of and CAF by eliminating x to derive Jakes budget equation. (c) What is Jakes MRS between of and CNF? (d) What is Jakes optimal choice of insurance, i.e., what is the optimal x? 2. Suppose Jim has the following utility function for coffee, x, and all other goods, y U(x,y) = 10x- 2 + y Coffee sells for pr per cup and the price of y is 1. (a) What type of utility function is this? (b) What is the equation for Jim's demand curve (price as a function of the quantity demanded holding income and other prices fixed)? (c) If the price of coffee is $5, how many cups of coffee will Jim consume? How much y will he consume? (d) Derive the total value of this consumption to Jim as well as his consumers surplus. (e) Write down Jim's utility if his income is m = $100. (f) Now suppose that the price of coffee falls to $3. What is his new level of utility? (g) What is the value of the compensating variation associated with this price change? (h) What is the value of the equivalent variation associated with this price change? 3. Jane's utility function for pizzas (Z) and softdrinks ($) is U(Z,S) = ZS'. She has $18 to spend on these two goods and a pizza costs $6 and a softdrink costs $2. (a) Write down Jane's demand function for pizzas and for softdrinks. How many pizzas and softdrinks does she buy at the above prices and income? (b) Suppose that pizzas are on sale for $3. How many pizzas and softdrinks will she now buy? (c) What is the value of the compensating variation associated with the change in the price of pizzas? (d) What is the value of the equivalent variation associated with the change in the price of pizzas? Problem ? (20 points) An investor constructs an optimal-portfolio P with two risky stocks X and Y. The expected rate of return of stock X is 15% and standard deviation is 29%% and expected return of stock Y is 12%% and standard deviation is 20%. The risk-free rate is 5%. The correlation coefficient between the stocks is 0.15. The optimal-portfolio weights of X and Y are 67.04% and 32. 96%% respectively. A. Compute the expected return and standard deviation of the optimal portfolio. (5 points) B. If the investor wants an expected return of 18%% from a complete-portfolio C formed by using the optimal-portfolio P and risk-free rate, what proportion of X. Y. and risk-free asset should the investor invest in the complete portfolio? (5 points) Problem 2 (Continued) C. What is the standard deviation of the above complete-portfolio C that provides 18% return? (5 points) D. What are the reward-to-risk ratios of the optimal-portfolio P and the complete-portfolio C? Explain your results. Why they are same or different. Provide an argument by reflecting on the capital allocation line's on which the positions of C and P can be plotted. (5 points)Problem 4 (15 marks). Consider the following information about a risky portfolio that you manage, and a risk-free asset: E(rp) = 11%, op = 15%, ry = 5%. a) Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 8%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset? [5 marks b) What will be the standard deviation of the rate of return on her portfolio? [5 marks] c) Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse? [5 marks]
