Question 1 i. Consider the following four risk-free government bonds: A, B, C, and D. All four bonds have a face value of 100 and pay annual coupons, but the coupon rates are different. Bond A has a coupon rate of 6%, B 7%, C 8%, and D 9%. Both A and B mature in two years while C and D mature in four years. Bonds A, B, C, and D are currently trading at 102.78, 104.65, 112.62, and 116.22, respectively. a. Calculate the 1-year, 2-year, 3-year, and 4-year spot rate. What is the shape of the term structure? [10 marks] b. Which theory of the term structure can explain the shape above? Explain the intuition. (5 marks] ii. Suppose the price of espresso machines is risky, with a CAPM beta of 0.8. The monthly storage cost is $10, and the current spot price is $1,000. However, one can also rent out the machine to earn $5 per month. Storage costs and rent are paid at the end of each month. The expected rate of return on the market is 1.5% per month, with a risk-free rate of 0.5% per month. [Hint: for the purpose of this question, you may assume that there is no depreciation on the espresso machine.] a. What is the required monthly return on an asset with the espresso machine's beta? [2 marks] b. Using your answer above, work out what price the espresso machine should sell for in 3 months (excluding storage costs). [3 marks] c. Suppose that you need an espresso machine in 3 months. You believe that the price of the espresso machine in 3 months will be $1,050. Which of the following would be cheaper overall: buying the espresso machine today or buying it in 3 months? [5 marks]