Question: the attached file question 2 to question 3

(a) What is the term structure of spot interest rates implied by these instruments?What is the term structure of forward rates?(b) What are the YTMs (yields to maturity) of these three instruments? Write downthe equation that you need to solve to compute YTMs. Solve the equations for thethree-year zero-coupon bond and the annuity. Solve the third equation numerically,that is, compute the YTM using the function IRR (or using Goal Seek or Solver Tool)in Excel.Suppose now that there is also a fourth instrument: a zero-coupon bond with the facevalue of $1,000 and two years to maturity. This bond trades at $857.34.(c) Create a portfolio of the original three instruments that replicates the cash flowsof the two-year zero-coupon bond.(d) What is the YTM of the two-year zero-coupon bond? What is the YTM of thereplicating portfolio you found in part (c)? (Try to answer this question without doingany calculations. However, if you wish, use whichever method you like to compute theYTM.)(e) Suppose now that the two-year zero-coupon bond trades at $900.00 (all other pricesare unchanged). Is there a free lunch available here? Describe a trading strategy thatwill allow you to get it.

UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #2 1. You just signed a 30-year lease agreement for a business property. The monthly rent for the first year is $1,000/month, with the first month's rent due today. Starting from the second year onward, the monthly rent will be increased by 5%/year (i.e., the monthly rent for the second year will be $1,050, the monthly rent for the third year will be $1,000(1.05)2 = $1,102.5, and so on). Assuming the annually compounded interest rate is 12%/year, what is the present value of the 360 rental payments. 2. Consider three risk-free securities: a zero-coupon bond with a face value of $1,000 and 3 years to maturity, trading at $711.78, an annuity that pays $1,000 in year 1 and year 2. The annuity costs $1,809.72, a bond that pays off $1,000 in one year, $2,000 in two years, and $3,000 in three years. This bond trades at $4,802.40. (a) What is the term structure of spot interest rates implied by these instruments? What is the term structure of forward rates? (b) What are the YTMs (yields to maturity) of these three instruments? Write down the equation that you need to solve to compute YTMs. Solve the equations for the three-year zero-coupon bond and the annuity. Solve the third equation numerically, that is, compute the YTM using the function IRR (or using Goal Seek or Solver Tool) in Excel. Suppose now that there is also a fourth instrument: a zero-coupon bond with the face value of $1,000 and two years to maturity. This bond trades at $857.34. (c) Create a portfolio of the original three instruments that replicates the cash flows of the two-year zero-coupon bond. (d) What is the YTM of the two-year zero-coupon bond? What is the YTM of the replicating portfolio you found in part (c)? (Try to answer this question without doing any calculations. However, if you wish, use whichever method you like to compute the YTM.) (e) Suppose now that the two-year zero-coupon bond trades at $900.00 (all other prices are unchanged). Is there a free lunch available here? Describe a trading strategy that will allow you to get it. 1 3. You have data on prices of two level-coupon bonds. Both of them have two years to maturity, face value of $1,000 and pay annual coupons. The first bond pays a 5% coupon and sells for $1,000.92, and the second one pays a 1% coupon and sells for $925.81. You also know that the price of a three-year zero-coupon bond with face value of $1,000 is $816.30. (a) Using any approach you want, determine the term structure of the spot interest rates and the term structure of the forward rates. (b) Suppose that a bank offers you a forward rate of f3 = 9%. If there is an arbitrage opportunity, describe how you would take advantage of it. (c) Determine the prices of the 1- and 2-year zero-coupon bonds with face value of $1,000. (d) Suppose there is a 3-year level-coupon bond with coupon rate of 10% and face value of $1,000 currently trading at $1,000. Describe an investment strategy that uses this level-coupon bond along with the three zero-coupon bonds to earn an arbitrage profit . 4. How to Retire in just 10 Years? Rent, Apparently. Before you answer this question, read the article at http://www.millennial-revolution.com/rent/444/ (a) Verify that the monthly mortgage payment is $2,065. (b) In the first graph of the article, it shows that by assuming an investment return of 6%/year and a 30% saving rate, you can accomplish \"financial independence\" in 30 years. How long does it take for you to achieve \"financial independence\" if your investment return can only yield 4%/year. (c) By renting, the article suggests that Selena and Rick can accomplish \"financial independence\" in 20 years by renting instead of buying an apartment. Do you find any flaw in the argument of the article? 2