Assume that you just won the government vaccination lottery

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Assume that you just won the government vaccination lottery. Your prize can be taken either in the form of $100,000 at the end of each of the next 20 years (i.e., $2 million over 20 years) or as a lump sum of $1,000,000 paid immediately.  

(a) If you expect to invest $100,000 annually that earns 6% annually on your investments over the next 20 years, calculate the current value of future payments from an annuity. Explain how you would use time value of money analysis to choose between the annuity and the lump sum. 

(b) If you expect to invest $100,000 annually that earns 8% annually on your investments over the next 20 years, calculate the current value of future payments from an annuity. Explain how you would use time value of money analysis to choose between the annuity and the lump sum. 

c) Using interpolation based on your answers in part (a) and (b), at approximately what interest rate would you be indifferent when choosing between the two plans? 

(d) You can earn 3 percent, compounded monthly at your bank. If you deposit $1,000,000 at age 28, how old will you be when your account has grown to $2,000,000? What is the effective annual rate? 

 

Question 2 Becky Kwok is currently considering investing specified amounts in the following two investment opportunities described below. 

• Investment A: Invest a lump sum of $52,000 today in an account that pays 8% annual interest, compounded monthly and leave the funds on deposit for exactly 10 years.

 • Investment B: Invest $1,200 at the beginning of each month for the next 5 years in an account that pays 10% annual interest, compounded monthly. 

(a) For investment A, draw the necessary timeline and determine the account balance at the end of year 10. 

 (b) For investment B, draw the necessary timeline and determine the account balance at the end of year 5. 

 

 Question 3 Four years ago, SONO Ltd. raised $30 million by issuing 15-year $1,000 par value bonds that carry 6.8% coupon rate, payable semiannually. SONO Ltd. is currently announcing to raise another $20 million by issuing 15-year zero coupon bonds that discount semi-annually. The current YTM on these bonds is 9%. 

(a) Calculate the number of the 15-year coupon bonds that SONO Ltd. issued to raise the $30 million four years ago. What will be the company's repayment be at the maturity date of the 15-year coupon bonds? 

 (b) Calculate the current bond prices of the 15-year coupon bonds and 15-year zero coupon bonds. 

 (c) Calculate the number of the 15-year zero coupon bonds that SONO Ltd. currently issues to raise the $20 million. What will be the company's repayment be at the maturity date of the 15-year zero coupon bonds? 

 (d) Are 15-year 6.8% coupon bonds or 15-year zero coupon bonds more sensitive to changes in market interest rates? (2 marks)