Question

Ques 1 a) Assume an original issue bond with 30 years remaining to maturity which has a coupon rate of 4.5 % and the going rate of interest in the market is 4.5%. Its par value is $1000.

b. What would its price be? Show all calculations, either in formulas or in Excel.

c. In a above, did you actually have to calculate the price? Could make a reason that the price should be $1000.

Ques 2. a) If the coupon rate of an inflation protection bond (TIPS) is 2.75% and it is sold at par or $1,000. What is the annual real return on this bond for a buy and hold investor. Assume inflation is +2%.

b) If the coupon rate of an inflation protection bond (TIPS) is 2.75% and it is sold at par or $1,000. What is the annual real return on this bond for a buy and hold investor. Assume inflation is -2% (that is, minus 2%).

c) List 3 important features of inflation protection bonds.

d) Explain one that you listed above in 3 lines.

Answer 1

1)
a)
Face Value, FV = 1000
Annual Coupon interest, PMT = 4.5% * 1000 = 45
Period to Maturity, n = 30 years
Market Interest rate, i = 4.5%

b)
Price = Present value of Future Cash Flows
Price = Present value of Annual Coupon + Present Value of Face Value of Maturity
Price = PMT/ i *(1 - (1+i)^-n) + FV * (1+i)^-n
Price = 45/4.5% *(1 - (1+4.5%)^-30) + 1000 * (1+4.5%)^-30
Price = 1000*(1 - (1.045%)^-30) + 1000 * (1.045)^-30
Price = 1000*(1 - 0.2670) + 1000 * 0.2670
Price = 1000*0.7330 + 1000 * 0.2670
Price = 733 + 267
Price = 1000

c) No, there is no need to actually needed to calculate the price as annual coupon rate is equal to market interest rate. In such case bond will sell at par value or face value which is $ 1000, irrespective of years left to maturity

PS: Only 1 question with maximum 4 sub parts are allowed to answer at a time