Question 3 You just started work at a wealth management firm and your boss asks

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Question 3 You just started work at a wealth management firm and your boss asks you to evaluate a 30-year bond with a face value of $1,000 that, according to the prospectus, you can purchase next month (01-June-2016) when it is initially issued. The bond is designed to provide a 6.5% yield-tomarket (YTM) and makes annual 01 June coupon payments. Your plan is purchase the bond for face value (par) at issuance.

A. What is the coupon (interest rate) attached to this bond? B. If the YTM is expected to remain constant, what is the minimum price you would accept to sell the bond on May 31, 2023, the day before you receive the 7th coupon payment? (Show your work by solving without the “PRICE” function first, then check with the function if you want.) ?

C. What is the duration on June 2, 2023, two days after the sale (i.e., the new buyer has already received the June 1, 2023 coupon payment)? (Show your work by solving using the stream of cash inflows—without the “DURATION” function. You can then check with the function if you want.)?

D. What is the modified duration at that same time

Explanation / Answer

A. Since the plan to purchase the bond is at Par, the the Yield to maturity(YTM) is the coupon rate. Hence, in the present case the coupon rate is 6.5% for the bond.

Minimum price that can be accepted is equal to the present value of cash inflow. Step-1: Present value of 7th coupon payment on the date before receive the 7th Payment = Coupon payment*discount factor = 1000*6.5%*1 Cumulative discount factor = 65 = {1-(1+i)^-n}/i = {1-(1+.065)^-23}/.065 Present value of future cash flow from bond throughout the life of bond. = 11.77 (i) Present value of coupon interest = Coupon payment*cumulative discount factor @6.5% for remaining 23 year = 65*11.77 = 765.05 (ii) Present value of redemption amount = redemption amount*discount factor = 1000*.235 = 235 Totalof (i) and (ii) = 1000 Thus, minimum price is even $ 1,000 in this time.

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