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

Question

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

Answer

A) Coupon rate will be 6.5% which is equal to YTM

B) if ytm is constant then minimum price of bond :-

1000 * PVIF( 6.5 %, 7) + 65 * (PVIF 6.5 % 7)

= 643.506 + 41.827 = 685.333

because we are investor and received interest on yearly so minimum price at the end of 7th year is equal to the discounted face value for 7 year and PV of interest of 7th year which is not received.

c) calculation of duration on 2nd june 2023

so duration is 5.84 years

D) modified duration = duration /1+ytm

so 5.84 years /1+0.065

= 5.48%

year cash flow PV factor pv of CF WEIGHT PRODUCT 1 65 0.9389 61.0285 0.061029 0.061029 2 65 0.88165 57.30725 0.057308 0.114616 3 65 0.82784 53.8096 0.05381 0.161431 4 65 0.77732 50.5258 0.050526 0.202106 5 65 0.72988 47.4422 0.047443 0.237214 6 65 0.68533 44.54645 0.044547 0.267282 7 1065 0.6435 685.3275 0.685336 4.797353 999.9873 Duration 5.841031

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