MGMT 326-Fundamentals of Corporate Finance-Berk/DeMarzo Gabriel Pacheco 1 3418 1

Question

MGMT 326-Fundamentals of Corporate Finance-Berk/DeMarzo Gabriel Pacheco 1 3418 10:54 Homework: Chapter 6 Homework (Copy) Score: 0 of 1 pt P 6-21 (similar to) 10of22 (4 complete) HW Score: 16 67%, 4 of 24 Question He Your company currently has S1 00 coupon bonds at par, what coupon rate do you need to set? Assume that for both bonds, the next coupon payment is due in exacly si months Opar 6% coupon bonds with 10 years to maturity and a price of $10 67. If you want to issue new 10-year You need to set a coupon rate of %. (Round to two decimal places) Enter your answer in the answer box and then click Check Answer Clear Al

Explanation / Answer

Solution:

Face value of bond = $1,000

Coupon rate = 6% annual

Issue price of bond = $1,067

Maturity = 10 years, 20 semiannual period

Now I want to issue new 10 year coupon bond at par, then coupon rate will be set equal to yield of the bonds. Let us assume that market yield on bond is 2i annual. now at 2i rate, present value of interest and principal will be equal to issue price i.e. $1,067

($1,000*6%*6/12) * cumulative PV factor at i for 20 periods + $1,000* PV factor at i at 20th period = $1,067

Lets calculate present value of cash flow at 5% annual rate and 6% annual rate

Now Present value of cash flows at 6% will be equal to par value of bond as YTM and coupon rate is same.

Present value of cash flows =$1,000

Present value of cash flows at 5%

= ($1,000*6%*6/12) * cumulative PV factor at 2.50% for 20 periods + $1,000* PV factor at 2.50% at 20th period

= $30 * 15.58916 + $1,000 * 0.610271 = $1,077.95

i = 2.50% + ($1,077.95 - $1,067) / ($1,077.95 - $1,000)*0.5

= 2.57%

Market Yield = 2.57%*2 = 5.14%

Hence coupon rate to be set is 5.14% in order to issue new bonds at par value.

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