Question

Stella Artois Corp. has bonds outstanding with a coupon rate of 3.7% paid semiannually and 16 years to maturity. The yield to maturity on these bonds is 3.9%, and the bonds have a par value of $5,000. Four years from today, Still Artois develops a more efficient way to distribute their beer. The WSJ quotes the price of the bonds at $5,021.63. Assuming that you sell at the time of this announcement, what was your realized return?

PLEASE EXPLAIN THE STEPS, I do not want only a formula answer. I want to understand the steps.

Answer 1

Par value of Bond = 5000
YTM = 3.9%
Since it is semiannual compounding YTM = 3.9%/2 = 1.95%
Coupon = Coupon rate * Par value/2 = 3.7%*5000/2 = 92.5
Number of Periods = 16* 2= 32
Price of Bond = PV of Coupons using PV of annuity formula + PV of Par value
Price of bond = Coupon*(1-(1+r)^-n)/r + Par value/(1+r)ⁿ = 92.5*(1-(1+1.95%)^-32)/1.95% + 5000/(1+1.95%)³² = 4881.80

Realized return = (Bond Price after 4 years - Bond Price + 8 no of coupons * Coupon value)/ Bond Price
= (5021.63 - 4881.80 + 8*92.5)/4881.80 = 18.02%

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