Question

You have just purchased 10 newly-issued $100 five-year Avco Ltd. debentures at par. These debentures pay $6 (per debenture) in interest semi-annually. You are also negotiating the purchase of 10 $100 debentures issued by Sabco Ltd. four years ago that return $3 per debenture in semi-annual interest payments and have six years remaining to maturity. What is the maximum price you should offer for the Sabco Ltd. debentures assuming Sabco Ltd. is now in the same risk class as the Avco Ltd.?

Answer 1

Discount rate or yield to maturity we will use for our calculations =6% per half year
Semiannual interest payment on debentures of Sabco Ltd.=$3
Payment of principal (year 6)=$100

Bond price is calculated as:
Bond price=Payment*[{1-(1+r)^(-n)}/r] + (Face value)*(1+r)^(-n)
=$3*[{1-(1+6%)^(-12)}/6%]+$100*(1+6%)^(-12)
=$3*[{1-(1.06)^(-12)}/6%]+$100*(1.06)^(-12)
=$3*[{0.503030636}/6%]+$100*(1.06)^(-12)
=$3*(8.383843933)+$49.69693636
=$25.1515318+$49.69693636
=$74.84846816 or $74.85 (Rounded up to two decimal places)

Hence, maximum price we should offer for 10 debentures of Sabco Ltd=10*$74.85=$748.50