1. Charles River Associates is considering whether to call either of the two per
ID: 2772164 • Letter: 1
Question
1.
Charles River Associates is considering whether to call either of the two perpetual bond issues the company currently has outstanding. If the bond is called, it will be refunded, that is, a new bond issue will be made with a lower coupon rate. The proceeds from the new bond issue will be used to repurchase one of the existing bond issues. The information about the two currently outstanding bond issues is:
What is the NPV of the refunding for each bond?
2. Consider the prices of the following three Treasury issues as of February 24, 2012:
The bond in the middle is callable in February 2013. What is the implied value of the call feature? (Hint: Is there a way to combine the two noncallable issues to create an issue that has the same coupon as the callable bond?) (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the call Value?
Bond A Bond B Coupon rate 7 % 8 % Value outstanding $ 138,000,000 $ 145,000,000 Call premium 7.6 % 8.2 % Transaction cost of refunding $ 12,800,000 $ 19,500,000 Current YTM 6.25 % 6.9 %Explanation / Answer
As per the rule, I can answer first question only.
Bond A
NPV = PV of gain – PV of cost
PV of gain = value of the bond x(coupon rate – ytm)/ ytm
=138,000,000x(0.07-0.0625)/ 0.0625
=16,560,000
Assume there is tax benefit on call premium:
PV of cost = value of the bond x call premium x(1- tax rate) +cost of refunding x (1- tax rate)
= 138,000,000x 0.076 x( 1-0.40) + 12,800,000x(1-0.40)
= 6,292,800 +7,680,000
= 13,972,800
Npv = 16,560,000 - 13,972,800
= 2,587,200
Bond B
NPV = PV of gain – PV of cost
PV of gain = value of the bond x(coupon rate – ytm)/ ytm
=145,000,000x(0.08-0.069)/ 0.069
=23,115,942
Assume there is tax benefit on call premium:
PV of cost = value of the bond x call premium x(1- tax rate) +cost of refunding x (1- tax rate)
= 145,000,000x 0.082 x( 1-0.40) + 19,500,000x(1-0.40)
= 7,134,000 +11,700,000
= 18,834,000
Npv = 23,115,942 -18,834,000
= 4,281,942
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