Posted: March 7th, 2014

Taxation-PV of the firm’s “perpetual” obligation = ($2 million/0.16) = $12.5 million.

(a) · PV of the firm’s “perpetual” obligation = ($2 million/0.16) = $12.5 million. · Based on the duration of a perpetuity, the duration of this obligation = (1.16/0.16) = 7.25 years. Denote by w the weight on the 5-year maturity bond, which has duration of 4 years. Then, w x 4 + (1 – w) x 11 = 7.25, which implies that w = 0.5357. Therefore, 0.5357 x $12.5 = $6.7 million in the 5-year bond and 0.4643 x $12.5 = $5.8 million in the 20- year bond. The total invested amounts to $(6.7+5.8) million = $12.5 million, fully matching the funding needs. (b) The price of the 20-year bond is 60 x PA(16%, 20) + 1000 x PF(16%, 20) = $407.11. Therefore, the bond sells for 0.4071 times its par value, and Market value = Par value x 0.4071 => $5.8 million = Par value x 0.4071 => Par value = $14.25 million. Another way to see this is to note that each bond with a par value of $1,000 sells for $407.11. If the total market value is $5.8 million, then you need to buy 14,250 bonds, which results in total par value of $14,250,000.

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