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333final10a - UNIVERSITY OF TORONTO Joseph L Rotman School...

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UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Apr. 23, 2010 Buti/Farooqi RSM333 FINAL EXAMINATION Ganguly SOLUTIONS 1. (a) First we use the CAPM to obtain the cost of equity for firm ABC: k e = 0 . 08 + 1 . 1 × 0 . 07 = 0 . 157 . Then we compute the WACC of firm ABC. As both firms pay no taxes, the WACC is invariant to the capital structure. Hence the WACC of firm ABC is also the cost of capital for XYZ’s project: k wacc = D D + E k d + E D + E k e = 1 2 × 0 . 09 + 1 2 × 0 . 157 = 12 . 35% . (b) Compute the NPV of the project: NPV = - $30 m + 0 . 4($160 m ) + 0 . 6($70 m ) - 75 m 1 + 0 . 1235 = - $2,407,655 < 0 . Firm XYZ should not start the project. (c) If demand is high after one year, the firm can spend the $75 million and get $160 - $75 = $85 million. If demand is low after one year, the firm can spend the $75 million but would only get $70 - $75 = - $5 million. Therefore the firm will prefer to abandon the project if demand is low. The NPV of the project becomes: NPV(with option) = - $30 m + 0 . 4($160 m - $75 m ) + 0 . 6($0) 1 + 0 . 1235 = $262,572 > 0 . The firm should now accept the project. (d) To compute the option value, compare the NPVs with and without the option: Option value = $262,572 - ( - $2,407,655) = $2,670,227 . The maximum amount that XYZ is willing to pay for this option is $262,572 ( not $2,670,227). Any higher amount would make the NPV of the project negative. (e) The managers are wrong: the correct discount rate for the project is still k wacc = 0 . 1235, so EDF should make the investment as the project has a positive NPV. The higher cost of equity capital could be due either to a higher leverage of the company or to the firm being highly diversified, so that the project does not necessarily belong to the firm’s core activity. 1
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2. (a) Synergies will arise due to the tax shield on the $10 million loan and the interest rate subsidy. PV(tax shield) = (0 . 30)(0 . 04)($10,000,000) × A 4 0 . 13 = $356,937 , PV(interest subsidy) = (0 . 13 - 0 . 04)($10,000,000) × A 4 0 . 13 = $2,677,024 , Synergies = PV(tax shield) + PV(interest subsidy) = $356,937 + $2,677,024 = $3,033,961 . (b) Value of firm B before the acquisition = $2.3 × 1 million = $2.3 million. The total value of the cash offer is $2,300,000 + 0 . 8 × $3,033,961 = $4,727,169 . (c) Compute first the post acquisition value of the firm: V AB = $8 × 5,000,000 + $2,300,000 + $3,033,961 = $45,333,961 . Solve the following equation, where x is the number of shares offered to firm B’s shareholders: x x + 5,000,000 = $4,727,169 $45,333,961 x = 582,066 .
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