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RSM333mid10 SOLUTION - UNIVERSITY OF TORONTO Joseph L...

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UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Feb. 24, 2010 Buti/Farooqi RSM333 MID-TERM EXAMINATION Ganguly SOLUTIONS 1. (a) The value of firm A and the value of firm B are V A = EBIT(1 - T C ) k 0 = 15m × 0 . 7 0 . 15 = $70m , V B = V U + T C D = V A + T C D = $70m + 0 . 3 × 20m = $76m . (b) Owning 1% of firm A or firm B respectively provides an annual cashflow of: CF A = 0 . 01 × EBIT(1 - T C ) = $105,000 , CF B = 0 . 01 × (EBIT - k d D )(1 - T C ) = 0 . 01 × (15m - 0 . 08 × 20m)(1 - 0 . 3) = $93,800 . (c) The costs are the following: Cost of 1% of equity of firm A = 0 . 01 × $73m = $730 , 000 , Cost of 1% of equity of firm B = 0 . 01 × ($77m - $20m) = $570 , 000 . (d) The payoff of 1% ownership in firm A is: 0 . 01EBIT(1 - T C ). It can be decomposed as: 0 . 01 × EBIT(1 - T C ) = 0 . 01(EBIT - k d D )(1 - T C ) + 0 . 01 k d D (1 - T C ) . Since this payoff equation holds for every state of the world, the riskiness of 0 . 01 × EBIT(1 - T C ) is the same as that of 0 . 01(EBIT - k d D )(1 - T C ) + 0 . 01 k d D (1 - T C ). The payoff 0 . 01(EBIT - k d D )(1 - T C ) can be achieved by investing in 1% of firm B’s equity and the payoff of 0 . 01 k d D (1 - T C ) can be achieved by investing 0 . 01 D (1 - T C ) in firm B’s debt. To summarize: 1
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Original strategy Cost Expected cashflow 1% of A’s equity $730,000 $105,000 New strategy Cost Expected cashflow 1% of B’s equity $570,000 $93,800 $140,000 of B’s debt $140,000 $11,200 Total $710,000 $105,000 2. (a) Before the repurchase, the firm is an all equity firm and we have k 0 = r f + β XY Z ( E [ r m ] - r f ) = 0 . 05 + 1 . 2 × 0 . 08 = 0 . 146 , V U = EBIT(1 - T C ) k 0 = $4,000,000 × 0 . 6 0 . 146 = $16,438,356 . (b) Since a higher level of debt is always better due to the larger tax shield effect, the optimal debt level is D = $8,000,000. The value of the company becomes: V L = V U + T C D = $16,438,356 + 0 . 4 × $8,000,000 = $19,638,356 . (c) Now the highest level of debt is not necessarily optimal, the preferred amount of debt will be the one that gives higher net benefits after taking into account both the tax shield benefits and the expected costs of financial distress. Value of debt Tax shield Expected costs of financial distress Net benefits $2,500,000 1,000,000 80,000 920,000 $5,000,000 2,000,000 640,000 1,360,000 $7,500,000 3,000,000 1,760,000 1,240,000 $8,000,000 3,200,000 2,400,000 800,000 The net benefits are maximized at D = $5,000,000 and the value of the company will be V L = $16,438,356 + $1,360,000 = $17,798,356.
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