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Unformatted text preview: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM333 PROBLEM SET #1 SOLUTIONS 1. Let&s denote the payment to the manufacturer by x . The following cash ¡ows are created by the project: & Selling the existing machine: its book value is $45 ; 000 ¡ 5 ¢ $3 ; 000 = $30 ; 000 . So selling the machine will produce a capital gain equal to $35 ; 000 ¡ $30 ; 000 = $5 ; 000 , and the ¢rm will pay taxes on the capital gain so that the net cash in¡ow is CF ( selling existing machine ) = $30 ; 000 + $5 ; 000(1 ¡ : 35) = $33 ; 250 : & Cash ¡ow increments over years 110, given by the changes in operation costs and in tax savings due to depreciation: & OC ¢ (1 ¡ t ) + t ¢ & depreciation = ($12 ; 000)( : 65) + : 35 & x ¡ 8000 10 ¡ $3 ; 000 ¡ = : 035 x + $6 ; 470 & Selling the asset in the ¢nal period: we need to compare the CF we would obtain by selling either the existing machine or the new machine. CF ( salvage existing machine ) = 0 , CF ( salvage new machine ) = $8 ; 000 , so incremental CF = $8 ; 000 . We can now compute the NPV of the project and solve for the price of the machine that sets it equal to zero: ¡ x + $33 ; 250 + 10 P t =1 : 035 x + $6 ; 470 (1 : 15) t + $8 ; 000 (1 : 15) 10 = 0 = ) x = $82 ; 124 : 7 2. (a) Share price A = $50 m= 100 ; 000 = $500 , Share price B = ($50 m ¡ $20 m ) = 100 ; 000 = $300 : (b) Let&s de¢ne Company A&s periodic cash ¡ows as X, which depends purely on Company A&s assets. If we purchase a share of Company A we are entitled to X/100,000 each period. In order to replicate this periodic cash ¡ow we have to construct a portfolio that consists of n shares of Company B and an investment of D in the riskfree asset: X= 100 ; 000 = ( n= 100 ; 000) ¢ ( X ¡ $20 m ¢ r ) + D ¢ r X= 100 ; 000 = n ¢ X= 100 ; 000 ¡ n ¢ 200 ¢ r + D ¢ r 1 This last equation is satis&ed if: X= 100 ; 000 = n & X= 100 ; 000 and n & 200 & r = D & r . Solving the two equations (after simplifying for r the second one), we have n = 1 and D = 200 , which means that the replicating portfolio is long on 1 stock of Company B and lends 200 dollars at the riskfree rate. (c) Currently, Company B¡s debt to equity ratio is D=E = $20 m= ($50 m ¡ $20 m ) = 2 = 3 . To achieve the target debttoequity ratio of 0.5, Company B has to buy back debt and pay for it with additional equity (since in the question it is stated that a buyback of equity or debt is targeted)....
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 Spring '11
 SabrinaButti
 Cost Of Capital, ModiglianiMiller theorem, con…dence interval, target debttoequity ratio

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