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solnpproblec5

# solnpproblec5 - CARNEGIE MELLON UNIVERSITY Tepper School of...

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CARNEGIE MELLON UNIVERSITY Tepper School of Business Finance Summer 2009 Practice Problems Topic 5 Solution CONCEPT QUESTIONS 1. Quiz from Chapter 6 - Brealey, Myers and Allen. 2. See the table given below: We begin with cash °ows given in the table and utilize the following relationships. Real Cash Flow = Nominal Cash Flow/(1 + in°ation rate) Here the nominal rate is 20% , the expected rate of in°ation is 10% and the real rate is (1 + r nominal ) = (1 + r real ) (1+in°ation rate) 1 : 20 = (1 + r real )(1 : 1) r real = 0 : 909 = 9 : 09% As may be seen from the following table, the NPV is unchanged (to within a rounding error). 0 1 2 3 4 5 6 7 Net cash °ows - Nominal -12,600 -1,484 2,947 6,323 10,534 9,985 5,757 3,269 Net cash °ows - Real -12,600 -1,349 2,436 4,751 7,195 6,200 3,250 1,678 NPV of real cash °ows at 9.09% = \$3,803. 3. Unfortunately, there is no simple adjustment to the discount rate that will take care of taxes. Mathematically, C 1 1 : 10 6 = C 1 = (1 ° : 34) 1 : 15 and C 2 1 : 10 2 6 = C 2 = (1 ° : 34) 1 : 15 2 4. Even when the capital budgeting calculations are done in real terms, an in°ation forecast is needed because: (a) Some real °ows depend on the the in°ation rate, e.g. real taxes and real proceeds from collecting receivables; and, 1

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(b) Real discount rates are often estimated by starting with nominal rates and ±taking out² in°ation. 5. If the \$50,000 is expensed at the end of year 1, the value of the tax shield is: : 35 ± 50 ; 000 1 : 05 = \$16 ; 667 If it is capitalized and then depreciated, the value of the tax shield is: [ : 35 ± 50 ; 000] ° : 20 1 : 05 1 + : 32 1 : 05 2 + : 192 1 : 05 3 + : 1152 1 : 05 4 + : 1152 1 : 05 5 + : 0576 1 : 05 6 ± = \$15 ; 287 Not surprisingly, the tax shield is larger if the cost can be expensed. 6. NPV A = ° 100 + 5 P t =1 26 1 : 08 t = \$3 ; 810 NPV B = - Investment + PV(After tax cash °ow)+PV(depreciation tax shield) NPV B = ° 100+ 5 P t =1 26(1 ° : 35) 1 : 08 t + : 35 ± 100 ² : 20 1 : 08 1 + : 32 1 : 05 2 + : 192 1 : 08 3 + : 1152 1 : 08 4 + :
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solnpproblec5 - CARNEGIE MELLON UNIVERSITY Tepper School of...

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