# Answer 4 cfat t cfbt t 1 t dts t inserting our values

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ANSWER (4): CFAT t = CFBT t (1 – T) + DTS t . Inserting our values just computed, we have CFAT t = \$3.25M + \$0.7M = \$3.95M . ANSWER (5): Since the equipment is sold \$2M above its book value of zero, we have to pay taxes of T times the capital gains. Thus, the net salvage value (NSV) = \$2M – T\$2M = \$2M – 0.4(\$2M) = \$2M – \$0.8M = \$1.3M . [NOTE. If the equipment is sold at t = n above book value, then we can also express net salvage value as: NSV = S – (S – B)T where S is market value or salvage value of the equipment, B is the book value of the equipment, and T is tax rate. We have: NSV = \$2M – (\$2M – 0)0.35 = \$1.3M. If B is zero, then the equation reduces to NSV = S – TS or (1 – T)S. If it is sold below book value, then NSV = B + (B – S)T. WARNING. It is hard to get a formula that is applicable in all situations. Do not apply this formula for a replacement project or for unequal cash flows.] ANSWER (6): The terminal value (TV n ) = NSV + ΔWC = \$1.3M + \$2.2M = \$3.5M . ANSWER (7): For this problem, the revenues, expenses, and depreciation are the same each year. Thus, we have annuity, and can express the net present value as: NPV = CF 0 + CFAT(PVAF r,n ) + (TV)(PVF r,n ). Inserting in our previously computed values, we have NPV = –\$18.2M + \$3.95M(PVAF 16%,8 ) + \$3.5M(PVF 16%,8 ) = (–\$18.2M) + \$3.95M(4.3435909) + \$3.5M(0.3050254) = –\$18.2M + \$17.157184M + \$1.0675889 = \$0.0247729M or about \$24,773 . ANSWER (8): Yes, we accept the project because the NPV is positive. 73. A new product is being considered by Brooks’ Books, Inc. The after-tax cash flows at time zero include an outlay for depreciable equipment (I 0 ) of \$16M (M = million) and \$2.2M for additional net working capital (ΔW). The project is expected to have an 8-year life (n=8), and the equipment will be depreciated on a straight-line basis to a zero book value (B=0) over 8 years. When the project terminates in eight years, it is anticipated that the market or salvage value (S) will be \$2M and the net working capital will be released. The cash flows before tax (CFBT t ) for the project are expected to be \$5M per year. The cost of capital (r) is 16%, and the relevant tax rate (T) is 35%. Use the below NPV to determine if we will accept the project. (I 0 + ΔWC) + [(ΔR – ΔE)(1 – T) + (I 0 / n) T]{[(1+r) n – 1] / [r(1+r) n ] } + {[S – (S – B)T] + ΔWC] [1 / (1+r) n ]. ANSWER: Our values are: I 0 = –\$16M; ΔWC = –\$2.2M; CFBT = (ΔR – ΔE) = \$5M; T = 0.35; DEP = (I 0 / n) = \$16M / 8 = \$2M; r = 0.16: S = \$2M; B = 0. Using the above formula and inserting our values, we have:

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(I 0 + ΔWC) + [(ΔR – ΔE)(1 – T) + (I 0 / n) T]{[(1 + r) n – 1] / [r(1 + r) n ] } + {[S – (S – B)T] + ΔWC]}[1 / (1+r) n ] = (–16 + –2.2) + [(5)(0.65) + (2)0.35]{ [(1.16) 8 – 1] / [0.08(1.16) 8 ] } + {[2 – (2 – 0)0.35] + 2.2}[1 / (1.08) 8 ] = –18.2M + [3.25M + 0.7M]{4.3435909} + {[1.3M] + 2.2} / 3.2784149 –\$18,200,000 + \$17,157,184 + {\$3,500,000}[(0.3050254)] = –\$18,200,000 + \$17,157,184 + \$1,067,589 = about \$24,773 . Thus, we accept the project . 74. A new product is being considered by Brooks’ Books, Inc. The after-tax cash flows at time zero include an outlay for depreciable equipment (I 0 ) of \$16M (M = million) and \$2.2M for additional net working capital (ΔW). The project is expected to have an 8-year life (n=8), and the equipment will be depreciated on a straight-line basis to a zero book value (B=0) over 8 years.
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