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# 4 what is the present value annuity of this amount in

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(4) What is the present value annuity of this amount in (3)? (5) Given your answer in (4), what does this tell you about the needed price increase if you are to equal the NPV of \$342,266 from expanding? Show this is true by computing the NPV with the increase in annual net CFA caused by this price increase. ANSWER (1): The formula is: NPV = PMT(PVAF r,n ) – costs = PMT([(1 + r) n 1] / [r(1 + r) n ]) – costs = \$102,000([(1.16) 10 – 1] / [0.16(1.16) 10 ]) – 0 = \$492,989.20 . This is \$150,732.20 greater than the \$342,266 from the expansion plan. Therefore, although the expansion plan is better than the status quo, the alternative of increasing the price is even better than expansion. Thus, raise price . ANSWER (2): The formula is: NPV = PMT(PVAF r,n ) – costs = PMT([(1 + r) n 1] / [r(1 + r) n ]) – costs = \$70,800([(1.16) 10 – 1] / [0.16(1.16) 10 ]) – 0 = \$342,192.51 . This is \$73.49 less than the \$342,266 from the expansion plan. Therefore, the expansion plan is better but only slightly.] ANSWER (3): An increase of \$0.017 generates an increase of \$102,000. Since \$0.017 divided by 17 equals \$0.001 this implies that \$0.001 will generate an increase of \$102,000 / 17 = \$6,000 in after-tax revenues. ANSWER (4): The formula is: PVA n = PMT(PVAF r,n ) = PMT([(1 + r) n 1] / [r(1 + r) n ]) = \$6,000([(1.16) 10 – 1] / [0.16(1.16) 10 ]) = \$28,999.36 . ANSWER (5): With an increase of \$28,999.36 in today’s dollars for every \$0.001 increase in price, this tells us that (\$342,266 / \$28,999.36)(0.001) = \$0.011802534 or about \$0.0118 increase will achieve a NPV of \$342,266. To prove this we take \$0.011802534 times \$10 million and get \$118,025.34. After-taxes, we have: \$118.025.34(1 – 0.04) = \$70,815.20.Taking the present value of these cash flows, we have: PVA n = PMT(PVAF r,n ) = PMT([(1 + r) n 1] / [r(1 + r) n ]) = \$70,815.20([(1.16) 10 – 1] / [0.16(1.16) 10 ]) = \$342,266.00 which is the same as the NPV of the expansion . It is also the NPV from the price increase since costs are zero. 72. 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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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%. Answer the below questions. (1) What are the initial costs (CF 0 )? (2) What is the after-tax value of the revenues minus expenses for each year (CFBT t )? (3) What is the depreciation tax shield per year (DTS t )? (4) What at the cash flows after tax for each year (CFAT t )? (5) What is the net salvage value (NSV)? (6) What is the terminal value (TV n ) ? (7) What is the NPV? (8) Do we accept the project? ANSWER (1): CF 0 = I 0 + ΔWC = \$16M + \$2.2M = \$18.2M ANSWER (2): CFBT t (1 – T) = (ΔR – ΔE)(1 – T) = \$5M(1 – 0.35) = \$3.25 for each of the eight years (t = 1, 2, . . . , 8). ANSWER (3): The depreciation tax shield per year (DTS t ) = (DEP)T = (I 0 / n)(T) = (\$16M / 8)(0.35) = \$0.7M .
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