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# 7211TutAnswersWk10_109 - 9-10 NPV and the cost of capital C...

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9-10 NPV and the cost of capital a. We can use the annuity formula + - = T r r C PV ) 1 ( 1 1 with r = k = 0.10 and T = 4 for the present value of the future cash flows 46 . 679 , 12 \$ ) 1 . 1 ( 1 1 10 . 0 4000 4 = - = PV NPV = PV – Initial cost = \$12,679.46 – \$13,000 = - \$320.54 Reject this project due to its negative NPV. b. To get a positive NPV, k must be smaller than 10%. Try k =9%. 88 . 958 , 12 \$ ) 09 . 1 ( 1 1 09 . 0 4000 4 = - = PV NPV = PV – Initial cost = \$12,958.88 – \$13,000 = - \$41.12 Similarly, when k = 8% then NPV = \$248.51. Thus 8% is maximum whole-percentage rate cost of capital that would still allow the project to be acceptable. In fact, the IRR (the k that makes NPV =0) for this project is 8.86%.

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9.12 PV - mutually exclusive projects a and b. Project PV of future cash inflows; NPV A 79 . 771 , 80 \$ ) 15 . 1 ( 1 1 15 . 0 18000 8 = - = PV NPV = PV – Initial cost = \$80,771.79 – \$85,000 = - \$4,228 Reject B Year CF n k ) 1 ( 1 + PV 1 \$12,000 0.870 \$10,435 2 14,000 0.756 10,586 3 16,000 0.658 10,520 4 18,000 0.572 10,292 5 20,000 0.497 9,944 6 25,000 0.432 10,808 \$62,584.34 NPV = \$62,584.34 – \$60,000 NPV = \$2,584 Accept
C Year CF n k ) 1 ( 1 + PV 1 \$50,000 0.870 \$ 43,500 2 30,000 0.756 22,680 3 20,000 0.658 13,160 4 20,000 0.572 11,440 5 20,000 0.497 9,940 6 30,000 0.432 12,960 7 40,000 0.376 15,040 8 50,000 0.327 16,350 \$145,043.89 NPV = \$145,043.89 – \$130,000 NPV = \$15,044 Accept c. Ranking - using NPV as criterion Rank Press NPV 1 C \$15,044 2 B 2,584 3 A -4,228

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7211TutAnswersWk10_109 - 9-10 NPV and the cost of capital C...

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