8-1 Solutions to Chapter 8 Net Present Value and Other Investment ...

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Chapter 08 - Net Present Value and Other Investment Criteria12. NPV = $2.2 billion + [$0.3 billion annuity factor (r, 15 years)] [$0.9 billion/(1 + r) 15 ]11 $0.9 billion= – $2.2 billion $0.3billion 1515r r (1 r) (1r)r = 5% NPV = $2.2 billion + $2.681 billion = $0.481 billionr = 18% NPV = $2.2 billion + $1.452 billion = $0.748 billionEst time: 01–0513. IRR A = discount rate (r), which is the solution to the following equation:11 $21,000 $30,0002(1 ) r = IRR A = 25.69%rr r IRR B = discount rate (r), which is the solution to the following equation:11 $33,000 $50,0002(1 ) r = IRR B = 20.69%rr r The IRR of project A is 25.69%, and that of B is 20.69%. However, project B hasthe higher NPV and therefore is preferred. The incremental cash flows of B over Aare $20,000 at time 0 and +$12,000 at times 1 and 2. The NPV of the incrementalcash flows (discounted at 10%) is $826.45, which is positive and equal to thedifference in the respective project NPVs.Est time: 01–05$4,000 $11,00014. NPV $5,000 $197.7021.12 (1.12)Because the NPV is negative, you should reject the offer. You should reject theoffer despite the fact that the IRR exceeds the discount rate. This is a “borrowingtype”project with positive cash flows followed by negative cash flows. A highIRR in these cases is not attractive: You don’t want to borrow at a high interest rate.Est time: 01–0515. a. r = 0% NPV = –$6,750 + $4,500 + $18,000 = $15,750$4,500 $18,000r = 50% NPV= $ 6,750 $4, 25021.50 1.50$4,500 $18,000r = 100% NPV= $ 6,750 $ 022.00 2.00b. IRR = 100%, the discount rate at which NPV = 0.Est time: 01–058-4
Chapter 08 - Net Present Value and Other Investment Criteria$7,500 $8,50016. NPV $10,000 $2,029. 092 31.12 1.12Since the NPV is positive, the project should be accepted.Alternatively, you can compute the IRR by solving for r, using trial and error, in thefollowing equation:$7,500 $8,500 $ 10,000 0 IRR = 20.61%23(1 r)(1 r)Since the IRR of the project is greater than the required rate of return of 12%, the projectshould be accepted.Est time: 01–0517. NPV 9% = –$20,000 + [$4,000 annuity factor (9%, 8 periods)] 1 1 = – $20,000 $4,000 $2,139. 288 0.090.09 (1.09) NPV 14% = –$20,000 + [$4,000 annuity factor (14%, 8 periods)] 1 1 = – $20,000 $4,000 $1,444.548 0.140.14(1.14) IRR = discount rate (r), which is the solution to the following equation:11 $4,000 $20,0008(1 ) r = IRR = 11.81%rr r [Using a financial calculator, enter PV = ()20,000; PMT = 4,000; FV = 0; n = 8,compute i.]The project will be rejected for any discount rate above this rate.Est time: 06–1018. a. The present value of the savings is $1,000/r.r = 0.08 PV = $12,500 and NPV = –$10,000 + $12,500 = $2,500r = 0.10 PV = $10,000 and NPV = –$10,000 + $10,000 = $0b. IRR = 0.10 = 10%At this discount rate, NPV = $0.c. Payback period = 10 yearsEst time: 01–0519. a. NPV for each of the two projects, at various discount rates, is tabulated below.8-5
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8-1 Solutions to Chapter 8 Net Present Value and Other Investment ...

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