Ventura, Mary Mickaella R - Chapter9 (No.4,5,7,8,9,10,16) [PDF]

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Mary Mikaella R. Ventura BSA 3-A Net Present Value (Chapter 9 no. 4,5,7,8,9,10,16)

4. Calculating Discounted Payback [LO3] An investment project has annual cash inflows of $4,200, $5,300, $6,100, and $7,400, and a discount rate of 14 percent. What is the discounted payback period for these cash flows if the initial cost is $7,000? What if the initial cost is $10,000? What if it is $13,000?

Solution: Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21 Value today of Year 2 cash flow = $5,300/1.142 = $4,078.18 Value today of Year 3 cash flow = $6,100/1.143= $4,117.33 Value today of Year 4 cash flow = $7,400/1.144= $4,381.39

Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 years

Discounted payback = 2 + ($10,000 – 3,684.21 – 4,078.18)/$4,117.33 = 2.54 years

5. Calculating Discounted Payback [LO3] An investment project costs $15,000 and has annual cash flows of $4,300 for six years. What is the discounted payback period if the discount rate is zero percent? What if the discount rate is 5 percent? If it is 19 percent? Solution: R = 0%: 3 + ($2,100 / $4,300) = 3.49 years discounted payback = regular payback = 3.49 years

R = 5%: $4,300/1.05 + $4,300/1.052 + $4,300/1.053 = $11,709.97 $4,300/1.054= $3,537.62 discounted payback = 3 + ($15,000 – 11,709.97) / $3,537.62 = 3.93 years

R = 19%: $4,300(PVIFA19%,6) = $14,662.04

7. Calculating IRR [LO5] A firm evaluates all of its projects by applying the IRR rule. If the required return is 16 percent, should the firm accept the following project?

Solution: 0 = – $34,000 + $16,000/(1+IRR) + $18,000/(1+IRR)2+ $15,000/(1+IRR)3

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation: IRR = 20.97% Since the IRR is greater than the required return, ACCEPT THE PROJECT.

8. Calculating NPV [LO1] For the cash flows in the previous problem, suppose the firm uses the NPV decision rule. At a required return of 11 percent, should the firm accept this project? What if the required return was 30 percent? Solution: 11%: NPV = – $34,000 + $16,000/1.11 + $18,000/1.112 + $15,000/1.113= $5,991.49 At an 11 percent required return, the NPV is positive, ACCEPT THE PROJECT.

30%: NPV = – $34,000 + $16,000/1.30 + $18,000/1.302 + $15,000/1.303 = –$4,213.93 At a 30 percent required return, the NPV is negative, REJECT THE PROJECT:

9. Calculating NPV and IRR [LO1, 5] A project that provides annual cash flows of $28,500 for nine years costs $138,000 today. Is this a good project if the required return is 8 percent? What if it’s 20 percent? At what discount rate would you be indifferent between accepting the project and rejecting it?

Solution: NPV = –$138,000 + $28,500(PVIFA8%, 9) = $40,036.31 At an 8 percent required return, the NPV is positive, ACCEPT THE PROJECT.

20%: NPV = –$138,000 + $28,500(PVIFA20%, 9) = –$23,117.45 At a 20 percent required return, the NPV is negative, REJECT THE PROJECT.

Required return NPV is 0 , the IRR: 0 = –$138,000 + $28,500(PVIFAIRR, 9) IRR = 14.59%

10. Calculating IRR [LO5] What is the IRR of the following set of cash fl ows?

Solution: 0 = –$19,500 + $9,800/(1+IRR) + $10,300/(1+IRR)2 + $8,600/(1+IRR)3 IRR = 22.64%

16. Problems with Profitability Index [LO1, 7] The Weiland Computer Corporation is trying to choose between the following two mutually exclusive design projects:

a. If the required return is 10 percent and the company applies the profitability index decision rule, which project should the firm accept? Solution: PII = $27,000(PVIFA10%,3 ) / $53,000 = 1.267 PIII = $9,100(PVIFA10%,3) / $16,000 = 1.414 The profitability index decision rule implies that we accept project 2, since PI II is greater than the PII. b. If the company applies the NPV decision rule, which project should it take? Solution: NPVI = –$53,000 + $27,000(PVIFA10%,3) = $14,145.00 NPVII = –$16,000 + $9,100(PVIFA10%,3) = $6,630.35 The NPV decision rule implies accepting Project I, since the NPVI is greater than the NPVII. c. Explain why your answers in (a) and (b) are different. Solution: By means of Profitability Index formula I can now simply compare mutually the exclusive projects that can be vague when the cash flow is proportionate for the 2 projects especially on different scales. Project 1 is 3 times as large as project 2 and produces a larger Net Present Value, yet the profitability index criterion states that project 2 is more acceptable than project 1.