im struggling with question 2. the solution says PV of cash outflows - PV of cash inflows but i dont know how to solve for PV of cash inflows and get the correct NPV

Problems for Investment Rules 1.Heritage Inc. has the option to buy a widget machine. The initial investment required today is $240,000. The machine is expected to generate revenues of $65,000 each year for the next 5 years, at which time it can be sold for $20,000 after-tax. If the firm's hurdle rate is 15%, what is the NPV? What is the IRR? 2.The current cost of an investment is $1.11 million and it will have cash inflows of $55,555 every six months for the next 22 years, beginning 6 months from now. The appropriate annual discount rate is 11%. Find the NPV of this investment. Is this a good investment? 3.Two projects being considered by a firm are mutually exclusive and have the following projected cash flows: Year 0 1 2 3 Project A Cash Flows -$100,000 $39,500 $39,500 $39,500 Project B Cash Flows -$100,000 0 0 $133,000 Based only on the information given, which of the two projects would be preferred, and why? 4.Texas Utensils is considering a new project outside of its current line of business. The project would cost $500,000 initially and would generate revenue of $60,000 next year, which would grow at 4% per year indefinitely. Since the project is outside the current line of business, managers at Texas Utensils are finding it difficult to agree on the appropriate risk-adjusted discount rate to use in valuing the project. What is the highest discount rate that could be used for the project before it would appear unprofitable? 5.Green Grocers is deciding between two mutually exclusive projects. The two projects have the following cash flows: Year 0 1 2 3 4 Project A Project B Cash Flow Cash Flow -$50,000 -$30,000 10,000 10,000 15,000 12,000 40,000 18,000 20,000 12,000 The company's cost of capital is 10% (WACC = 10%). What are the net present values (NPV) and internal rate of returns (IRR) of the projects? What is the Incremental IRR if we expand from project B to project A? Do the two methods give consistent results? 1 6.Two projects being considered by a firm are mutually exclusive and have the following projected cash flows: Year Project A cash flow Project B cash flow 0 -2,000 -1,100 1 495 700 2 495 800 3 400 -300 4 500 400 5 500 -500 6 330 600 Based on the comparison of MIRR of Project A and MIRR of Project B, which of the two projects would be preferred? The appropriate discount rate is 12 percent? 8. A project is expected to produce FCFF of $500 every year for 5 years starting in 3 years. If the project's initial cost is $1000, and 14.6% is the proper discount rate, what is the NPV? 9. The investment in project A is $1m and the investment in project B is $2m. Both projects have a unique internal rate of return of 20%. Is the following statement true or false? 'For any discount rate from 0% to 20%, project B has an NPV twice as great as that of project A.' Explain your answer. 10. Suppose you are offered $5,000 today but must make the following payments. Year CF ($) 0 5,000 1 -2,500 2 -2,500 3 -1,000 4 -1,000 (1) what is the IRR of this offer? (2) If the appropriate discount rate is 10%, should you accept this offer? (3) If the appropriate discount rate is 20%, should you accept this offer? (4) What is the NPV of the offer is the appropriate discount rate is 10%? 20%? (5) Are the decisions under the NPV rule in part (d) consistent with those of the IRR rule? 11. Fuji Software, Inc. has the following mutually exclusive projects. Year Project A Project B 0 -7,500 -5,000 1 4,000 2,500 2 2 3 3,500 1,500 1,200 3,000 (1) Suppose Fuji's payback period cutoff is two years. Which of these two projects should be chosen? (2) Suppose Fuji uses the NPV rule to rank these two projects. Which project should be undertaken if the proper discount rate is 15%? Questions 12-15 are on Page 7. 3 Answers to Capital Budgeting 1 PV(cash outflows) PV(cash in-flows) = $240,000 = 65,000 PVIFA5,15% + 20,000/(1.15)5 = $217,890 + 9,944 = 227,834 NPV = PV(cash in) - PV(cash out) = -12,166 IRR: The IRR is defined as the rate at which the NPV=0. Yes, in other words, it is the discount rate (\"I/Y\") that equates the PV of all future cash inflows with the current cost (investment, cash outflows), as those questions that you saw before mid-term. With you financial calculator, PV = -240,000, PMT = 65,000, N = 5, FV = 20,000, CPT I/Y; then you should get 12.91%. IRR: We have to use our calculators to figure out IRR. Enter: Cfo= -240,000 enter C01=65,000 enter F01=1 enter C02=65,000 enter F02=1 enter C03=65,000 enter F03=1 enter C04=65,000 enter F04=1 enter C05=65,000+20,000=85,000 enter F05=1 enter . Hit IRR then CPT . Wait for a while, and it gives us IRR=12.91% 2. Use the CF mode, NPV = PV(cash in) - PV(cash out) = -195,684.11. No, because NPV IRRA; Project B is preferred. 4 4. PV(cash outflows) = $500,000 The cash inflows are just a growth perpetuity, with g=4%. The question is, what is the discount rate rs? PV(cash in-flows) = 60,000 / (rs-g) = 60,000 / (rs- .04). The project is \"just profitable\" when NPV=0. NPV = PV(cash in) - PV(cash out) = 60,000 / (rs- .04) - 500,000 = 0 60,000 / (rs- .04) = 500,000 (rs- .04) = 60,000/500,000 = .12 rs= .12+.04 = .16 5. Enter the cash flows for each project into the cash flow register on the calculator and get the NPV and IRR. NPVA = $15,200; IRRA = 21.38%. NPVB = $10,728; IRRB = 24.67%. NPV rule: Project A has the higher NPV, so we should choose project A. IRR rule: Project B has higher IRR than project A. However, the two projects have different size, so we cannot compare the two IRRs directly. We need to calculate the Incremental IRR if we expand from B to A. Project A-B has the following cash flows: Year 0 1 2 3 4 Project A-B -$20,000 0 3,000 22,000 8,000 The IRR of project A-B is 17.37%, which is higher than the cost of capital. So it is profitable to expand from B to A. Therefore, we should take project A. 6. Find the MIRR of Project A: PV of cash outflows at time 0 = FV of cash inflows at time 6 = 2,000 495(1.12)5 + 495(1.12)4 +400(1.12)3 +500(1.12)2 + 500(1.12)1 + 330 = 3,730.42 MIRR of Project A : PV=-2000, FV=3730.42, N=6, CPT I/Y=10.95% (this is the MIRR) 5 Find the MIRR of Project B: PV of Cash outflows at time 0 = 1100 + 300/(1.12)3 + 500/(1.12)5 = -1,597.25 FV of Cash inflows at time 6 = 700(1.12)5 + 800(1.12)4 + 400(1.12)2 + 600 = 3,594.22 MIRR of Project B : = 14.47% PV=-1597.25, FV=3594.22, N=6, CPT I/Y Since Project B has higher internal return, we will choose B. Also, the NPV of Project A = -110.05 EAAA PV=257.79(+/-), I=10, N=13, CPT PMT=?=36.29 => EAAB Project B is preferred. 14. NOTE: all numbers are COSTS! Project (1) has NPV==-500/0.1-12,000=-17,000. Here we applied the perpetuity present formula PV=PMT/r. To get its EAA, we set NPV=-17,000=PMT/0.1. So PMT =1700. Use CF mode to get NPVB over one cycle=-13,513.56 To get EAA, PV=-13,513.56, N=20, I=10, CPT PMT=-1587.20 Use CF mode to get NPVc over one cycle=-12,627.30 To get EAA, PV=-12,627.30, N=15, I=10, CPT PMT=-1660.16 Choose B for its lower annual costs! 15. Project cost A (20) B (36) C (45) WACC=20% Go with the 3-year plan. PMT N 1 2 3 8 NPV (20) (36) (45) EAA (24) (23.56) (21.36)