A B C D E F G H I J K Net Present Value & IRR Investment Criteria Analyzing capital projects with the NPV and IRR methods. Problem 1: Lin Land Lid. (LLL) is considering investing in an apartment complex. The sale price is $450,000 and LLL expects to have positive after-tax cash flows from rents of $20,000 for the next three years. At the end of the third year, LLL anticipates selling the apartment complex 11 10 for a net after-tax gain on sale of $500,000. If LLL's required return is 15%, should LLL go ahead and purchase the apartment complex? 12 Finance Concept: The net present value rule states that accepting all projects that are worth more than they cost increases shareholder value. The decision rule is to accept all positive NPV projects. The internal rate of return on an 13 investment is the rate that makes the NPV equal to zero. 14 15 16 Numerical Solution: NPV = PV - required investment 17 18 - PV cash flows - selling price = CF /(1+r) + CF,/(1+r)' + CF;/(1+r)' + ATGS/(1+r)' - SP 19 20 = 20,000/1.15 + 20,000/1.15' + 20,000/1.153 + 500,000/1.153 - 450,000 21 = 17,391 + 15,123 + 13,150 + 328,758 - 450000 =-75,578; decision - do not accept the project 23 Using Goal Seek: 24 25 Let's find the required return that makes the NPV equal to zero. The cash flows are already entered for you from the inputs table. 26 NPV & IRR Table: year cash flow Inputs: 0 Initial outlay CF ATGS NPY Enter =NPV(G31,D29:D31)+D28 IRR Enter: =IRR(D28:D31) Using Goal Seek: Step 1. Make sure your computer has this option installed. If you can't install it on your own computer, feel free to use one of UTA's. Step 2. Go to the menu bar and hit Tools and then Goal Seek. Step 3. When the Goal Seek box appears fill in the inputs: set cell = Senter D32, which is the NPV to value -> enter 0, which is what we want NPV to be by changing -> enter G31, which is the rate then hit the OK buttonA B C D E F G H I J K 44 Step 4. See the results. Goal Seek will change the r to make the NPV =0. 45 This is also the IRR. 46 Test your skills with this problem: 47 What is the annual cash flow required to be to have the NPV = 0 and the IRR =15%? 48 set cell => enter D32 49 to value =>0 50 by changing => CF (G29) 51 $53, 101 is the answer. 52 53 Problem 2: Finding the NPV with Incremental Cash Flows. LLL is also considering two different commercial buildings (Warehouse or Tower) and wants to know how to choose the best one. Should LLL calculate the IRR and NPV for each one and then choose? Lets analysize the incremental cash flow method, assuming a 10% cost of 54 capital. 55 56 57 Cash Flow Projections: Project Delta" 58 Project Warehouse Project Tower (Tower-Warehouse) 59 Year Incremental CF 60 @18 89882889 ($15,000) ($35,000) $3,000 $9,000 $3,000 $9,000 $3,000 $9,000 $3,000 $9,000 $3,000 $3,500 $3,000 $3,500 $3,000 $3,500 $3,000 $3,500 IRR NPV 74 E 75 1 To find IRR: Enter =IRR(D60:D68) and =IRR(F60:F68) for both projects. 76 2 To find NPV: Enter =NPV(0.1,D61:D68)+D60 for the Warehouse, and likewise for Tower (w/ F column) 77 We use (+) NPV ( cost of capital at 10%, cash flows) + Initial Investment (a negative number 78 3 Would you choose Warehouse or Tower if you rely on IRR? 79 4 Would you choose Warehouse or Tower if you rely on NPV? 80 5 We can see if it is advantageous to invest more initially in Tower by comparing the differences. 81 82 This is looking at the incremental cash flows and finding the IRR and NPV of the differences, called Delta. For the Delta column, subtract Warehouse from Tower for each cash flow. 83 6 Find the IRR and the NPV for the Delta.G J A C D F H K B E 84 85 Conclusion: The project Delta's NPV is positive, and the IRR is greater than the cost of capital. 86 This confirms the choice of Tower over Warehouse. 87 8.8 89 Test your skills with this problem: 90 S. S. Sarkar (S.S.S.), a real estate investment company, is considering investing in a shopping center. The sale price is $5,000,000 and S.S.S. expects to have positive after-tax and after-mortgage payment cash flows from rents of $600,000 for the next three years. S.S.S. can obtain a mortgage with a downpayment of $3,000,000. At the end of the third year, S.S.S. anticipates selling the shopping center for a net 91 after-tax gain on sale of $4,500,000. If S.S.S.'s required return is 30%, should S.S.S. go ahead and purchase the shopping center? 92 93 NPV & IRR Table: Fill in the inputs 94 year cash flow Inputs: 95 0 Initial outlay 96 - CF 97 2 ATGS 98 3 99 NPV 100 IRR 101 102 Calculate the NPV and the IRR. Indicate the investment decision in cell E104. 103 104 Decision => 105 106 What is the maximum down payment S.S.S. needs to make, assuming it does not effect 107 the yearly cash flows, for S.S.S. to exactly meet its required return of 30%? 108 109 110 Hint: Use Goal Seek: set IRR (cell D100) at 0, r at .30, and the changing cell at Initial outlay, 111 and click okay. [The amount is greater than the initial outlay of $3,000,000.] 112 113 114 115 116 117 18 19