Lesson FA xx Capital Budgeting Part 2C

- - - - - - Cover Page - - - - - - Lesson FA-20-170-xx Capital Budgeting Part 2C These notes and worksheets accompany the corresponding video lesson available online at: Permission is granted for educators and students to make copies and redistribute this document without fee provided the copyright notice and page footer is retained. Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 1 of 23

Capital Budgeting - Part 2C [Clip 20a] Internal Rate of Return Overview Capital Budgeting Concepts Internal Rate of Return Internal Rate of Return (IRR) a discounted cash flow rate of return method that expresses the rate of return that yields a net present value of zero Solution Techniques: IRR is generally difficult to solve for using manual procedures, thus financial calculators and spreadsheet software is often used instead. There are two basic manual solution techniques for determining IRR: Universal Trial and Error Technique involves solving for the NPV at various discount rates to determine which discount rate yields a NPV of zero. This technique works for any set of future cash flows. Equal Cash Flows Special Case Technique - a technique that provides a correct answer ONLY if all future cash flows in all future years are equal (i.e., an ordinary fixed annuity). o This technique relies upon the availability of present value of an ordinary annuity tables and often allows only an approximation of a range of discount rates that include the internal rate of return. Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 2 of 23

Capital Budgeting Concepts Internal Rate of Return (continued) Decision Criterion: Once an IRR has been calculated the decision criterion is whether the IRR is greater than or equal to the hurdle rate or the required rate of return. If yes, the investment is acceptable on the basis of IRR. However, the higher the IRR, the better. In ranking alternative investments, or choosing among alternative investments, the IRR is preferred over NPV for ranking since, like the profitability index, the determination of IRR implicitly adjusts for the relative size of the initial investment. If the amount of the initial investment is the same in all alternative investment choices, both IRR and NPV will result in the same ranking of investments Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 3 of 23

[Clip 20b] Internal Rate of Return Trial and Error Solution Approach Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Evaluate the investment using: a. internal rate of return (trial and error technique) b. internal rate of return (equal cash flow special case technique) Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 4 of 23

Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Evaluate the investment using: a. internal rate of return (trial and error technique) 12% discount rate Year(s) Nominal Cash Flows PV of a SS of $1 (12%) Discounted Cash Flow 1 $17,160 2 $17,160 3 $17,160 4 $17,160 Present Value of Future Cash Flows Less Initial Investment Net Present Value = Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 5 of 23

Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Evaluate the investment using: a. internal rate of return (trial and error technique) 15% discount rate Year(s) Nominal Cash Flows PV of a SS of $1 (15%) Discounted Cash Flow 1 $17,160 2 $17,160 3 $17,160 4 $17,160 Present Value of Future Cash Flows Less Initial Investment Net Present Value = Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 7 of 23

Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Evaluate the investment using: a. internal rate of return (trial and error technique) 14% discount rate Year(s) Nominal Cash Flows PV of a SS of $1 (14%) Discounted Cash Flow 1 $17,160 2 $17,160 3 $17,160 4 $17,160 Present Value of Future Cash Flows Less Initial Investment Net Present Value = Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 9 of 23

[Clip 20c] Internal Rate of Return Equal Cash Flows Special Case Approach Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Evaluate the investment using: b. internal rate of return (equal cash flow special case technique) Internal Rate of Return Factor (equal annual net cash inflows) = Initial Investment Annual net cash inflow Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 11 of 23

[Clip 20d] Internal Rate of Return Using the Texas Instruments BA II Financial Calculator Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. r = 12% 0 1 2 3 4 ($50,000) $17,160 Using the Texas Instruments BA II Financial Calculator (using the time value of money functions) 1. Reset TVM and memory -2nd- ++ - RESET- -ENTER- -2nd- -CPT QUIT- +2nd- -FV CLR TVM- 2. Specify annuity amount 17160 PMT- 3. Specify number of compounding annual periods 4 -N- 4. Specify initial investment -50000 PV- 5. Calculate IRR CPT I/Y- Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 13 of 23

Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. r = 12% 0 1 2 3 4 ($50,000) $17,160 Using the Texas Instruments BA II Financial Calculator (using the cash flow worksheet) 1. Reset memory 2. Specify initial investment -2nd- ++ - RESET- -ENTER- -2nd- -CPT QUIT- CF- -50000 -ENTER- - 3. Specify 1 st year cash flow 4. Specify frequency of 1 st year cash flow 17160 -ENTER- 4 -ENTER- - 5. Calculate IRR IRR CPT- Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 14 of 23

[Clip 20e] Internal Rate of Return Using the IRR Spreadsheet Function Capital Budgeting Concepts Internal Rate of Return (continued) Internal Rate of Return: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Evaluate the investment using: b. internal rate of return (equal cash flow special case technique) Solve using internal rate of return (IRR) spreadsheet function: r = 12% 0 1 2 3 4 ($50,000) $17,160 IRR Spreadsheet Function (Microsoft Excel) General Form: =IRR( values, [guess] ) Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 15 of 23

Capital Budgeting Concepts Internal Rate of Return (continued) Solve using internal rate of return (IRR) spreadsheet function: r = 12% 0 1 2 3 4 ($50,000) $17,160 IRR Spreadsheet Function (Microsoft Excel) General Form: =IRR( values, [guess] ) AApplied to this problem: =IRR( B3:B7,.1 ) Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 16 of 23

[Clip 21] Accounting Rate of Return Capital Budgeting Concepts Accounting Rate of Return Accounting Rate of Return an average return on investment method, sometimes referred to as return on investment (ROI) The accounting rate of return compares the average annual net income and the average value of the investment as follows: Accounting Rate of Return (ARR) or Return on Investment (ROI) = Average Net Income Average Investment where: Average Net Income = Sum of Net Income Over All Investment Years Estimated Life of Investment Average Investment = Initial Investment + Salvage Value 2 Decision Criterion: Accounting Rate of Return (ARR) is NOT considered an appropriate criterion for determining whether an investment is acceptable because ARR uses nominal net income rather than discounted cash flow for analysis. However, ARR may be calculated as a descriptive measure of the investment since it expresses the return on investment using accounting net income. Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 18 of 23

Capital Budgeting Concepts Accounting Rate of Return (continued) Accounting Rate of Return Example: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Assume Nebraska Company uses straight line depreciation and the investment has no salvage value. Evaluate the investment using the accounting rate of return. Average Net Income = Sum of Net Income Over All Investment Years Estimated Life of Investment Average Investment = Initial Investment + Salvage Value 2 Accounting Rate of Return (ARR) or Return on Investment (ROI) = Average Net Income Average Investment Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 19 of 23

Capital Budgeting Concepts Accounting Rate of Return (continued) Accounting Rate of Return Example: The management of Nebraska Company has an investment opportunity requiring a $50,000 investment today that will yield nominal future net cash inflows of $17,160 for four years. Nebraska Company has a required rate of return of 12%. Assume Nebraska Company uses straight line depreciation and the investment has no salvage value. Evaluate the investment using the accounting rate of return. Average Net Income = Sum of Net Income Over All Investment Years Estimated Life of Investment Year(s) Cash Flows minus Straight-line Depreciation equals 1 $17,160 - = Net Income 2 $17,160 - = 3 $17,160 - = 4 $17,160 - = Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 20 of 23

Capital Budgeting Concepts Accounting Rate of Return (continued) Summary Accounting Rate of Return an average return on investment method, sometimes referred to as return on investment (ROI) The accounting rate of return compares the average annual net income and the average value of the investment as follows: Accounting Rate of Return (ARR) or Return on Investment (ROI) = Average Net Income Average Investment Decision Criterion: Accounting Rate of Return (ARR) is NOT considered an appropriate criterion for determining whether an investment is acceptable because ARR uses nominal net income rather than discounted cash flow for analysis. However, ARR may be calculated as a descriptive measure of the investment since it expresses the return on investment using accounting net income. Copyright 2014 by Rocky Spears Enterprises LLC, All Rights Reserved Page 23 of 23