Mastery Problem: Net Present Value and Internal Rate of Return Part One Companies use capital investment analysis to evaluate long-term investments. Capital investment evaluation methods that use present values are (1) Net present value method (NPV) and (2) Internal rate of return (ERR) method. Methods That Use Present Values Of the two capital investment evaluation methods, a dening characteristic NPV and IRR is that they consider V J the time value of money. This means that money tomorrow is worth less than V if money today. And, that cash invested today has the potential to earn income and increase V J in value over time. True or False: When making an investment decision between two mutually exclusive projects, the project with the greatest return on investment should be chosen. True V J Feedhadc ' Check My Work Part Two Net Present Value Method Net present value (NPV) is one method that can be used to evaluate the nancial viability of potential projects. It determines the present value of all future cash flows associated with potential prejects and measures this against the cost of the project. To use net present value, a required rate of return must be dened. The required rate of return is the minimum ' V' acceptable rate of return that an investment must yield For it to make sense economically. Managers often choose a required rate of return above their cost of capital to ensure that the inherent uncertainties surrounding future cash Flows is addressed. This can be risky, however, as it biases the process toward shortsterm projects. If the NPV is positive, then the project should be accepted V J ; if it is negative, then the project should be rejected V if . Let's look at a net present value example using the present value of an ordinary annuity table. The company has a project With a Seyear life that reqUires an initial investment of $200,000, and is expected to yield annual cash ows oic 561000. What is the net present value of the pro]ect if the required rate of return is set at 8%? Calculatior Steps jresent Value of an Annuity of 51 at Compound Interest. Note: Round your answer to the nearest whole dollar. What NPV does the previous calculation yield? 515:] Based on the NPV computed above, what IS indicated? ) 1. The project is profitable ' J 2. Yes ' if , the initial investment will be recovered. 3. Yes V if , the reqUired rate of return will be recovered. 4_ A positive V VI NPV in excess of the Initial investment and required rate of return has been achieved. Feedback ' Check My Work Click on the Present Value of an Annuity of $1 at Compound Interest link and look torthe intersection of the number of years row and the required rate of return column. Part Three Present Value Index When funds for capital Investments are limited, prOJECtS can be ranked using a p"eseit value intiex. A project With a negative net present value will have a present value index below 1.0. Also, it lS important to note that a prOJect with the largest net present value may, in fact, return a lower present value per dollar invested. Let's look at an example of how to determine the present value index. The company has a project With a Seyear life, an initial investment of $220,000. and is expected to yield annual cash ows oic 558,000. Whathat is the present value index of the project if the reqwred rate of return IS set at 10%? Total present value of net cash Flows Present value index : Initial investment Caltt latior Steps Note: Round total present value of net cash ows and initial investment to nearest dollar. Round present value index to two decimal places. Present value index = D = [:l Feedback " Check My Work To calculate the total present value of net cash flows. nd the correct present value discount factor. Then multiply it by the annual cash flow for the proiect. To calculate the total present value of net cash flows. nd the correct presentvalue discount factor. Then multiply it by the annual cash flow for the project Part Four Irte'nal Rate of Return Method The internal rate of return (IRR) method uses present value concepts to compute the rate of return from a capital investment proposal based on its expected net cash flows. This method, sometimes called the timeeadjusted rate of return method, starts with the proposal's net cash flows and works backward to estimate the proposal's expected rate of return. Let's look at an example of internal rate of return calculation with even cash flows. A company has a project with a 4-year life, requiring an Initial Investment of $182,900, and is expected to yield annual cash flows of $54,000. What is the internal rate of return? IRR b Investment FactorEl Annual cash flowsc E'IRR Factor: This is the factor which blnvestment: This is the present cAnnual Cash Flows: you'll use on the table for the value of cash outflows associated This is the amount of present value of an annuity 0t 51 with a project. If all of the cash ows to be dollar in order to find the investment is up front at the received annually as percentage which corresponds to beginning of the project, the present a result of the the internal rate of return. value factor is 1.000. project. Calct latior Steps Present Value of an Annuity of 51 at Compound Interest. S[:1 IRR Factor 2 5:] = l:] , rounded to 6 deCimals The calculated factor corresponds to which percentage in the present value of ordinary annuity table? \"In Feedba ck Check My Work The internal rate of return calculation is a twoestep process First you must diVIde the present value of the initial investment by the annual cash ows of the project to arrive at the IRR factor Next use the table for the present value of an annuity of S1 at compound interest looking down the row of the number otyears the project will exist. At the column where you hit the value closest to your computed value. you have determined a percentage that is the internal rate of return for the project. D Part Five APPLY THE CONCEPTS: Net present value and Present value index Sutherland Corp. is lool-(ing to invest in PrOJect A or PrOJect B. The data surrounding each project IS prowded below. Sutherland's cost of capital is 11%. Pro'ect A Project B This preject requires an initial investment of This preject reqwres an initial investment of $165,000. The project Will have a life of 6 $130,000. The project Will have a life of 4 years. Annual revenues associated With the years. Annual revenues associated With the preject Will be $130,000 and expenses preject Will be $109,000 and expenses Project A Project B This project requires an initial investment of This project requires an initial investment of $165,000. The project will have a life of 6 $130,000. The project will have a life of 4 years. Annual revenues associated with the years. Annual revenues associated with the project will be $130,000 and expenses project will be $109,000 and expenses associated with the project will be $35,000. associated with the project will be $60,000. Calculate the net present value and the present value index for each project using the present value tables provided below. Present Value of $1 (a single sum) at Compound Interest. Present Value of an Annuity of $1 at Compound Interest. Note: . Use a minus sign to indicate a negative NPV. . If an amount is zero, enter "0". . Enter the present value index to 2 decimals. Project A Project B Total present value of net cash flow Amount to be invested Net present value Present value index: Project A Project BProject B :l Based upon net present value, which preject has the more favorable prot prospects? Project A V / Based upon the present value index, which pi'OJect l5 ranked higher? Project A v J Feedback ' Check My Work Subtract the expenses from the revenues to determtne net cash ow for each year Since this lS an annuity cash ow, use the appropnate table to look up the present value fador for the project life and required rate of return. Part Six > APPLY THE CONCEPTS: Irte'ra rate of ram 'r The Sutherland purchasmg department has made revisions to their costs and annual cash flows For Project A and Preject B, as outlined below. Eject A miject B Project A's revtsed investment is $241,000. The Project B's revised investment is $130,700. prOJect's life and cash How have changed to 7 The prOJect's life and cash ow have changed years and $49,500, respectively, while expenses to 5 years and $85,000 while expenses have been eliminated. reduced slightly to $55,000. Compute the internal rate of return factor for Project A and Project B and then identify each project's cori'espondtng percentage from the PV ordtnary annuityr table. Mject A mject B Project A's revrsed investment lS $241,000. The Project B's reVIsed investment Is $130,700. prOJect's llfe and cash How have changed to 7 The project's life and cash flow have changed years and $49,500, respectlvely, while expenses to 6 years and $85,000 WhllE expenses have been eliminated. reduced slightly to $55,000. Compute the internal rate of return factor for Project A and Project B and then identify each project's corresponding percentage from the PV ordinary annuity table. Note: Enter the IRR factor, to 5 declmal places. \"/0 Project A: The calculated IRR factor Is and thlS value corresponds to which percentage in the present value of ordlnary annuity table? :] Project B: The calculated IRR factor is :l and this value corresponds to whlch percentage in the present value of ordlnary annuity table? > Feedback " Check My Work As done in a prior section, divtde the initial investment by the annual cash flow to compute the present value factor Then use the table to look up where the factor resides on the row corresponding lo the prolect life. Feedback "' Check My Work Partially correct