Blueprint Problem: Net Present Value and Internal Rate of Return Companies use capital investment analysis to evaluate long-term investments. Capital investment evaluation methods that use present values are (1) Net present value method and (2) Internal rate of return method. Discounting Models One type of model with which to assess the viability of a potential capital investment is a discounting model. A defining characteristic of discounting models is that they the time value of money. This means that money tomorrow is worth money today as a result of investment yields. True or False: When making an investment decision between mutually exclusive projects, the project with the greatest return on investment should be chosen. Hide Feedback Correct Check My Work Feedback Review the definition of Discounting Models by rolling your mouse over the underlined item. Review the definition of Mutually Exclusive Projects by rolling your mouse over the underlined item. Net Present Value Introduced Net present value (NPV) is one useful discounting method that can be used to evaluate the financial viability of potential projects. It relies upon using discounting to determine the present value of all future cash flows associated with potential projects and measuring this against the cost of the project. To use net present value, a required rate of return must be defined. The required rate of return is the 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 deal with the inherent uncertainties surrounding future cash flows. This can be risky, however, as it biases the process toward short-term projects. If the NPV is positive, then the project should be ; if it is negative, then the project should be . Calculation Steps If a project has a 5-year life, requires an initial investment of $210,000, and is expected to yield annual cash flows of $58,500, what is the net present value of the project if the required rate of return is set at 12%? If required, round your answer to the nearest cent. Present Value Tables The Present Value of an Ordinary Annuity is the value of a stream of expected or promised future payments that have been discounted to a single equivalent value today. It is extremely useful for comparing two separate cash flows that differ in some way. Present Value of an Annuity of $1 at Compound Interest. Net Present Value Computation = ( $ x ) – $ What NPV does the previous calculation yield? $ Which of the following pieces of information are indicated by a positive net present value? Select "Yes" for all that apply. 1. The project is profitable. 2. The initial investment has been recovered. 3. The required rate of return has been recovered. 4. A return in excess of #2 and #3 has been received. Hide Feedback Partially Correct Check My Work Feedback Click on the Present Value of an Annuity of $1 at Compound Interest link and look for the intersection of the number of years row and the required rate of return column. Internal Rate of Return Introduced 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 time-adjusted rate of return method, starts with the proposal's net cash flows and works backward to estimate the proposal's expected rate of return. Internal Rate of Return Calculation (Even Cashflows) IRR Factor = Investment Annual cash flows If a project has a 6-year life, requires an initial investment of $139,930, and is expected to yield annual cash flows of $35,000, what is the internal rate of return? IRR Factor = $ = $ The calculated value corresponds to which percentage in the table for the present value of ordinary annuities? (Present Value of an Annuity of $1 at Compound Interest.) Hide Feedback Partially Correct Check My Work Feedback The internal rate of return calculation is a two-step process. First, you must divide the present value of the the initial investment by the annual cash flows of the project to arrive at the discount factor. Next, use the table for the present value of an annuity of $1 at compound interest, looking down the row of the number of years 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. APPLY THE CONCEPTS: Net present value Project A This project requires an initial investment of $145,800. The project will have a life of 4 years. Annual revenues associated with the project will be $90,000 and expenses associated with the project will be $45,000 for an annual net cash flow of $ . Note: Enter cash flows as positive numbers. Cash Flows Year 0 -$145,800 Year 1 Year 2 Year 3 Year 4 Project B This project requires an initial investment of $135,480. The project will have a life of 4 years. Annual revenues associated with the project will be $100,000, and expenses associated with the project will be $60,000, for an annual net cash flow of $ . Cash Flows Year 0 -$135,480 Year 1 Year 2 Year 3 Year 4 The cost of capital for the company is 6%. Present Value Tables Present Value of $1 (a single sum) at Compound Interest. Present Value of an Annuity of $1 at Compound Interest. Use the minus sign to indicate a negative NPV. If an amount is zero, enter"0". Project A NPV Analysis Year Cash Flow Discount Factor Present Value 0 $145,800 1.000 $145,800 1–4 45,000 NPV $ Project B NPV Analysis Year Cash Flow Discount Factor Present Value 0 $135,480 1.000 $135,480 1–4 40,000 NPV $ Based upon net present value, which project has the more favorable profit prospects? Hide Feedback Partially Correct Check My Work Feedback Subtract the expenses from the revenues to determine the cash flows for each year. Since this is an annuity cash flow, use the appropriate table to look up the present value discount factor for the project life and required rate of return. APPLY THE CONCEPTS: Internal rate of return Calculate the internal rate of return for Project A and Project B (defined previously). Enter the IRR with the percent sign (i.e. 4%). Project A: IRR Analysis With an initial investment of $145,800 and annual cash flows of $ , the internal rate of return for Project A is . Project B: IRR Analysis With an intial investment of $135,480 and annual cash flows of $ , the internal rate of return for Project B is .