Time Value of Money PDF

Time Value of Money Copyright © 2009 Pearson Prentice Hall. All rights reserved. Basic Concepts Future Value: Is the value at a given future date of an amount placed on deposit today, compounding or growth over time Present Value: discounting to today’s value Single ca...

Time Value of Money Copyright © 2009 Pearson Prentice Hall. All rights reserved. Basic Concepts Future Value: Is the value at a given future date of an amount placed on deposit today, compounding or growth over time Present Value: discounting to today’s value Single cash flows & series of cash flows can be considered  Principal: Is the amount of money on which interest is paid. Time-lines are used to show the timing of cash flow Computational Aids (Cont.) Compounding and Discounting Future Values A dollar in hand today is worth more than a dollar to be received in the future because, if you had it now, you could invest it, earn interest, and end up with more than a dollar in the future. The process of going to future values (FVs) from present values (PVs) is called compounding.  Assume that you plan to deposit $100 in a bank that pays a guaranteed 5 percent interest each year. How much would you have at the end of Year 3? Present Value Finding a present value is the reverse of finding a future value. What Is A Discount Rate? The discount rate is a critical financial metric used to determine the present value of future cash flows generated by an investment or project. It reflects the opportunity cost of capital, which is the return that investors expect to earn on their investments elsewhere. Role Of The Discount Rate In Evaluating Project Cash Flows Present Value Calculation: Future cash flows are uncertain and must be discounted back to their present value to assess their worth in today's terms. The formula for calculating the present value (PV) of future cash flows is:  Where: CF = Future cash flow r = Discount rate 𝑛 = Number of periods until the cash flow is received  Copyright © 2009 Pearson Prentice Hall. All rights reserved. 9-11 NET PRESENT VALUE Copyright © 2009 Pearson Prentice Hall. All rights reserved. Net Present Value (NPV) Net Present Value (NPV): Net Present Value is found by subtracting the present value of the after-tax outflows from the present value of the after-tax inflows. Copyright © 2009 Pearson Prentice Hall. All rights reserved. Net Present Value (NPV) (Cont.) Net Present Value (NPV): Net Present Value is found by subtracting the present value of the after-tax outflows from the present value of the after-tax inflows. Decision Criteria If NPV > 0, accept the project If NPV < 0, reject the project If NPV = 0, technically indifferent  Overview of Capital Budgeting Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the firm’s goal of maximizing owner wealth. A capital expenditure is an outlay of funds by the firm that is expected to produce benefits over a period of time greater than 1 year. An operating expenditure is an outlay of funds by the firm resulting in benefits received within 1 year.  Capital Budgeting Techniques Bennett Company is a medium sized metal fabricator that is currently contemplating two projects: Project A requires an initial investment of $42,000, project B an initial investment of $45,000. Capital Expenditure Data For Bennett Company Bennett Company’s Projects A And B First Technique Payback Period The payback method is the amount of time required for a firm to recover its initial investment in a project, as calculated from cash inflows. The length of the maximum acceptable payback period is determined by management. – If the payback period is less than the maximum acceptable payback period, accept the project. – If the payback period is greater than the maximum acceptable payback period, reject the project.  Payback Period (Cont.) We can calculate the payback period for Bennett Company’s projects A and B using the data in Table 10.1. – For project A, which is an annuity, the payback period is 3.0 years ($42,000 initial investment ÷ $14,000 annual cash inflow). – Because project B generates a mixed stream of cash inflows, the calculation of its payback period is not as clear-cut.  In year 1, the firm will recover $28,000 of its $45,000 initial investment. By the end of year 2, $40,000 ($28,000 from year 1 + $12,000 from year 2) will have been recovered. At the end of year 3, $50,000 will have been recovered. Only 50% of the year-3 cash inflow of $10,000 is needed to complete the payback of the initial $45,000. – The payback period for project B is therefore 2.5 years (2 years + 50% of year 3).  Second Technique Net Present Value (NPV) Net present value (NPV) is a sophisticated capital budgeting technique; found by subtracting a project’s initial investment from the present value of its cash inflows discounted at a rate equal to the firm’s cost of capital. NPV = Present value of cash inflows – Initial investment  Net Present Value (NPV) (Cont.) Decision criteria: – If the NPV is greater than $0, accept the project. – If the NPV is less than $0, reject the project. If the NPV is greater than $0, the firm will earn a return greater than its cost of capital. Such action should increase the market value of the firm, and therefore the wealth of its owners by an amount equal to the NPV. Bennett Company (Cont.) Capital Expenditure Data For Bennett Company If the company has a 10% cost of capital, what is the NPV of each project? Calculation Of NPVs For Bennett Company’s Capital Expenditure Alternatives