Chapter 6 Time Value of Money

Introduction Why money has a time value –The opportunity cost of capital concept Time value of money and risk –Typically risk and expected returns are related to each other Investment decisions and the Time Value of Money –Allows us to compare present and future cash flows on a comparable basis (apples to apples).

Basic Time Diagram

Principal (P): The amount borrowed or invested Interest rate (i): A percentage of the outstanding principle. Number of periods (n): (years or fractional of) that principal is outstanding. Present value (PV): present value of a single amount of cash, or series of cash flows. Future value (FV): future value of a single amount of cash, or series of cash flows. Variables Used in Time Value of Money Computations

Time Value of Money – From Present Value to Future Value and Back A simple case is investing $1.00 Use of a time line is helpful

Present and future values are calculated for us in the text: Future value of $1, Table 6.2 Present value of $1, Table 6.3 Future value of an annuity of $1, Table 6.5 Present value of an annuity of $1, Table 6.7 Compound Interest Tables

Present Value of a Single (Lump) Sum Excerpt from Present Value of $1, Table 6.3

Present Value of a Single (Lump) Sum Present value factor of $1 for 2 periods at 12%. Present value factor of $1 for 2 periods at 12%. $100 × = $79.70 present value

Future Value Exercise $100,000 is put into a mutual fund yielding a 12% annual return. How much would the fund be worth in 23 years? $100,000 * = $1,355,200

Present Value of a Series of Cash Flows Annuity – a series of receipts (or payments) of the same amount spaced over regular time intervals (periods) –Example –Beauty of the PV factors for annuities Uneven series of receipts (or payments) –Example –No single PV factor may be used, the present value of each cash flow must be calculated, then summed

Annuity $100$100$100$100$100$100 annuity An investment that involves a series of IDENTICAL cash flows at the end of each year is called an annuity.

PV of An Annuity Example Lacey Company purchased a tract of land on which a $60,000 payment will be due each year for the next five years. What is the present value of this stream of cash payments when the discount rate is 12%?

PV of An Annuity Example We could solve the problem like this... Present Value of an Annuity of $1 Excerpted from Table 6.6

PV of An Annuity Example We could solve the problem like this... $60,000 × = $216,300

Future Value of a Series of Cash Flows The same techniques applied to calculating the PV of an annuity or uneven stream of cash flows may be used to calculate the FV of cash flows –Example

The Rule of 72 A quick way to estimate the approximate number of periods it takes to double the value of an investment. 72 % return

Text Problems Note: some problems require the use of formulas )or tables outside the text) E 33(a)FV single sum E 33(b)““ E 34(a)PV single sum E 34(b)PV series of cash receipts E 35(a)FV annuity + lump sum E 35(b)“” E 36(a)Lottery winnings – PV vs. annuity E 36(b)Lottery winnings – PV vs. annuity

The Net Present Value Method To determine net present value we...  Calculate the present value of cash inflows,  Calculate the present value of cash outflows,  Subtract the present value of the outflows from the present value of the inflows.

Typical Cash Outflows Initialinvestment Repairs and maintenance Incrementaloperatingcosts Workingcapital

Typical Cash Inflows Reduction of costs Salvage value Incrementalrevenues Release of workingcapital

The Net Present Value Method (NPV) General decision rule...

The Net Present Value Method Lester Company has been offered a five year contract to provide component parts for a large manufacturer.

The Net Present Value Method At the end of five years the working capital will be released and may be used elsewhere by Lester. Lester Company uses a discount rate of 10%. Should the contract be accepted?

The Net Present Value Method Annual net cash inflows from operations

The Net Present Value Method

Present value of an annuity of $1 factor for 5 years at 10%.

The Net Present Value Method Present value of $1 factor for 3 years at 10%.

The Net Present Value Method Present value of $1 factor for 5 years at 10%.

The Net Present Value Method positive Accept the contract because the project has a positive net present value.

Expanding the Net Present Value Method To compare two competing investment projects we can use the following net present value approaches: –Total-cost – Calculate NPV for each project. Accept the project with the higher NPV –Incremental cost – Determine the cash flow differences between alternatives, and calculate the NPV of these cash flows. Accept one alternative over the other if the differential NPV is positive.

Least Cost Decisions In decisions where revenues are not directly involved, managers should choose the alternative that has the least total cost from a present value perspective. Let’s look at the Home Furniture Company.

Least Cost Decisions Home Furniture Company is trying to decide whether to overhaul an old delivery truck now or purchase a new one. The company uses a discount rate of 10%. Home Furniture

Least Cost Decisions Information about the trucks...

Least Cost Decisions

Home Furniture should purchase the new truck.

The Internal Rate of Return Method The internal rate of return is the interest yield promised by an investment project over its useful life. The internal rate of return is computed by finding the discount rate that will cause the net present value of a project to be zero.

The Internal Rate of Return Method Decker Company can purchase a new machine at a cost of $104,320 that will save $20,000 per year in cash operating costs. The machine has a 10-year life.

The Internal Rate of Return Method Future cash flows are the same every year in this example, so we can calculate the internal rate of return as follows: Investment required Net annual cash flows PV factor for the internal rate of return = $104, 320 $20,000 = 5.216

The Internal Rate of Return Method 14% Find the 10-period row, move across until you find the factor Look at the top of the column and you find a rate of 14%. Using the present value of an annuity of $1 table...

The Internal Rate of Return Method Decker Company can purchase a new machine at a cost of $104,320 that will save $20,000 per year in cash operating costs. The machine has a 10-year life. internal rate of return The internal rate of return on this project is 14%. If the internal rate of return is equal to or greater than the company’s required rate of return, the project is acceptable.

Net Present Value vs. Internal Rate of Return Net Present Value vEasier to use. vAssumes cash inflows will be reinvested at the discount rate. This is a realistic assumption.