In this case, the payback period is calculated using the cumulative total of net cash flows. Uneven Cash Flows Net present value analysis can also be applied when net cash flows are uneven (unequal). Future net cash flows for each project are shown in the first three number columns of Exhibit 11.8.
Compute the present value factor for the investment project
When the cash flows are equal, as with Project A, we calculate the present value factor (as shown in Exhibit 11.9) by dividing the original investment by its annual net cash flows. We then use an annuity table to determine the discount rate corresponding to this present value factor. For FasTrac's project A, we look across the three-period series in Table B.3 and find that the discount rate corresponding to the present value factor of 2.4000 is roughly equal to the value of 2.4018 for the 12%.
A more accurate IRR estimate can be calculated by following the procedure shown in the note to Exhibit 11.9. We show how to use an Excel function to calculate the IRR in the Appendix of this chapter. Unequal Cash Flows If the net cash flows are unequal, we must use trial and error to calculate the IRR.
If the amount is positive (negative), we recalculate the NPV using a higher (lower) discount rate. Since the NPV when using IRR is zero, we know that the IRR is between these two discount rates.
Identify the discount rate (IRR) yielding the present value factor
Decision Insight
Using Internal Rate of Return When we use IRR to evaluate a project, com- C2. Neither the payback period nor the accounting rate of return take into account the time value of money. On the other hand, both the present value and the internal rate of interest do.
For projects financed by borrowed funds, the marginal interest rate must exceed the interest paid on these funds. Remember that lower risk investments require a lower rate of return compared to higher risk investments. If the project is internally financed, the hurdle rate is often based on actual returns from comparable projects.
Several projects are often ranked by the extent to which their IRR exceeds the hurdle rate. Bottom line: Research reports that 41% of senior managers would reject a project with an internal rate of return higher than the cost of capital if the project caused the company to miss its earnings forecast.
Decision Maker
It can be applied to even and uneven cash flows and can reflect changes in the level of risk over the life of a project. Two investment alternatives are expected to generate annual cash flows with the same net present value (assuming the same discount rate applied to each). When two investment alternatives have the same total expected cash flows but differ in the timing of those flows, which method of valuing these investments is best, (a) accounting rate of return or (b) present value.
Its calculation provides a measure of expected time, which represents the time period until the present value of the net cash flows from an investment equals the initial cost of the investment. In basic terms, breakeven time is calculated by recalculating future cash flows in terms of present values and then determining the payback period based on these present values. We interpret this as the cash flows earned after 5.2 years contribute to a positive net present value which in this case ultimately amounts to $5,872.
Breakeven time is a useful measure for managers because it identifies the point in time at which they can expect cash flows to begin producing net positive returns. Present value Present value Cumulative cash flows in the current year 1 at 10% of the value of the cash flows.
Planning the Solution
Solution to Demonstration Problem
Calculating net present values and internal rates of return for projects with uneven cash flows is tedious and error-prone. To illustrate, consider Fastrac, a company considering investing in a new machine with the expected cash flows shown in the following spreadsheet. Cash flows are entered as negative numbers and cash flows are entered as positive numbers.
APPENDIX
It involves predicting the cash flows that will be received from the alternatives, evaluating their merits, and then choosing which alternatives to pursue. Break-even time (BET) is a method of evaluating capital investments by restating future cash flows in terms of their present values (discounting the cash flows) and then calculating the payback period using these present values of cash flows. A payback period analysis does not reflect the risk of the cash flows, differences in the timing of cash flows within the payback period, and cash flows that occur after the payback period.
This technique can handle any pattern of expected cash flow and applies a superior concept of return on investment. When the cash flows are equal, we can calculate the present value factor corresponding to the IRR by dividing the initial investment by the annual cash flows. This instructs Excel to use its NPV function to calculate the present value of the cash flows in cells C4 to C11, using the discount rate in cell C1, and then add the amount of the (negative) initial investment.
This instructs Excel to use the IRR function to calculate the internal rate of return of the cash flows in cells C2 through C11. One investment may continue to generate cash flows for a longer period after the payback period than another.
Additional Quiz Questions are available at the book’s Website
Circuit City is considering expanding a store
Apple's management plans to purchase new equipment to manufacture some of its computer equipment and intends to evaluate that investment decision using net present value. What are some of the costs and benefits that would be included in Apple's analysis.
Discussion Questions
QUICK STUDY
- Payback period P1
- Computation of
- Computation of
- Profitability index
Fast Feet, a shoe manufacturer, is evaluating the costs and benefits of new equipment that would custom fit each pair of athletic shoes. The customer would have their foot scanned with digital computer equipment; this information would be used to cut the raw materials to ensure a perfect fit for the customer. The new equipment costs $300,000 and is expected to incur additional costs. interest rate for the purchase of this equipment.
Camino Company is considering an investment that is expected to generate an average after-tax net income of $3,825 over three years. Calculate the accounting rate of return for this investment; assume the company uses straight-line depreciation. Present value Present value Cumulative present value Present value Cash flows of the year* of 1 to 8% of cash flows of cash flows.
EXERCISES
Accounting rate of return
Create an Excel spreadsheet to calculate the internal rate of return for each of the projects.
NPV and profitability index
A Using Excel to compute IRR
PROBLEM SET A
Analysis and computation of
Create a five-column table reporting amounts (assuming straight-line depreciation) for each of the following for each of the six years: (a) pre-tax income before depreciation, (b) straight-line depreciation expense, (c) taxable income, (d) income taxes, and (e) net cash flow. Create a five-column table reporting the amounts (assuming the use of MACRS depreciation) for each of the following for each of the six years: (a) pre-tax income before depreciation, (b) MACRS Problem 11 -3A. The project would generate $71,000 in pretax income, before depreciation, at the end of each of the next six years.
In preparing the tax return and calculating income tax payments, the company can choose between the two alternative depreciation schedules shown in the table.
Computing net present
Management claims a three-year investment payback period and claims a 10% return on its investments.
PROBLEM SET B
Analysis and computation of
When preparing its tax return and calculating its income tax payments, the company can choose between two alternative depreciation schedules as shown in the table.
Computation of cash flows
Lee Corporation is considering a new project that requires an investment of $300,000 in an asset that has no salvage value. The project would generate $125,000 in pre-tax income before depreciation at the end of each of the next six years. The investment will require an initial outlay of $800,000 and yield the following expected cash flows.
Archer Foods has a freezer in need of repair and is considering whether to replace the old freezer with a new freezer or whether the old freezer needs extensive repair. If the old freezer is repaired, it will be stored for another 8 years and then sold for its salvage value. The new freezer is larger than the old one and will allow the company to expand its product range and thus generate more income.
The investment will require an initial outlay of $800,000 and will yield the following expected cash flows.
SERIAL PROBLEM
Management requires that investments have a payback period of two years and a return of 10% on investments.
BEYOND THE NUMBERS
REPORTING IN ACTION
Access Best Buy's financial statements for fiscal years ended after March 3, 2007, via its website (BestBuy.com) or the SEC's website (SEC.gov). Determine the amount Best Buy invested in similar store-related projects over the past year. What is the amount of cash flow that Best Buy should earn from these new projects.
Suppose these projects have a term of seven years and that management requires an internal rate of return of 15% on these projects. What is the amount of annual cash flows that Circuit City must earn from these retail-related projects to achieve a 15% internal rate of return. Tip: Identify the 7-period, 15% factor from the present value of an annuity table and then divide $108 million by the factor to obtain the required annual cash flows.
How does your answer to part 1 compare to Best Buy's required cash flows determined in BTN 11-1.
COMPARATIVE ANALYSIS
ETHICS CHALLENGE
COMMUNICATING IN PRACTICE
TAKING IT TO THE NET
Calculate the payback period and net present value (assuming a required rate of return of 10%) of the following investment—assume its cash flows occur at the end of the year. Compared to the case of the example on the website, the largest cash inflows in the example below occur in the later years of the project's life.
TEAMWORK IN ACTION
Read the chapter opener about Brian Scudamore and his company, 1-800-GOT-JUNK
ENTREPRENEURIAL DECISION
HITTING THE ROAD
ANSWERS TO MULTIPLE CHOICE QUIZ
GLOBAL DECISION C1
