Capital Budgeting Net Present Value (NPV) Internal Rate of Return (IRR) NPV and IRR compared Payback Method Accounting Rate of Return

Net Present Value  NPV = - What is the project worth, in today’s dollars? n  i = 1 Annual net Cash Inflows (1+k)i NPV = Net Investment - k = the discount rate (cost of capital) n = life of the project

Net Present Value  NPV = - What is the project worth in today’s dollars? Now assume annual cash inflows are constant for the life of the project. n  i = 1 Annual net cash Inflows NPV = 1 _ (1+k)i - Net Investment x k = the discount rate (cost of capital) n = life of the project

Net Present Value Table 1 Number of Periods 8% 10% 12% 1 .926 .909 .893 2 .857 .826 .797 3 .794 .751 .712 4 .735 .683 .636 5 .681 .621 .567

Net Present Value Advantages: Disadvantages: For choosing among projects, this is probably the best method. Disadvantages: No significant disadvantages, although NPV assumes cashflows can be reinvested for a return of k.

Net Present Value Example Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 3 years. The cost of the investment is $15,000. What is the net present value of the investment using a 10% cost of capital.

Net Present Value Table 1 Table 2 Number of Periods 8% 10% 12% 10% 1 .926 .909 .893 0.909 2 .857 .826 .797 1.736 3 .794 .751 .712 2.487 2.486

Net Present Value Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 3 years. The cost of the investment is $15,000. What is the net present value of the investment using a 10% cost of capital. $8,000 x 2.487 = 19,896 $19,896 - $15,000 = $4,896

Internal Rate of Return IRR is the interest rate computed such that the NPV of the project is zero. Let: n  i = 1 Annual net Cash Inflows (1+k)i 0 = Net Investment - And solve for k. This is the IRR.

Internal Rate of Return Advantages: IRR is a measure of profitability that is independent of the size of the project. Disadvantages: Can motivate managers to forego positive net present value projects. Assumes cash flows can be reinvested at the same internal rate of return.

Internal Rate of Return Example Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 4 years. The cost of the investment is $25,920. What is the internal rate of return on the investment.

Internal Rate of Return Example Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 4 years. The cost of the investment is $25,920. What is the internal rate of return on the investment. $25,920 ÷ $8,000 = 3.24

Net Present Value So interpolating, the IRR is approximately 9% Table 2 Number of Periods 8% 10% 12% 1 .926 .909 .893 2 1.78 1.74 1.69 3 2.58 2.49 2.40 4 3.31 3.17 3.04 5 4.00 3.79 3.61 So interpolating, the IRR is approximately 9%

IRR and NPV Compared If the IRR is less than the discount rate, NPV is negative. If NPV > 0, IRR is greater than the discount rate.

IRR and NPV Compared Calculate the NPV and IRR of each project. EXAMPLE Year-end Project Initial Cost Cash Flow A $1,000 $1,200 B $ 50 $ 100 The project life for both projects is 1 year. Let K = 10%

IRR and NPV Compared EXAMPLE Project Initial Cost Cash flow IRR NPV B $ 50 $ 100 100% $41

Payback How long will it take to recover the investment? Advantages: PAYBACK = NET INVESTMENT AVERAGE EXPECTED CASH FLOW Advantages: Easy to Calculate. Disadvantages: Fails to account for the time value of money. Ignores returns after the payback period.

Accounting Rate of Return Average annual net income Average book investment In the simplest scenario, the numerator, net income, is cash flow less depreciation expense; and the denominator, book investment, is the cost of the project, net of accumulated depreciation. Disadvantage: Ignores the time value of money.

Accounting Rate of Return Average annual net income Average book investment Example: A machine costs $100,000, and has a useful life of 2 years. The machine will generate revenues net of operating expenses of $70,000 per year. The tax rate is 40%. The company uses straight-line depreciation.

Accounting Rate of Return A machine costs $100K and has a useful life of 2 years. It will generate annual revenues net of operating expenses of $70K. The tax rate is 40%. Depreciation expense is $50,000 per year ($100,000/2). The average book investment is also $50,000.

Accounting Rate of Return The average of any straight line is the midpoint: $100 K $ 50 K Zero because the machine has zero salvage value. $ 0 1 2 Year 1 Year 2

Accounting Rate of Return Average annual net income Average book investment Numerator: Revenues less operating exp.s $70,000 Depreciation expense 50,000 Income before taxes 20,000 Tax Expense (40% of $20K) 8,000 Net Income 12,000

Accounting Rate of Return Average annual net income Average book investment $12,000 = 24% $50,000