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

2. 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

3. 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+k)i -
Net Investment x
k = the discount rate (cost of capital)
n = life of the project

4. Net Present Value Table 1 Number of Periods 8% 10% 12%

5. 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.

6. 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.

7. Net Present Value Table 1 Table 2 Number of Periods 8% 10% 12% 10%
2.486

8. 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 = 19,896
$19,896 - $15,000 = $4,896

9. 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.

10. 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.

11. 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.

12. 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

13. Net Present Value So interpolating, the IRR is approximately 9%
Table 2
Number
of Periods 8% 10% 12%
So interpolating, the IRR is approximately 9%

14. 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.

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

16. IRR and NPV Compared EXAMPLE Project Initial Cost Cash flow IRR NPV
B $ $ % $41

17. 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.

18. 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.

19. 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.

20. 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.

21. 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

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

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