1. Other Investment Criteria and Free Cash Flows in Finance
Capital Budgeting Decisions
Financial management: lecture 6

2. Financial management: lecture 6
Today’s agenda
Midterm exam
Net Present Value (revisit)
Other two investment rules
Free cash flows calculation
A specific example
Financial management: lecture 6 2

3. Financial management: lecture 6
Mid-term exam
The midterm exam score and the solution were posted on my website last Friday:
Most students have done very well in the first midterm exam. If you don’t do very well, don’t worry about it and you can try your best to do much better in the second midterm and the final.
Remember the weight of 0.2 for the midterm with a lower score.
Financial management: lecture 6

4. Net Present Value rule (NPV)
NPV is the present value of a project minus its cost
If NPV is greater than zero, the firm should go ahead to invest; otherwise forget about this project
A hidden assumption: there is no budget constraint or money constraint.
Financial management: lecture 6 4

5. Financial management: lecture 6
NPV (continue)
In other words:
Managers can increase shareholders’ wealth by accepting all projects that are worth more than they cost.
Therefore, they should accept all projects with a positive net present value if there is no budget constraint.
Financial management: lecture 6 13

6. Net Present Value NPV = PV - required investment
Financial management: lecture 6 11

7. Financial management: lecture 6
Net Present Value
Example
You have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building?
Financial management: lecture 6 14

8. Financial management: lecture 6
Net Present Value
$466,000
Example - continued
$450,000
$16,000
$16,000
$16,000
Financial management: lecture 6 15

9. Financial management: lecture 6
Net Present Value
$466,000
$450,000
Example - continued
$16,000
$16,000
$16,000
Present Value
14,953
380,395
$409,323
Financial management: lecture 6 16

10. Financial management: lecture 6
Net Present Value
Example - continued
If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?
Financial management: lecture 6 17

11. Financial management: lecture 6
Net Present Value
Example - continued
If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building?
Financial management: lecture 6 18

12. Another example about NPV
An oil well, if explored, can now produce 100,000 barrels per year. The well will produce forever, but production will decline by 4% per year. Oil prices, however, will increase by 2% per year. The discount rate is 8%. Suppose that the price of oil now is $14 for barrel.
If the cost of oil exploration is $12.8 million, do you want to take this project?
Financial management: lecture 6

13. Financial management: lecture 6
Solution
Visualize the cash flow patterns
C0=1.4, C1=1.37, C2=1.34, C3=1.31
What is the pattern of the cash flow?
g=C1/C0 -1 = =-2.1%
PV( the project) =C0+C1/(r-g)=15
NPV=PV( the project ) -12.8>0
What’s your decision?
Financial management: lecture 6

14. Two other investment rules
IRR rule
Payback period rule
Financial management: lecture 6

15. Financial management: lecture 6
IRR rule
Internal Rate of Return (IRR) – Single discount rate at which NPV = 0.
IRR rule - Invest in any project offering a IRR that is higher than the opportunity cost of capital or the discount rate.
Financial management: lecture 6 20

16. Financial management: lecture 6
IRR rule
Example
You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?
Financial management: lecture 6 21

17. Internal Rate of Return
Example
You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?
Financial management: lecture 6 22

18. Internal Rate of Return
Example
You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment?
IRR = 12.96%
Financial management: lecture 6 23

19. Internal Rate of Return
IRR=12.96%
Financial management: lecture 6 24

20. Financial management: lecture 6
What’s wrong with IRR?
Pitfall 1 - Mutually Exclusive Projects
IRR sometimes ignores the magnitude of the project.
The following two projects illustrate that problem.
Example
You have two proposals to choose between. The initial proposal (H) has a cash flow that is different from the revised proposal (I). Using IRR, which do you prefer?
Financial management: lecture 6

21. Internal Rate of Return (1)
Example
You have two proposals to choose between. The initial proposal (H) has a cash flow that is different from the revised proposal (I). Using IRR, which do you prefer?
Financial management: lecture 6

22. Internal Rate of Return
Financial management: lecture 6

23. What’s wrong with IRR (2)?
Pitfall 2 - Lending or Borrowing?
Example
project C0 C1
IRR (%)
NPV at 10%
-100
+150
+50
+$36.4 J K
-150
+50
-$36.4
+100
Financial management: lecture 6

24. What’s wrong with IRR (3)?
Pitfall 3 - Multiple Rates of Return
Certain cash flows can generate NPV=0 at two different discount rates.
The following cash flow generates NPV=0 at both (-50%) and 15.2%.
Example
A project costs $1000 and produces a cash flow of $800 in year 1, a cash flow of $150 every year from year 2 to year 5, and a cash flow of -150 in year 6.
Financial management: lecture 6

25. Financial management: lecture 6
Payback period rule
Payback period is the number of periods such that cash flows recover the initial investment of the project.
The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this rule.
Financial management: lecture 6 28

26. Financial management: lecture 6
Payback period rule
The following example shows that all the three projects have a payback period of 2. If the payback period used by the firm is 2, the firm can take project C and lose money.
Cash Flows
Prj. C0 C1 C2 C Payback
A ,429 B C
Financial management: lecture 6 30

27. Some points to remember in calculating free cash flows
Depreciation and accounting profit
Incremental cash flows
Change in working capital requirements
Sunk costs
Opportunity costs
Forget about financing
Financial management: lecture 6

28. Cash flows, accounting profit and depreciation
Discount actual cash flows
Using accounting income, rather than cash flows, could lead to wrong investment decisions
Don’t treat depreciation as real cash flows
Financial management: lecture 6

29. Financial management: lecture 6
Example
A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income.
Financial management: lecture 6

30. Solution (using accounting profit)
Financial management: lecture 6

31. Solution (using cash flows)
Financial management: lecture 6

32. Forget about financing
When valuing a project, ignore how the project is financed.
You can assume that the firm is financed by issuing only stocks; or the firm has no debt but just equity
Financial management: lecture 6 17

33. Incremental cash flows
Incremental cash flows are the increased cash flows due to investment
Do not get confused about the average cost or total cost?
Do you have examples about incremental costs?
Incremental Cash Flow
cash flow with project
cash flow without project = -
Financial management: lecture 6

34. Financial management: lecture 6
Working capital
Working capital is the difference between a firm’s short-term assets and liabilities.
The principal short-term assets are cash, accounts receivable, and inventories of raw materials and finished goods.
The principal short-term liabilities are accounts payable.
The change in working capital represents real cash flows and must be considered in the cash flow calculation
Financial management: lecture 6

35. Financial management: lecture 6
Example
We know that inventory is working capital. Suppose that inventory at year 1 is $10 m, and inventory at year 2 is $15. What is the change in working capital? Why does this change represent real cash flows?
Financial management: lecture 6

36. Financial management: lecture 6
Sunk costs
The sunk cost is past cost and has nothing to do with your investment decision
Is your education cost so far at SFSU is sunk cost?
Financial management: lecture 6

37. Financial management: lecture 6
Opportunity cost
The cost of a resource may be relevant to the investment decision even when no cash changes hands.
Give me an example about the opportunity cost of studying at SFSU?
Financial management: lecture 6

38. Financial management: lecture 6
Inflation rule
Be consistent in how you handle inflation!!
Use nominal interest rates to discount nominal cash flows.
Use real interest rates to discount real cash flows.
You will get the same results, whether you use nominal or real figures
Financial management: lecture 6 12

39. Financial management: lecture 6
Example
You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?
Financial management: lecture 6 14

40. Financial management: lecture 6
Inflation
Example - nominal figures
Financial management: lecture 6 15

41. Financial management: lecture 6
Inflation
Example - real figures
Financial management: lecture 6 16

42. How to calculate free cash flows?
Free cash flows = cash flows from operations + cash flows from the change in working capital + cash flows from capital investment and disposal
We can have three methods to calculate cash flows from operations, but they are the exactly same, although they have different forms.
Financial management: lecture 6

43. How to calculate cash flows from operations?
Method 1
Cash flows from operations =revenue –cost (cash expenses) – tax payment
Method 2
Cash flows from operations = accounting profit + depreciation
Method 3
Cash flows from operations =(revenue –cost)*(1-tax rate) + depreciation *tax rate
Financial management: lecture 6

44. Financial management: lecture 6
Example
revenue ,000
Cost
Depreciation
Profit before tax
Tax at 35%
Net income
Given information above, please use three methods to calculate
Cash flows
Financial management: lecture 6

45. Financial management: lecture 6
Solution:
Method 1
Cash flows= =330
Method 2
Cash flows = =330
Method 3
Cash flows =( )*(1-0.35)+200*0.35
=330
Financial management: lecture 6

46. A summary example ( Blooper)
Now we can apply what we have learned about how to calculate cash flows to the Blooper example, whose information is given in the following slide.
Financial management: lecture 6

47. Financial management: lecture 6
Blooper Industries
(,000s)
Financial management: lecture 6 18

48. Cash flows from operations for the first year
Financial management: lecture 6 19

49. Financial management: lecture 6
Blooper Industries
Net Cash Flow (entire project) (,000s)
12% = $3,564,000
Financial management: lecture 6 20