1. Investment Decisions and Capital Budgeting
Fuqua School of Business
Duke University

2. Overview Capital Budgeting Techniques
Net Present Value (NPV)
Criterion for capital budgeting decisions
Special cases:
Repeated projects
Optimal replacement rules
Alternative criteria
Internal Rates of Return (IRR)
Payback period
Profitability Index

3. Net Present Value 1) Identify base case and alternative
2) Identify all incremental cash flows (Be comprehensive!)
3) Where uncertain use expected values
Don’t bias your expectations to be “conservative”
4) Discount cash flow and sum to find net present value (NPV)
5) If NPV > 0, go ahead
6) Sensitivity Analysis 3

4. NPV - The Two-Period Case
Suppose you have a project which has:
An investment outlay of $100 in 1997 (period 0)
A safe return of $110 in 1998 (period 1)
Should you take it?
What is your alternative?
Put your money into a bank account at 6%, receive $106
Gain 4$ in terms of 1998 money
The project has a positive value! 4

5. Formal Analysis - The Idea
Denote the 1997 and 1998 cash flows as follows:
CF0 = Cash outflow in period 0
CF1 = Cash return in period 1
Your comparison is a rate of return r of 6% or r=0.06. You invest only if:
The NPV expresses the gain from the investment in 1998 dollars.
The factor 1/1.06=0.943 which multiplies the period 1 cash flow is called the discount factor, whereas 6% is the discount rate.
Exercise:
If the present value of $150 paid at the end of 1 year is $130, what is the discount factor? What is the discount rate? 5

6. Calculating NPVs You have incremental cash flows:
CF0, CF1, CF2, ... , CFT
NPV in year 0 is: 6

7. Computing NPVs Example Year 1997 1998 1998 2000 CF -100 -50 30 200
Use discount tables:
DF Total
DCF = 29.6
Use spreadsheet:
On Lotus/Excel if data are in cells A2..D2, the function NPV (0.1, A2..D2) gives you the NPV in 1996
Exercises:
1) What is the present value (year 0) of a payment of $152 paid in period 3 if the discount rate is 15%?
2) An investment of $232 will produce $ in 2 years. What is the annual interest rate?
3) A factory costs $4m to build. You reckon that it will produce an inflow after operating costs of $1m in year 1, $2m in year 2, and $3m in year 3. The opportunity cost of capital is 12%. Draw up a worksheet and a table with the discount factors (like in the slide above) to calculate the net present value. 7

8. Why Use the NPV Rule? We showed that a project with a cash flow:
had an NPV of 10%. So what?
Suppose the only shareholder has a bank account where she can borrow or deposit at 10%.
Take on the project, draw out 29.6 and spend:
Fill in the blanks as follows:
In the first period, the shareholder takes out 29.6, spends 29.6 on consumption, and invests 100 in the project. In every following year she borrows from the bank whenever there is a cash outflow, and repays the loan whenever there is a cash inflow from the project. In each period, remember that the account accrues interest from the balance of the previous year. What is the closing balance of the bank account at the end? What are the residual cash flows to the shareholder?
Exercises:
1) Suppose you can borrow at 10%, but deposit positive balances at only 8%. How does this affect your answer?
2) Suppose you can borrow/deposit at 10%, and you have a project with the following cash flows:
Perform the same calculations as on the slide above. How is your answer to exercise 1) affected now? 8

9. Net Present Value (NPV)
The NPV measures the amount by which the value of the firm’s stock will increase if the project is accepted.
NPV Rule:
Accept all projects for which NPV > 0.
Reject all projects for which NPV < 0.
For mutually exclusive projects, choose the project with the highest NPV. 9

10. NPV Example
Consider a drug company with the opportunity to invest $100 million in the development of a new drug that is expected to generate $20 million in after-tax cash flows for the next 15 years. What is the NPV of this investment project if the required return is 10%? What if the required return is 20%? 10

11. NPV Example (cont.)
rp = 10%
rp = 20% 11

12. Eurotunnel NPV
One of the largest commercial investment project’s in recent years is Eurotunnel’s construction of the Channel Tunnel linking France with the U.K.
The cash flows on the following page are based on the forecasts of construction costs and revenues that the company provided to investors in 1986.
Given the risk of the project, we assume a 13% discount rate. 12

13. Eurotunnel’s NPV 13

14. Special Topics: Comparing Projects with Different Lives
Your firm must decide which of two machines it should use to produce its output.
Machine A costs $100,000, has a useful life of 4 years, and generates after-tax cash flows of $40,000 per year.
Machine B costs $65,000, has a useful life of 3 years, and generates after-tax cash flows of $35,000 per year.
The machine is needed indefinitely and the discount rate is rp = 10%. 14

15. Comparing Projects with Different Lives
Step 1: Calculate the NPV for each project.
NPVA=$26,795
NPVB=$20,040
The NPV of A is received every 4 years
The NPV of B is received every 3 years 15

16. Comparing Projects with Different Lives
Step 2: Convert the NPVs for each project into an equivalent annual annuity. 16

17. Comparing Projects with Different Lives
The firm is indifferent between the project and the equivalent annual annuity.
Since the project is rolled over forever, the equivalent annual annuity lasts forever.
The project with the highest equivalent annual annuity offers the highest aggregate NPV over time.
Aggregate NPVA = $8,453/.10 = $84,530
Aggregate NPVB = $8,863/.10 = $88,630 17

18. Special Topics: Replacing an Old Machine
The cost of the new machine is $20,000 (including delivery and installation costs) and its economic useful life is 3 years.
The existing machine will last at most 2 more years.
The annual after-tax cash flows from each machine are given in the following table.
The discount rate is rp = 10%. 18

19. Replacing an Old Machine
Step 1: Calculate the NPVof the new machine.
Step 2: Convert the NPV for the new machine into an equivalent annual annuity. 19

20. Replacing an Old Machine
The NPV of the new machine is equivalent to receiving $6,544 per year for 3 years.
Operate the old machine as long as its after-tax cash flows are greater than EANew = $6,544.
Old machine should be replaced after one more year of operation.
How did we know that the new machine itself would not be replaced early? 20

21. Alternatives to NPV Internal Rate of Return (IRR) Payback
Profitability Index 21

22. Internal Rate of Return
Method
Calculate the discount rate which makes the NPV zero
Question: How high could the cost of capital be, so that the NPV of a project is still positive?
The higher the IRR the better the project
Advantages
Calculation does not demand knowledge of the cost of capital
Many people find it a more intuitive measure than NPV
Usually gives the same signal as NPV 22

23. Internal Rate of Return (IRR)
The IRR is the discount rate, IRR, that makes NPV = 0.
IRR Rule for investment projects:
Accept project if IRR > rp.
Reject project if IRR < rp. 23

24. IRR Example
Consider, once again, the drug company that has the opportunity to invest $100 million in the development of a new drug that will generate after-tax cash flows of $20 million per year for the next 15 years. What is the IRR of this investment?
The IRR makes NPV = 0.
Trial and error (or a financial calculator) gives IRR = 18.4%.
Accept the project if rp < 18.4%. 24

25. IRR Problems: Borrowing or Lending?
Consider the following two investment projects faced by a firm with rp = 10%.
Both projects have an IRR = 50%, but only project A is acceptable.
IRR Rule for financing:
Accept project if IRR < rp.
Reject project if IRR >rp. 25

26. NPV Profiles 26

27. IRR Problems: Multiple IRRs
Consider a firm with the following investment project and a discount rate of rp = 25%.
This project has two IRRs: one above rp and the other below rp. Which should be compared to rp? 27

28. NPV Profile 28

29. IRR Problems: Mutually Exclusive Projects
Consider the following two mutually exclusive projects. The discount rate is rp = 20%.
Despite having a higher IRR, project A is less valuable than project B. 29

30. NPV Profiles 30

31. Payback
Method
Calculate the time for cumulative cash flows to become positive
The shorter the payback the better
Advantages
Does not demand input cost of capital
Don’t need to be able to multiply
Gives a feel for time at risk 31

32. Drawbacks Arbitrary Ranking. The following projects:
all look equally good
Better ways of coping with risk
if worried about eg confiscation, adjust cash flows (makes you think about consequences)
if worried about risk, use higher discount factor
recognise time profile of risks
Not additive, hence combining projects gives different results. 32

33. Payback Example
Consider the following two investment projects. Assume that rp = 20%.
Which project is accepted if the payback period criteria is 2 years? 33

34. Problems with Payback Ignores the Time Value of Money
Ignores Cash Flows Beyond the Payback Period
Ignores the Scale of the Investment
Decision Criteria is Arbitrary 34

35. Profitability Index Profitability Index PI = (I + NPV)/I = 1 + NPV/I
Used when the firm (or division) has a limited amount of capital to invest.
Rank projects based upon their PIs. Invest in the projects with the highest PIs until all capital is exhausted (provided PI > 1). 35

36. Profitability Index Example
Suppose your division has been given a capital budget of $6,000. Which projects do you choose? 36

37. Profitability Index Example
Suppose your budget increases to $7,000.
Choosing projects in decending order of PIs no longer maximizes the aggreagate NPV.
Projects A and C provide the highest aggregate NPV = $3,000 and stay within budget.
Linear programming techniques can be used to solve large capital allocation problems. 37

38. Conclusions NPV has strong attractions:
based on cash flows - so does not depend on accounting conventions
fully reflects time value of money
takes into account riskiness of project
gives clear go/no go answer
Note also that NPV aggregates well:
if A and B both good, then A+B is good
if A good and B bad then A+B is worse than A
if A better than B then A+C better than B+C 38