1. CAPITAL BUDGETING TECHNIQUES
CHAPTER 21

2. Capital Budgeting Techniques
PAY-BACK
AVERAGE RATE OF RETURN
DISCOUNTED CASH FLOW

3. PAYBACK FORMULA
INVESTMENT
PAYBACK =
CASH FLOW

4. PAYBACK EXAMPLE Investment = $100,000 Cash Flows: Year 1 $ 5,000

5. SOLUTION TO PAYBACK Unrecovered Investment
Year , ,000
Year , ,000
Year , ,000
Year , ,000
Year , ,000
The payback is:
3 2/3 years

6. PAYBACK EXERCISE INVESTMENT OF $250,000 CASH FLOWS: YEAR 1 $-10,000
CALCULATE THE PAYBACK

7. SOLUTION TO EXERCISE Unrecovered Investment
Year , ,000
Year , ,000
Year , ,000
Year , ,000
Year , ,000
Year , ,000
The payback is:3 years and 11 months

8. PAYBACK
The payback method estimates the length of time it takes to recover the investment
Payback is widely used.
It is simple to understand and apply
HOWEVER
It lacks economic substance, it disregards
The time value of money
Cash flows after the payback period

9. AVERAGE RATE OF RETURN FORMULA
Average Positive Cash Flow
R of R =
Investment

10. RATE OF RETURN EXAMPLE Investment = $100,000 Cash Flows:
Year $ 5,000
Year ,000
Year ,000
Year ,000
Year ,000

11. RATE OF RETURN SOLUTION
Profit
165,000 – 100,000 = $65,000
Average Profit
$65,000 / 5 = $13,000 per year
Average Rate of Return
13,000 / 100,000 = 13%

12. RATE OF RETURN EXERCISE
INVESTMENT OF $250,000
CASH FLOWS:
YEAR $ -10,000
YEAR ,000
YEAR ,000
YEAR ,000
YEAR ,000
YEAR ,000
CALCULATE THE RATE OF RETURN

13. SOLUTION Profit = 340,000 - 250,000 = $ 90,000 Average profit =
340, ,000 = $ 90,000
Average profit =
$90,000 / 6 = $15,000
Rate of Return =
$15,000 / $250,000 = 6%

14. AVERAGE RATE OF RETURN
The average rate of return estimates the average rate of return over the life of the project
It is simple to apply
Considers the cash flow after payback
HOWEVER
Like payback, it ignores the time value of money

15. DISCOUNTED CASH FLOW There are two discounted cash flow techniques
Internal Rate of Return - The economic (real) rate of return on the investment
Net Present Value - The net cash value after charging a capital cost

16. FUTURE AMOUNT OF ONE INVEST $1,000 IN THE BANK AT 10%
YEAR O INVESTMENT IS $1,000
YEAR INVESTMENT IS $1,100
YEAR 2 INVESTMENT IS $1,210
YEAR 3 INVESTMENT IS $1,331

17. FORMULA FOR THE FUTURE AMOUNT OF ONE
AMOUNT = INVESTMENT ( 1 + r ) n
Where r = rate of return
n = number of years (periods)
AMOUNT is the future value
INVESTMENT is the amount put in initially, or
the PRESENT VALUE

18. PRESENT VALUE FORMULA FOR SINGLE AMOUNT
Simple math on the amount formula yields
Present Value = AMOUNT / ( 1 + r ) n

19. APPLY FORMULA Present value = $1,331 / (1.00 + 0.10) 3
= 1,331 / (1.1) 3
= 1,331 / 1.331
= $1,000

20. WHAT TO DO WHEN WE HAVE MANY CASH FLOWS?

21. NET PRESENT VALUE FORMULA
Where:
r = minimum acceptable rate of return and
= cash flow in period n

22. DETERMINING THE INTERNAL RATE OF RETURN
The Internal Rate of Return is that rate which yields a Net Present Value of zero. If cash flows are not uniform, then the solution is found by trial-and-error.

23. PROBLEMS WITH THE INTERNAL RATE OF RETURN
There are two majors problems with the Internal Rate of Return method:
Mathematically, there can be more than one internal rate of return, one for each change in direction of cash flow and
The important thing is not the rate of return but the amount of money earned.

24. NPV EXAMPLE Investment = $100,000 Cash Flows: Year 1 $ 5,000
Discount Rate of 9%

25. SOLUTION TO NPV EXAMPLE
Cash Flows PV factor PV
Investment = $-100, $ -100,000
Year , ,585
Year , ,840
Year , ,020
Year , ,480
Year , ,205
Net Present Value $ 20,130

26. NPV EXERCISE CALCULATE THE NET PRESENT VALUE WITH A 10% DISCOUNT RATE
INVESTMENT OF $250,000
CASH FLOWS:
YEAR $ -10,000
YEAR ,000
YEAR ,000
YEAR ,000
YEAR ,000
YEAR ,000
CALCULATE THE NET PRESENT VALUE WITH A 10% DISCOUNT RATE

27. SOLUTION TO NPV EXERCISE
Cash Flows PV factor PV
Investment $ -250, ,000
YEAR , ,090
YEAR , ,560
YEAR , ,590
YEAR , ,960
YEAR , ,100
YEAR , ,280
NET PRESENT VALUE ,160

28. NET PRESENT VALUE
The Net Present Value method resolves all of the problems inherent in the other methods.
It considers all flows,
It considers the time value of money,
There is a unique solution, and
It solves for profit in excess of capital costs

29. APPLICATION OF NPV
Often the NPV method is applied without regard to the relative risk of the cash flows.
Only one discount rate is applied to all cash flow estimates.
This approach should, inadvertently, lead to higher risk opportunities.

30. ADJUSTING FOR RISK There are two methods used to adjust for risk:
Adjust the cash flow or
Adjust the discount rate.
The cash flow can be adjusted to the Certainty Equivalent (CE) cash flow.
The Discount Rate can be adjusted directly. Conventionally, there is a direct relationship between the discount rate and risk.

31. Estimating the Certainty Equivalent
Estimate the Cash Flow in a period:
e.g., $ 1,000,000 in year 3
Evaluate the risk of that cash flow
Estimate the amount you would be willing to receive, with certainty, instead of the $1,000,000
e.g., $ 850,000
Discount these CEs at the risk-free rate of return

32. ADJUSTING THE DISCOUNT RATE
Estimate the cash flow in a period:
e.g., $1,000,000 in year 3
Determine the minimum rate of return that would be acceptable for the particular cash flow.

33. RELATIONSHIP OF RISK TO DISCOUNT RATE

34. RELATIONSHIP OF DISCOUNT RATE TO NET PRESENT VALUE
NPV

35. CONFLICT OF NEGATIVE CASH FLOWS
If cash flows are negative, investors should prefer lower net present values.
Lower net present values result from higher discount rates.
THEREFORE

36. THERE SHOULD BE AN INVERSE RELATIONSHIP OF RATE OF RETURN TO RISK.
THAT IS, THE GREATER THE RISK, THE LOWER THE DISCOUNT RATE.

37. GRAPHICALLY
Discount Rate
RISK

39. PROPOSED SOLUTION
Group cash flows according to the activities that drive the cash flows.
If the net cash flow is positive, discount in the conventional method, i.e., the greater the risk, the greater the discount rate.
If the net cash flow is negative, adjust the discount rate inversely to risk.

40. WHAT METHODS ARE GENERALLY USED?
Studies indicate that the payback method is widely used, probably the most used.
Net present value, without adjusting for risk, is the second most common method.
Many companies use a combination of these two methods.
However, I suspect that the MOST commonly used method is:

41. I WANT IT

42. IMPACT OF TAXES
ONE OF THE NICE ASPECTS OF CAPITAL BUDGETING IS THAT YOU ARE CONCERNED ONLY WITH CASH FLOW.
TAXES ARE A CASH OUT-FLOW, SO,
REDUCE THE CASH FLOW FOR THE TAX EFFECTS

43. DEPRECIATION DEPRECIATION IS A TAX DEDUCTION, THUS
IT MAY BE A REDUCTION OF CASH OUTFLOW.
FOR ANALYTICAL PURPOSES, THE TAX EFFECT OF DEPRECIATION CAN BE TREATED AS A CASH INFLOW, BUT
YOU SHOULD KNOW THAT IT IS NOT A CASH INFLOW.

44. EXAMPLE NET CASH FLOW FROM OPERATIONS, DISREGARDING TAXES, WAS:
YEAR 1 $13,000
YEAR 2 $20,000
YEAR 3 $30,000
YEAR 4 $20,000
YEAR 5 $13,000
ASSET COST $60,000 WITH A 5 YEAR LIFE.
USE STRAIGHT-LINE DEPRECIATION
TAX RATE IS 40%

45. NET CASH FLOWS OPER CF DEPR TI TAX NET CF 13,000 12,000 1,000 400
12,600
20,000
8,000
3,200
16,800
30,000
18,000
7,200
22,800