Lets run through the principles of capital budgeting, making sound financial decisions to allocate resources and finances effectively. Capital budgeting is widely used in corporate finance, project appraisal and many other applications. We cover the important concepts of net present values (NPV) and internal rates of return (IRR).

1. All About
Capital Budgeting

2. Learning Outcomes
•What is corporate finance?
•The capital budgeting process
•Time value of money concepts
•Project appraisal techniques

3. Corporate Finance Fundamentals
•Any decision that affects the finances of a business is a
corporate finance decision.
•Corporate finance is focused on maximising the value of a
business for its shareholders through three decisions:
•Investments (eg. Mergers, Acquisitions, Joint Ventures,
Divestments)
•Financing (Raising Capital, Changing Capital Structure)
•Dividends (Changing Dividend Policy, Share
repurchases)

4. Corporate Finance Fundamentals
Corporate finance decisions are made to maximise a
company’s valuation.
What is the connection between these corporate finance
decisions and business valuation?
The value of a firm is the present value of its expected cash
flows (investment decision), discounted back at a rate that
reflects its risk and its financing structure (financing
decision).

5. Typical Corporate Finance Questions

6. Incremental Value from Corporate Finance Decisions
Firm Value
Created
Investments Financing Dividend

7. Capital Budgeting Principles
Capital Budgeting is the process of selecting and
analysing value-adding projects for a company.
The role of a financial analyst is to source, analyse and
evaluate projects using capital budgeting techniques.
Project examples include:

8. Capital Budgeting - Project Types
Replacement
Projects
Expansion
Projects
New Product
Mandatory
Projects
Other

9. Capital Budgeting Techniques
We are going to review five different capital budgeting techniques:
1. Net Present Value (NPV)
2. Internal Rate of Return (IRR)
3. Payback Period
4. Discounted Payback Period
5. Profitability Index

10. Time value of money: Simple Interest
•With simple interest, the interest generated in each subsequent year
will be exactly the same because it is based on the original capital
invested.
Example:
£100 deposit @ 10% interest
£100 deposit @ 10% interest over 5 years
Simple Interest = Do x r
Total Interest over n periods = n x (Do x r)

11. Time value of money: Compound Interest
Interest is described as compound interest if in each year, interest is
earned on the value of the deposit at the beginning of each year.
D1 = Do x (1+r)n
Example:
• £100 is deposited into an account paying 10% each year.
• How much interest will be earned at the end of (i) the first year, (ii)
third year

12. Time value of money: Terminal Values
• Using the concept of compound interest we can calculate terminal
values
• A terminal value is the value of a deposit at the end of a period
having received interest over that period.
D1 = Do x (1+r)n

13. Example: Terminal Values
• Lets say you have £100 to invest for 3 years and you have been
offered two options. The bank pays 10% interest per annum.
• Option 1: You can receive £50 per annum for three years
• Option 2: You will receive £140 at the end of the third year
D1 = Do x (1+r)n

14. Example: Terminal Values
• Leaving cash to earn interest in the bank
D1 = Do x (1+r)n
£133.10 = 100 x (1.10)3

15. Example: Terminal Values
• Option 1: Receive £50 per annum for three years
Initial
Balance
Interest
Annual
Return
Ending
Balance
Year 1 50 50
Year 2 50 5 50 105
Year 3 105 10.5 50 165.5
• Option 2: Receive £140 at the end of the third year

16. Example: Terminal Values
Which investment option should we choose?
The Bank: £133.10
Option 1: £165.50
Option 2: £140.00
To evaluate investment options we have to consider the
size and timing of cash flows.

17. • We have looked at compounding up deposits for interest generated
to their terminal value: Dn = Do x (1+r)n
• The reverse of this is discounting. ie. Determining these future cash
values in today’s terms using discount factors - present values.
Time value of money: The Concept of Discounting
Dn x 1 / (1+r)n = Do
Discount Factor

18. Example: Discounting to Present Value
Using our previous example, we had £133.10 as a terminal
value from investing £100 @ 10% interest for 3 years.
Discounting answers the question:
How much would we need to invest now to receive
£133.10 in three years?

19. Example: Discounting to Present Value
= £133.10
(1.10)3
£100
Discounting:
£133.10 = 100 x (1.10)3
Reverse of Compounding:
Leave cash in the bank earning interest:

20. Example: Discounting to Present Value
Option 1:
Time Deposit Discount Factor Present Value
Year 1 50.00 0.91 45.45
Year 2 50.00 0.83 41.32
Year 3 50.00 0.75 37.57
Present Value 124.34
Receive £124.34 today or earn £50 each year for three years

21. Example: Discounting to Present Value
Option 2:
Receive £105.18 today or earn £140 at the end of three
years, its the same
= £140
(1.10)3£105.18

22. Time value of money: Discount Factors
Single Cash Flow Discount Factor: Discount Factor =
1
(1+r)n
Annuity Discount Factor =
1
r
(1−
1
(1+r)n
)Annuity Discount Factor:
Perpetuity Discount Factor =
1
r
Perpetuity Discount Factor:

23. Time value of money: Annuity Discount Factors
When we have a fixed stream of payments over a period
of time, we can use this formula to calculate its present
value of an annuity:
Annuity Discount Factor =
1
r
(1−
1
(1+r)n
)

24. Time value of money: Annuity Discount Factors
Lets review Option 1: You receive £50 per annum for
three years.
Annuity Discount Factor =
1
0.10
x (1−
1
(1.10)3
)
= 2.487
ADF x Annual Cash Flow = 2.487 x £50 = £124.34
The present value of receiving £50 per annum for three
years is £124.34

25. Time value of money: Perpetuity Discount Factors
If we knew we were going to receive £100 each year
forever and had a 10% required rate of return - how would
we value this stream of payments?
To receive exactly £100 each year, we would need to
invest £1,000
£100 x Perpetuity Discount Factor = £1,000
Perpetuity Discount Factor = 1 / 0.10
= 1 / r

26. Time value of money: Net Present Value Profile
Here is the NPV of a project at various costs of capital
Cost of Capital (%)
NPV
• The higher the cost of capital / rate of
return, the lower the NPV of a project.

27. Time value of money: Present Values
Present values calculate how much cash we would need to have
invested now to generate a target level of funds at a future date.
It is dependent on:
• The size of each cash flow
• The timing of the cash flow
•Net present value simply deducts the initial outlay from the present
value of cash flows to arrive at an accept/reject decision for a project:
• NPV>0 = ACCEPT
• NPV<0 = REJECT

28. Fundamentals of Capital Budgeting
•Decisions are based on cash flows
•The timing of cash flows is crucial
•Cash flows are incremental
•Cash flows are on an after-tax basis
•Financing costs are ignored

29. Fundamentals of Capital Budgeting
Current Dec 2014 Dec 2015 Dec 2016 Dec 2017
Initial Outlay -100,000
Cash Flows +100,000 +100,000 +100,000 +100,000
Opportunity Cost -5,000
After-Tax CF
(@20%)
-105,000 +80,000 +80,000 +80,000 +80,000
Opportunity Costs
Cash Flow Timing
After-tax Cash Flow
Financing Cost
Incremental Cash Flows

30. Internal Rate of Return
The internal rate of return is the rate of return on a project.
If IRR > r (required rate of return)
• Accept Project: Investment is value adding
If IRR < r (required rate of return)
• Reject Project: Investment is not value adding

31. Internal Rate of Return
The IRR formula gives the rate of return when NPV=0
0 =
CF1
(1+IRR)
+
CF2
(1+IRR)2
+
CF3
(1+IRR)3

32. Internal Rate of Return (IRR)
•Internal Rate of Return (IRR) is the rate of interest that discounts the
investment flows to a net present value of zero.
•Inverse relationship between NPV and required rate of return.
•Use trial and error to estimate IRR:
If NPV>0, increase rate of return to reduce NPV
If NPV<0, decrease rate of return to increase NPV

33. Example Calculation: Internal Rate of Return
A sandwich shop wants to purchase a new industrial grill which costs
£1,000 and will generate cash flows over the next four years of:
Year 1: £300, Year 2: £400, Year 3: £500, Year 4: £500
Assuming a 20% required rate of return, what is the internal rate of return?

34. NPV vs IRR
•The NPV and IRR methods may rank projects differently.
•The source of the problem is different reinvestment rate
assumptions:
• NPV assumes reinvesting cash flows at the required
rate of return.
• Internal rate of return reinvests cash flows at the
internal rate of return.

35. Net Present Value Profile
Here is the NPV of a project at various costs of capital
Rate of Return
NPV • When NPV = O, this is the Internal Rate of Return
• When NPV > 0, the rate is too low. IRR is higher
• When NPV <0, the rate is too high. IRR is lower

36. Payback Period
The payback period is the length of time it takes to
recover the initial cash outlay of a project from future
incremental cash flows.

37. Example Calculation: Payback Period
A sandwich shop wants to purchase a new industrial grill which costs
£1,000 and will generate cash flows over the next four years of:
Year 1: £300, Year 2: £400, Year 3: £500, Year 4: £500
Assuming a 20% required rate of return, what is the payback period?

38. Discounted Payback Period
The discounted payback period is the length of time it takes for the
cumulative discounted cash flows to equal the initial outlay.
In other words, it is the length of time for the project’s cash flows to
reach NPV = 0

39. Example Calculation: Discounted Payback Period
A sandwich shop wants to purchase a new industrial grill which costs
£1,000 and will generate cash flows over the next four years of:
Year 1: £300, Year 2: £400, Year 3: £500, Year 4: £500
Assuming a 20% required rate of return, what is the discounted
payback period?

40. Profitability Index
•The profitability index is the ratio of the present value of future cash
flows to the initial outlay.
Profitability Index =
Present Value of Future Cash Flows
Initial Investment

41. Example Calculation: Profitability Index
A sandwich shop wants to purchase a new industrial grill which costs
£1,000 and will generate cash flows over the next four years of:
Year 1: £300, Year 2: £400, Year 3: £500, Year 4: £500
Assuming a 20% required rate of return, what is the profitability index?

42. Applications of Present Values
•The market value of a security at a point in time is determined by:
• The returns from (interest / dividend / capital growth)
• The rate of return investors require
Market Value = Present value of the future expected receipts
discounted at the investor’s required rate of return

43. Bond Valuation Using Present Values
•A bond pays an annual coupon of £9 and is to be redeemed at £100 in
three years.
•The required rate of return on the bond is 8%. What is the market value of
this bond?
Time Cash Flow Discount Factor Present Value
1 9 1/(1.08) 8.33
2 9 1/(1.08)^2 7.72
3 109 1/(1.08)^3 86.53
Market Value 102.58

44. Question
What should a company do when it has lots of profitable
investment opportunities but limited capital available?
Decision Making with Limited Capital

45. Decision Making with Capital Rationing
•In corporate finance, the objective is to maximise value
to shareholders.
•The key to decision making under capital rationing is to
select those projects that maximise the total net present
value given the limits on the capital budget.
•We must select the most value-adding projects within our
budget.
•This may result in rejecting other value-adding projects.

46. Limitations of Capital Budgeting Techniques
NPV
Specific measure of value creation. Not benchmarked against the size of a
project.
IRR
Show return on a investment. Can conflict with NPV results, create multiple
IRRs.
Payback Period
Doesn’t take into account time value of money. Doesn’t consider terminal
value.
Discounted Payback Period
Addresses time value of money but doesn’t consider terminal value.

47. Recap
•Capital budgeting is used by most large companies to select among
available long-term investments.
•The process involves generating ideas, analysing proposed projects,
planning the budget and monitoring and evaluating the results.
•Projects may be of many different types (eg. replacement, new product)
but the principles of analysis are the same.
•The preferred capital budgeting methods are the net present value,
internal rate of return and the profitability index.

48. Example: NPV
Year Project Alpha Project Beta
0 -1000 -5000
1 500 2000
2 600 3000
3 300 4000
Assuming a 20% cost of capital,
what is the Net Present Value for
each project?

49. Example: NPV
Year Project Alpha
0 -1000
1 500
2 600
3 300
NPV = −1,000+
500
(1.20)1
+
600
(1.20)2
+
300
(1.20)3
= 6.94

50. Example: NPV
= 1,064.81
Year Project Beta
0 -5000
1 2000
2 3000
3 4000
NPV = −5,000+
2,000
(1.20)1
+
3,000
(1.20)2
+
4,000
(1.20)3

51. Example: Payback Period
Year Project Beta Cummulated Cash Flows
0 -5000 -5000
1 2000 -3000
2 3000 0
3 4000 +4000
The payback period in this example is 2.0 years