All About Capital Budgeting

Learning Outcomes

•What is corporate finance?

•The capital budgeting process

•Time value of money concepts

•Project appraisal techniques

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)

•Div idends (Changing Div idend Pol icy, Share repurchases)

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).

Typical Corporate Finance Questions

Incremental Value from Corporate Finance Decisions

Firm Value Created

Investments Financing Dividend

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:

Capital Budgeting - Project Types

Replacement

Projects

Expansion

Projects

New Product Mandatory

Projects

Other

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

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)

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

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

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

Example: Terminal Values

• Leaving cash to earn interest in the bank

D1 = Do x (1+r)n

£133.10 = 100 x (1.10)3

Example: Terminal Values

• Option 1: Receive £50 per annum for three years

Initial Balance Interest Annual

ReturnEnding 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

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.

• 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

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?

Example: Discounting to Present Value

= £133.10 (1.10)3

£100

Discounting:

£133.10 = 100 x (1.10)3Reverse of Compounding:

Leave cash in the bank earning interest:

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

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

Time value of money: Discount Factors

Single Cash Flow Discount Factor: Discount Factor = 1(1+r)n

Annuity Discount Factor = 1r(1− 1

(1+ r)n)Annuity Discount Factor:

Perpetuity Discount Factor = 1r

Perpetuity Discount Factor:

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 = 1r(1− 1

(1+ r)n)

Time value of money: Annuity Discount Factors

Lets review Option 1: You receive £50 per annum for three years.

Annuity Discount Factor = 10.10

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

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

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.

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

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

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

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

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

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

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?

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.

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

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.

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?

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

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?

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 FlowsInitial Investment

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?

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

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

Question

What should a company do when it has lots of profitable investment opportunities but limited capital available?

Decision Making with Limited Capital

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.

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.

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.

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?

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

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

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