Capital Budgeting Techniques

Mona School of Business

Financial Management

Lecturer: Kathya Beckford

Capital Budgeting Techniques

By the end of this session you will

understand:

1. What capital budgeting is

2. How to calculate and interpret a project’s: Payback Period

Discounted Payback Period

Net Present Value (NPV)

Internal Rate of Return (IRR)

Profitability Index (PI)

3. How to choose projects when capital is rationed

What is capital budgeting?

Capital budgeting is the process of planning

expenditure on assets or projects that can have a

long-term impact on an institution.

Examples of capital projects

Adopting a new enterprise-wide software system

Launching a new advertising campaign

Replacing factory equipment

Expanding sales into a new market

Building a road

Why is capital budgeting

important?

Helps firm make smart decisions

Capital projects large and expensive- not easy to

change course

Allows management team to give input and be on

same page

Capital budgeting techniques

include:

Payback Period





Payback Period- The Concept

What is it?

The payback period for a project is the expected

time it will take to recover the original investment.

The decision rule:

Accept project if its payback period is less than the

maximum allowed.

Payback Period- An Example

A project requires a $100,000,000 investment and

is expected to generate the following cash flows in

the years after the investment is made

What is the payback period?

Year Cashflow ($)

1 20,000,000

2 40,000,000

3 60,000,000

4 30,000,000

5 10,000,000

Payback Period- Example cont’d

Workings:

The payback period is somewhere between the end

of year 2 and the end of year 3

Year Cashflow ($) Cumulative

Cashflow

1 20,000,000 20,000,000

2 40,000,000 60,000,000

3 60,000,000 120,000,000

4 30,000,000 150,000,000

5 10,000,000 160,000,000


Use linear interpolation to find the exact figure for payback

period

By using linear interpolation, the assumption is that cashflows

occur evenly throughout the year

We get:

X – 2 = 100,000,000 – 60,000,000

3 – 2 120,000,000 – 60,000,000

X = 2.67 years (This is the payback period)


If projects with a payback period of up to 4 years

are acceptable, should the firm accept this project?

Answer:

Yes, since the payback period is less than 4 years.

Payback Period- The Pros

It is easy to calculate

It is easy to explain

It uses cashflows (not accounting profits)

It gives a measure of the liquidity of a project

Payback Period- The Cons

How to decide maximum allowable payback period?

Very subjective

Time value of money not taken into consideration

Project’s riskiness not accounted for properly

Cashflows beyond the payback period are ignored

No connection to maximizing the firm’s value

Discounted Payback Period-

The Concept

What is it?

The discounted payback period for a project is the

expected time it will take for the discounted cash

flows to recover the original investment.

The decision rule:

Accept project if its discounted payback period is

less than the maximum allowed.


Example




What is the discounted payback period based on

a discount rate of 10%?

Year Cashflow ($)

1 20,000,000

2 40,000,000

3 60,000,000

4 30,000,000

5 10,000,000


Example cont’d

Workings:

The discounted payback period is somewhere

between the end of year 3 and the end of year 4

Year Cashflow ($) PV of

Cashflow ($)

Cumulative PV of

cashflow ($)

1 20,000,000 18,181,818 18,181,818

2 40,000,000 33,057,851 51,239,669

3 60,000,000 45,078,888 96,318,557

4 30,000,000 20,490,404 116,808,961

5 10,000,000 6,209,213 123,018,174


Example cont’d

Use linear interpolation to find the exact figure for the

discounted payback period

By using linear interpolation, the assumption is that the

discounted cashflows occur evenly throughout the year

We get:

Y – 3 = 100,000,000 – 96,318,557

4 – 3 116,808,961 – 96,318,557

Y = 3.18 years (This is the discounted payback period)


Example cont’d

If projects with a discounted payback period of up to

5 years are acceptable, should the firm accept this

project?

Answer:

Yes, since the discounted payback period is less

than 5 years.


The Pros & Cons

The pros and cons are almost the same as with the

basic payback period technique

Only improvement is that cashflows are discounted

However, since cashflows beyond discounted

payback period are ignored, TVM still not handled

adequately

Net Present Value (NPV)-

The Concept

What is it?

The net present value of a project is the sum of the

present values of its expected cash flows.

The decision rule:

Accept project if its NPV > 0.

NPV- An Example




What is the NPV for this project if the discount

rate is 10%?

Year Cashflow ($)

1 20,000,000

2 40,000,000

3 60,000,000

4 30,000,000

5 10,000,000

NPV- Example cont’d

Workings:

The NPV of the project is $23,018,174

Year Cashflow ($) PV of Cashflow ($)

0 -100,000,000 -100,000,000

1 20,000,000 18,181,818

2 40,000,000 33,057,851

3 60,000,000 45,078,888

4 30,000,000 20,490,404

5 10,000,000 6,209,213

Total 23,018,174

NPV- Example cont’d

Should this project be accepted?

Answer:

Yes, since NPV > 0.

NPV Exercise

1. Calculate the NPV of the same project we just

looked at, this time using a discount rate of 20%.

2. Would you still accept this project?

3. Why or why not?

4. Under what circumstances would a discount rate of

20% be more appropriate than a discount rate of

10% for this project?

NPV Exercise Results

1. NPV = -2,346,965

2. We would reject this project

3. Reject since NPV <0

Year Cashflow ($) PV of Cashflow ($)

0 -100,000,000 -100,000,000

1 20,000,000 16,666,666

2 40,000,000 27,777,777

3 60,000,000 34,722,222

4 30,000,000 14,467,592

5 10,000,000 4,018,775

Total -2,346,965

NPV-

The Discount Rate Used:

Has a significant impact on NPV result

Should be the required return on the project

Should be in line with the project’s risk Are the estimated cash flows almost a certainty or very

uncertain?

Will the fixed costs (operating leverage) be high ?

Will the amount of debt used (financial leverage) be high?

NPV-

The Discount Rate Selection Cont’d

Projects with higher risk should use higher discount

rate

Many firms use WACC and adjust up or down to

account for project’s riskiness

Alternatively, project’s beta can be calculated and

used to determine project’s required return via

CAPM

NPV- The Pros

Relatively easy to calculate

Uses cash flows (not accounting profits)

Time value of money handled properly

Project’s riskiness considered appropriately

Shows expected impact on company’s value

Internal Rate of Return (IRR)-

The Concept

A project’s IRR is the discount rate that causes the

NPV of all project cash flows to equal zero.

Set NPV to zero, and solve for r.

IRR- Decision Rule

A typical project has outflows at the beginning

For a typical project:

If IRR > Project’s required return, accept project

The required return is used as a hurdle rate

The required return should be in keeping with the

riskiness of the project

IRR- An Example




What is the IRR of this project?

Year Cashflow ($)

1 20,000,000

2 40,000,000

3 60,000,000

4 30,000,000

5 10,000,000

IRR- Example cont’d

To find IRR we would use:

Trial and error

A financial calculator, or

A spreadsheet

Result is IRR = 18.9%

IRR- Example cont’d

If required return = 10% accept project

(Since IRR > 10%)

If required return = 20%, reject project

(Since IRR < 20%)

Notice that IRR and NPV provide consistent accept/

reject decision here

IRR- Things to be mindful of

Projects with inflows first

Multiple IRRs

No real solution

The reinvestment rate assumption

Ranking projects

IRR- Projects with inflows first

The decision rule changes

Accept if IRR < Project’s required return

Reason: Having Inflows first is equivalent to

borrowing

Lower rate preferred when borrowing

IRR- Multiple IRRs

When cash flows alternate between negative an

positive values

Project can have more than one IRR

Incorrect conclusions can be made

Use NPV to make conclusion

IRR- No Real Solution

Sometimes, no interest rate exists that can make the

PV of cash flows equal zero.

The solution involves imaginary numbers

In these cases, calculator/ spreadsheet shows an

error message

IRR- The Reinvestment Rate

Assumption

Assumption is that interim cash inflows can be

invested at the IRR

If IRR is high, that assumption may not be met

Actual return will be lower than what IRR suggests

Exercise- IRR and Ranking Projects

1. Given the following, which project should be

ranked higher? Why?

2. Why might “Project Renovate” have the higher IRR

but the lower NPV?

Project Name NPV at 15% IRR

Renovate 25,000,000 42%

Totally New 53,000,000 18%

Exercise- Answers

Project “Totally New” should be ranked higher

Why? It has higher NPV

NPV shows value to shareholders

Exercise- Answers cont’d

Project “Renovate” may have higher IRR but lower

NPV due to:

1. Difference in project scale

2. Difference in timing of cash flows

IRR- The Scale Problem

When projects are of different size take care when

using IRR

Determine IRR of incremental project to rank them

Necessary when dealing with mutually exclusive

projects

Unnecessary otherwise (Accept both)

IRR- The Timing Problem

When the cash flow timing of two projects is

significantly different, take care when using IRR

Determine IRR of incremental project to rank them

Necessary when dealing with mutually exclusive

projects

Unnecessary otherwise (Accept both)

IRR- Pros

Results intuitive

Uses cash flows

Takes account of time value of money

Takes account of risk

Connected to impact on firm’s value

IRR- The Cons

Possibility of multiple IRRs

Possibility of no real solution

The reinvestment rate assumption

The scale problem

The timing problem


What is it?

Profitability = _PV of future cash flows__

Index Initial Investment

It shows the value created per dollar invested

PI- Decision Rule

If PI > 1, accept project

PI- An Example




What is the profitability index of this project based

on a discount rate of 10%?

Year Cashflow ($)

1 20,000,000

2 40,000,000

3 60,000,000

4 30,000,000

5 10,000,000

PI- Example cont’d

Workings:

PI = 123,018,174_ = 1.23

100,000,000

Year Cashflow ($) PV of

Cashflow ($)

1 20,000,000 18,181,818

2 40,000,000 33,057,851

3 60,000,000 45,078,888

4 30,000,000 20,490,404

5 10,000,000 6,209,213

Total 123,018,174

PI- Example cont’d

Should this project be accepted?

Answer:

Yes, since PI > 1.

PI- The Scale Problem

PI suffers same scale problem as IRR

Thus, care required when handling mutually

exclusive projects

Determine PI of incremental project to make

decision

Capital Rationing

Capital rationing is the act of putting a limit on

the amount of money that can be spent on new

projects.

Reasons for capital rationing

include:

Inability or unwillingness to issue more debt or

equity

Limited qualified personnel to implement all projects

Discouraging cash flow assumptions that are over-

optimistic

Choosing projects under capital

rationing

Objective: Choose combination of projects that

gives the highest NPV

Profitability Index can be useful in this regard

But take care when using PI due to scale problem

Capital Rationing Example

Which of the following independent projects should

be embarked upon if the capital constraint this year

is $300,000,000?

Project Investment NPV PI

A 70,000,000 59,200,000 1.8

B 80,000,000 52,000,000 1.6

C 100,000,000 59,600,000 1.6

D 150,000,000 38,400,000 1.3

E 200,000,000 71,000,000 1.4

Capital Rationing Example cont’d

Answer:

Projects A, B & C

No other combination that adheres to the capital

constraint gives a higher combined NPV

So, what have we learnt?

1. What capital budgeting is

2. How to calculate and interpret a project’s: Payback Period





3. How to choose projects when capital is rationed

Capital Budgeting Techniques

Documents

project payback period

payback period x

discounted payback period

basic payback period

discounted cashflows

discounted cash flows

end of year

examples of capital