capital budgeting - payback period tutorial · payback period • payback period in capital...

Capital BudgetingGavin Crosthwaite

Mindarie Senior College

Capital Budgeting

• Capital budgeting is difficult because it

involves estimates in cash flows over

time and the time value of money

should be incorporated into the

decision.

• Sometimes, it is also difficult to know

how long a particular asset will last.

Payback Period

• Payback period in capital budgeting

refers to the period of time required for

the return on an investment to "repay"

the sum of the original investment.

Payback Period

• It is considered to be one of the weaker

capital budgeting techniques due to its

limitations.

• It is, however, still widely used in

business today due to its ease of use.

Advantages of Payback

• It is easy to understand

• It provides some assessment of risk

Disadvantages of Payback

• It ignores cash flows after the payback

period and does not measure

profitability.

• It ignores the time value of money

because cash flows are not discounted.

(this is done in NPV)

Summary

• In summary, the payback period provides

information to managers that can be used as

follows:

• Help control the risks associated with the

uncertainty of future cash flows

• Help minimise the impact of an investment

on a firm’s liquidity problems

• Help control the risk of obsolescence

Payback Equation

Payback Period = Initial Investment

Payback Period = Net Cash Inflow

Options

• There are 2 different examples we will

look at using the payback period. One

involves having the same cash inflows

each period while the other one

involves different cash inflows each

period.

Example 1

• Project X costs $21 000 and will return a

net cash inflow of $5 000 per period.

What will the payback period be for

this project?

Example 1 Solution



Payback Period = $21 000

Payback Period = $5 000

Payback Period = 4.2

We keep the 4 years and now times the .2 by 12 for the number of months in a year.

This will give us 2.4 months which we can then round up to 3 as that will be the minimum amount of time

Example 2• Project Y has an initial investment of

$21 000 and will offer the following net

cash inflows over the next 5 years.

YEAR NET CASH INFLOW CUMULATIVE TOTAL

1 3 000 3 000

2 5 000 8 000

3 7 000 15 000

4 4 000 19 000

5 9 000 28 000

Example 2 Solution

YEARNET CASH

INFLOWCUMULATIVE TOTAL

1 3 000 3 000

2 5 000 8 000

3 7 000 15 000

4 4 000 19 000

5 9 000 28 000



$21 000

Example Solution 2• Therefore, we know that it will take at

least 4 years to pay the project back as

the cumulative net cash inflow up to

year 4 is $19 000.

• That leaves us to calculate how many

months it will take to get the extra

$2 000 from the $9 000 in Year 5.

9,000/12 = $750 per month. Thus it will take 3 months to reach $2 000. ie: $750 x 3 = 2 250

Example 1 and 2

• So we can see from these examples that

both projects would take the same

amount of time so how would we

choose which one to invest in?

Payback Student Example• Millipore Mechanics have decided that they need to

replace some of the machinery in their workshop. The

new assets will cost $80,000 and is depreciated at 20%

pa on cost using the straight line method.

• The estimated cash inflows over the next few years is

listed here: Year 1 15,000

2 16,000

3 10,000

4 11,000

5 16,000

6 16,000

7 19,000

8 21,000

Student Solution Payback Period =

Initial Investment Payback Period =

Net Cash Inflow

Year 1 15,000

2 16,000

3 10,000

4 11,000

5 16,000

6 16,000

7 19,000

8 21,000

$68,000

Student Solution• Therefore, we know that it will take at

least 5 years to pay the project back as

the cumulative net cash inflow up to

year 5 is $68 000.

• That leaves us to calculate how many

months it will take to get the extra

$12 000 from the $ 16 000 in Year 6.

16,000/12 = $1,333 per month. Thus it will take 9 months to reach $12 000. ie: $1,333 x 9 = $12 200

Thus it will take 5 years and 9 months

Payback + Cost Savings

• There are times when a business will

look at implementing some new

machinery in order to save costs and

they have to decide whether it’s

worthwhile investing in it.

• There normally is a time period

associated with these types of

investment.

Example 1

• Spacely Sprockets is looking to get a new piece

of machinery that will replace 5 workers who

currently do the packing manually on the

conveyer belt. The workers are each paid

$40,000 a year and the new machinery costs

$850,000.

• Spacely Sprockets has a rule that says the

payback period must be 5 years of less.

Example 1 Solution Payback Period =


Annual Net Cost Saving

Payback Period = $850,000


The payback period will be 4.25 years and thus would be accepted as it fits within the 5 year pattern.

Payback + Cost Savings + Different Inflows

• There are times when a business will

look at implementing some new

machinery in order to save costs but

will also have an impact on their overall

cashflows as well.

• There normally is a time period

associated with these types of

investment.

Example 1• Spacely Sprockets is looking to get a new piece

of machinery that will replace 5 workers who

currently do the packing manually on the

conveyer belt. The workers are each paid

$40,000 a year and the new machinery costs

$850,000. The business will have to pay

additional insurance costs of $20,000 per year

and repair and maintenance costs of $30,000.

• Spacely Sprockets has a rule that says the

payback period must be 5 years of less.

Example 1 Solution Payback Period =





The payback period will be 5.66 years & thus would NOT be accepted as it fits within the 5 year criteria.

Savings = 200,000 - 30,000 - 20,000 = $150,000

Payback Cost Saving Student Example

• Gledhow Industries are deciding whether to replace their manual packing system with a more automated approach. The cost of the automated system will set back the company $90,000.

• The business state the payback period must be less than 5 years to be accepted. The business will have the following additional costs and savings with the introduction of the new system.

Savings Per Year Costs Per Year

Wages 30,000 Electricity 4,000

Packing Materials 4,000 Repairs 2,000

Insurance 1,500

Parts 1,500

Student Solution Payback Period =





The payback period will be 3.6 years & thus WOULD be accepted as it fits within the 5 year criteria.

Savings = 30,000 + 4,000 - 4,000 - 2,000 - 1,500 - 1,500 = $25,000

Return on Average Investment

• This method is no longer popular for

assessing capital budgeting decisions

but is still important that you

understand it.

Advantages

• It is easy to understand

• Most people including managers are

familiar with the concepts of income,

book value, profit, residual value and

rate of return.

Disadvantages

• It ignores the time value of money

• It uses accounting measures of income

rather than cash flows. Income can be

easily manipulated by managers while

cash flow can’t.

Formula

Return on Average Investment = Average Profit after Tax

Return on Average Investment = Average Investment

Average Investment = Initial Investment + Residual Value

Average Investment = 2

Example 1



Average Investment = Initial Investment + Residual Value

Average Investment = 2

An investment proposal is being looked at by Business P. It has an initial investment of $500,000 and residual value of

$40,000 and should generate the following profits after tax:

Year 1 Year 2 Year 3

Profit after Tax $72 000 $60 000 $80 000

Example 1 Solution






Profit after Tax $72 000 $64 000 $80 000

Step 1: Average Profit 72,000 + 64,000 + 80,000 /3 $72 000

Example 1 Solution






Profit after Tax $72 000 $64 000 $80 000

Step 2: Average Investment 500,000 + 40,000 /2 $270 000

Example 1 Solution



Step 2: Average Investment 500,000 + 40,000 /2 $270 000

Step 1: Average Profit 72,000 + 64,000 + 80,000 /3 $72 000

Return on Average Investment = 72,000


Return on Average Investment = 26.67%

Things to be wary of

• When doing these questions, make sure

that you look carefully at the question,

particularly in terms of the following

items:

• Depreciation on Asset

• Prepaid and Accrued Items

Return on Investment Student example

• Forest Hill Couriers are looking to buy a new vehicle to

expand their business into the Albany area. The new

vehicle will cost $35,000 and have a residual value of

$9,000. They want a return of 15% to go ahead with it.

• By expanding the business into Albany they expect to have

the following estimates for income and expenses per year:

Income Expenses

Courier Fees 60,000 Petrol 15,000

Wages 30,000

Advertising 5,000

Return on Investment Student SolutionIncome

Courier Fees 60,000

Less Expenses

Petrol 15,000

Wages 30,000

Advertising 5,000

Profit $10,000



Return on Average Investment = 45 %

Therefore, we should progress with the investment.

Net Present Value

• This involves the discounting of the cash

flows for a project to a present value

using the minimum desired rate of

return as the discount rate.

• The decision criteria is to accept all

projects with a positive NPV except for

mutually exclusive ones where we

would choose the one with the highest

NPV.

Advantages

• It recognises the time value of money

• Dollars can be added because they are in

present values

• It gives correct ranking of mutually

exclusive projects

• It is dependant on future cash flows and

the opportunity cost of capital rather than

some arbitrary guess by management.

Disadvantages

• How do we determine the minimum

desired rate of return?

• How accurate are future cash forecasts

Formula

Present Value = Future Value

Present Value = (1 + i)n

where:

i = Interest rate per periodn = Number of periods

Example 1- Different inflows

• Dog Rock Industries have been handed a

proposal where they would invest in a new

piece of machinery. The piece of machinery is

going to cost $70 000 and have the following

net cash inflows over the 5 years of the assets

life and cost of capital is 10%:

Net Cash Inflow Yr 1 Yr 2 Yr 3 Yr 4 Yr 5

10,000 12,000 13,000 11,000 15,000

Example 1 Solution



10,000

(1.10)1

12,000

(1.10)2

13,000

(1.10)3

11,000

(1.10)4

15,000

(1.10)5+ +++

9090.90 9917.35 9767.09 7513.14 9313.81+ +++

Example 2

• There are times when we are doing the

Capital Budgeting NPV technique

where the net cash inflow will be the

same for each period. This allows us to

do the calculation much easier.

• Let’s look at an example of how this

works.

Different Inflows Student Example

• Walpole Investments have 3 projects presented

to them and they are not sure which one to

choose. Given the cost of capital is 10% which of

the following 3 projects would you recommend

and why?

Project Cost Year 1 Year 2 Year 3 Year 4

A 10,000 1,000 1,300 1,500 2,000

B 25,000 2,500 4,000 6,000 8,000

C 50,000 12,000 15,000 18,000 32,000

Different Inflows Student SolutionProject Cost Year 1 0.9091 Year 2 0.8264 Year 3 0.7513 Year 4 0.6830 Total

A 10,000 1,000 909.1 1,300 1074.38 1,500 1126.97 2,000 1366.02 4476.47

B 25,000 2,500 2272.72 4,000 3305.78 6,000 4507.88 8,000 5464.10 15550.5

C 50,000 12,000 10909.1 15,000 12396.7 18,000 13523.7 32,000 21856.4 58685.9

Total

The business should accept proposal C as it its the only one which has a positive NPV.

Project Future Value Initial Investment NPV

A 4 476.47 10 000 -$5 523.53

B 15 550.5 25 000 -$9 449.5

C 58 685.9 50 000 $8 685.9

Example 2 - Same inflows

• Walpole Manufacturers have been handed a

proposal where they would invest in a new

piece of machinery. The piece of machinery is

going to cost $50 000 and have the following

net cash inflows over the 5 years of the assets

life and cost of capital is 10%:


8,000 8,000 8,000 8,000 8,000

Example 2 - Solution

In this case the present value will be calculatedas follows:

PV = 8,000 x 3.7907 = $30,325.60

If we take this off the initial value of $50,000 it leaves us a negative value of $19,674.40. Therefore, we should reject this proposal.

Same Inflows Student Example

• Emu Point Sports Store is looking at 2 different sites in expand its business. Proposal A will cost $60,000 while Proposal B will cost $75,000. The business is expected to have the following net cash inflows over the next 5 years and the cost of capital will be 10%. Which one would you recommend?

Year 1 Year 2 Year 3 Year 4 Year 5

Proposal A 18,000 18,000 18,000 18,000 18,000

Proposal B 21,000 21,000 21,000 21,000 21,000

Same Inflows Student Solution

Year 1 Year 2 Year 3 Year 4 Year 5

Proposal A 18,000 18,000 18,000 18,000 18,000

Proposal B 21,000 21,000 21,000 21,000 21,000

Proposal A 18,000 * 3.7907 $68232.60 60,000 $8,232.6

Proposal B 21,000 * 3.7907 $79604.70 75,000 $4604.70

Example 3 - Same & Different inflows

• There are also scenarios that will show

inflows the same for a number of

periods and different for other periods.

• Depending on when the same period is

will determine how we will approach

the solution and which

recommendation we would make to the

business.

Example 3 - Same first• Denmark Timbers have been given the

opportunity to expand their business by investing in a new business opportunity. The cost to invest in the new business will be $35,000 and the business wants a minimum return of 8%.

• The business expects the following returns over the next 5 years.


8,000 8,000 8,000 11,000 15,000

Example 3 SolutionIn this case the present value will be calculatedas follows:

PV = 8,000 x 2.5770 = $20, 616

This will cover the first 3 years. For the next 2 years, we need to use table to calculate each year

individually.

Year 4 PV = 11,000 x .7351 = $8,086.10

Year 4 PV = 15,000 x .6806 = $10,209

Total = 20,616 + 8,086.10 + 10,209 = $38,911.10

Example 3 Solution cont.

• In this scenario, we can see that the

business would have a positive net value

by $38,911.10 - $35,000 = $3,911.10.

• Therefore, we would recommend that

Denmark Timbers invest in the new

business.

Situation 4 - Different First• Denmark Timbers have been given the

opportunity to expand their business by investing in a new business opportunity. The cost to invest in the new business will be $35,000 and the business wants a minimum return of 8%.

• The business expects the following returns over the next 5 years.


11,000 15,000 8,000 8,000 8,000

Different 4 Solution



11,000

(1.08)1

15,000

(1.08)2

8,000

(1.08)3

8,000

(1.08)4

8,000

(1.08)5+ +++

10,185.18 12,860.08 6,350.65 5,464.1 4,967.37


A 39827.38 35,000 $4,827.38

Same and Different Student Examples

• Little Grove Traders have the opportunity to

invest in a new property development down at

Goode Beach. The property development will

cost $250,000 and is expected to have the

following net cash inflows over the 10 years

with a cost of capital of 8%.Year Return Year Return

1 0 6 40,000

2 0 7 40,000

3 0 8 50,000

4 21,000 9 50,000

5 30,000 10 50,000

Same and Different Student SolutionYear Return Year Return

1 0 6 40,000

2 0 7 40,000

3 0 8 50,000

4 21,000 9 50,000

5 30,000 10 50,000

21,000

(1.08)4

30,000

(1.08)5++

40,000

(1.08)6

40,000

(1.08)7

50,000

(1.08)8

50,000

(1.08)9

50,000

(1.08)10+ +++

0

0 0 0 15,435.62 20,417.49

25,206.78 23,339.61 27,013.44 25,012.45 23159.67


A 159,585.06 250,000 -90414.94

capital budgeting - payback period tutorial · payback period • payback period in capital...

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