Capital budgeting

1
Capital budgeting

• It is a decision involving selection of capital
  expenditure proposals.
• The life of the project is atleast one year and
  usually much longer.
• Examples include decision to purchase new plant
  and equipment
• Introduce new product in the market
• Essentially it must be determined whether the
  future benefits are sufficiently large enough to
  justify the current outlays.

2
Capital budgeting

• A capital budgeting decision is one that involves
  the allocation of funds to projects that will
  have a life of atleast one year and usually much
  longer.
• Examples would include the development of a major
  new product, a plant site location, or an
  equipment replacement decision.
• Capital budgeting decision must be approached
  with great care because of the following reasons
• Long time period consequences of capital
  expenditure extends into the future and will have
  to be endured for a longer period whether the
  decision is good or bad.

3

• Substantial expenditure it involves large sums
  of money and necessitates a careful planning and
  evaluation.
• Irreversibility the decisions are quite often
  irreversible, because there is little or no
  second hand market for may types of capital
  goods.
• Over and under capacity an erroneous forecast of
  asset requirements can result in serious
  consequences. First the equipment must be modern
  and secondly it has to be of adequate capacity.

4
Difficulties

• There are three basic reasons why capital
  expenditure decisions pose difficulties for the
  decision maker. These are
• Uncertainty the future business success is
  todays investment decision. The future in the
  real world is never known with certainty.
• Difficult to measure in quantitative terms Even
  if benefits are certain, some might be difficult
  to measure in quantitative terms.
• Time Element the problem of phasing properly the
  availability of capital assets in order to have
  them come on stream at the correct time.

5
Decision process
INVESTMENT OPPORTUNITIES
PROPOSALS
PLANNING PHASE
REJECTED OPPORTUNITIES
Improvement in planning Evaluation procedure
Improvement in planning Evaluation procedure
PROPOSALS
NEW INVESTMENT OPPORTUNITIES
EVALUATION PHASE
Rejected Proposals
PROJECTS
SELECTION PHASE
Rejected projects
ACCEPTED PROJECTS
IMPLEMENTATION PHASE
ONLINE PROJECTS
CONTROL PHASE
PROJECT TERMINATION
AUDITING PHASE
6
Methods of classifying investments

• Independent
• Dependent
• Mutually exclusive
• Economically independent and statistically
  dependent

independent
Mutual Exclusive
Prerequisite
Weak complement
Strong substitute
Weak substitute
Strong complement
7
Profit (Service) Maintaining and profit (service)
adding investment

• Investment may fall into two basic categories,
  profit-maintaining and profit-adding when viewed
  from the perspective of a business, or service
  maintaining and service-adding when viewed from
  the perspective of a government or agency.

8
Option for replacement decision
How long? What problems? Can we go on?
Are there better opportunities? Is the product
life coming to an end?
Do nothing
Go out of business
Replace with same
What if volume increases? How secure are the
markets?
Replace larger or smaller
Replace different process
Should a margin of capacity Be provided?
Present point Of decision
Can we profit from new technology? What risks are
there?
Etc.
Etc.
9
Expansion and new product investment

• Expansion of current production to meet increased
  demand
• Expansion of production into fields closely
  related to current operation horizontal
  integration and vertical integration.
• Expansion of production into new fields not
  associated with the current operations.
• Research and development of new products.

10
Reasons for using cash flows

• Economic value of a proposed investment can be
  ascertained by use of cash flows.
• Use of cash flows avoids accounting ambiguities
• Cash flows approach takes into account the time
  value of money

11
Incremental cash flows

• For any investment project generating either
  expanded revenues or cost savings for the firm,
  the appropriate cash flows used in evaluating the
  project must be incremental cash flow.
• The computation of incremental cash flow should
  follow the with and without principle rather
  than the before and after principle

12
Investment decision
Cash
Investment Opportunity (real asset)
Investment Opportunities (financial assets)
shareholder
Firm
Alternative Pay dividend To shareholders
Shareholders Invest for themselves
invest
13
Different methods of measurement

• Payback
• Average return on book value
• Net present value
• Internal rate of return
• Profitability index

14
NPV

• NPV rule recognizes that a dollar today is worth
  more than a dollar tomorrow, because the dollar
  today can be invested to start earning interest
  immediately.
• Any investment rule which does not recognize the
  time value of money cannot be sensible
• NPV depends solely on the forecasted cash flows
  from the project and the opportunity cost of
  capital
• Because the present values are all measured in
  todays dollars, you can add them up.

15

• If you have two projects A and B, the net present
  value of the combined investment is
• NPV(AB) NPV(A) NPV(B)
• This additive property has important
  implications. Suppose project B has a negative
  NPV. If you tack it onto project A, the joint
  project (AB) will have a lower NPV than A on its
  own. Therefore, you are unlikely to be misled
  into accepting a poor project (B) just because it
  is packaged with a good one (A).

16
Payback

• Companies frequently require that the initial
  outlay on any project should be recoverable
  within some specified cutoff period.
• The payback period of a project is found by
  counting the number of years it takes before
  cumulative forecasted cash flows equal the
  initial investment.

17
Cash flows, dollars

• Consider project A and B

18

• NPV(A) -2,000

-182
2,000 1.10

1,000 (1.10)3
1,000 1.10
1,000 (1.10)2
3492


NPV(B) -2,000

Thus the net present value rule tells us to
reject project A and accept project B.
19
Payback rule
20

• The payback rule says that these projects are all
  equally attractive. But project B has a higher
  NPV than project C for any positive interest rate
  (1,000 in each of years 1 and 2 is more valuable
  than 2,000 in year 2). And project D has a
  higher NPV than either B or C.
• In order to use the payback rule a firm has to
  decide on an appropriate cutoff date. If it uses
  the same cutoff regardless of project life, it
  will tend to accept too many short-lived projects
  and too few long-lived ones. If, on average, the
  cutoff periods are too long, it will accept some
  projects with negative NPVs if, on average, they
  are too short, it will reject some projects that
  have positive NPVs.

21
Discounted Payback

• Some companies discount the cash flows before
  they compute the payback period. The discounted
  payback rule asks, How many periods does the
  project have to last in order to make sense in
  terms of net present value?
• The discounted cash flow surmounts the objection
  that equal weight is given to all flows starting
  in year1. The cash flow for investment before
  the cut off date.
• The discounted payback rule still takes no
  account of any cash flows after the cutoff date.

22
Example of Discounted payback method

• Suppose there are two mutually exclusive
  investments, A and B. Each requires a 20,000
  investment and is expected to generate a level
  stream of cash flows starting in year 1. The
  cash flow for investment A is 6,500 and lasts
  for 6 years. The cash flow for B is 6,000 but
  lasts for 10 years. The appropriate discount
  rate for each project is 10 percent. Investment
  B is clearly a better investment on the basis of
  net present value

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NPV(A) -20,000 ?6 t1 6,500 8,309
(1.10) t
NPV(B) -20,000 ?10 t1 6,000 16,867
(1.10) t
Yet A has higher cash receipts than B in each
year of its life, and so obviously A has the
shorter discounted payback. The
discounted Payback of B is a bit more than 4
years, since the present value of 6,000 for 4
years is 19,019. Discounted payback is a whisker
better than undiscounted payback.
24
Average return on book value

• Some companies judge an investment project by
  looking at its book rate of return.
• To calculate book rate of return it is necessary
  to divide the average forecasted profits of a
  project after depreciation and taxes by the
  average book value of the investment.
• This ratio is then measured against the book rate
  of return for the firm as a whole or against some
  external yardstick, such as the average book rate
  of return for the industry.

25

• Computing the average book rate of return on an
  investment of 9,000 in project A

Avg. book rate of return
avg. annual income
avg.annual investment

2,000 .44 4,500
26
Internal rate of return

• Alternatively, we could write down the NPV of
  the investment and find that discount rate which
  makes NPV 0
• Implies Discount rate

payoff _______________ - 1
Investment
Rate of return

C1 _______________ 0 1 discount
rate
NPV

Co

C1 - 1 - C0
27

• C1 is the payoff and C0 the required
  investment, and so our two equations say exactly
  the same thing. The discount rate that makes
  NPV 0 is also the rate of return.
• Unfortunately there is no wholly satisfactory
  way of defining the true rate of return of a
  long-lived asset. The best available concept is
  the so-called discounted cash-flow (DCF) rate of
  return or internal rate of return (IRR). The
  internal rate of return is frequently used in
  finance.
• The internal rate of return is defined as the
  rate of discount which makes NPV0. This means
  that to find the IRR for an investment project
  lasting T years, we must solve for IRR in the
  following expression
• NPV C0 C1 C1
  C1 .. CT
  0
• 1 IRR
  (1 IRR)2 (1 IRR)3
  (1 IRR)T
• Actual calculation of IRR usually involves trial
  and error. For example, consider a project which
  produces the following flows

28
The internal rate of return is IRR in the
equation
NPV - 4,000 2,000 4,000 0
1 IRR (1 IRR)2 Let us
arbitrarily try a discount rate of 25 percent.
In this case NPV - 4,000 2,000 4,000
160
1.25 (1. 25)2
29

• The NPV is positive therefore, the IRR must be
  greater than zero. The next step might be to try
  a discount rate of 30 percent. In this case net
  present value is
• NPV - 4,000 2,000 4,000 -
  94
• 1.30 (1.30)2
• In this case net present value is 94
  Therefore the IRR must lie between the rate of 25
  and 30. we can find the rate by interpolation.
• 25 5 X 160 25 5 X 160
• 160 (-94)
  254
• 28.15 percent is the IRR

30
Profitability index

• The profitability index ( or the benefit cost
  ratio) is the present value of forecasted future
  cash flows divided by the initial investment
• Profitability index PVCi
• PVC0
• The profitability index rule tells us to accept
  all projects with an index greater than 1. If
  the profitability index is greater than 1, the
  present value PV of Ci is greater than the
  initial investment - C0 and so the project must
  have a positive net present value.

31
Profitability index

• The benefit cost ratio in the case of previous
  example at the discount rate of 25 percent would
  be
• 4160
• 4000

1.04

32
Time value of money

• In 1624, the Indians sold Manhattan Island at the
  ridiculously low figure of 24.
• Was the amount really ridiculous?
• If the Indians had merely taken the 24 and
  reinvested it at 6 percent annual interest upto
  1992, they would have had 50 billion, an amount
  sufficient to repurchase most of New York City.
• If the Indians had been slightly more astutute
  and had invested the 24 at 7.5 compound
  annually, they would now have over 8 trillion
  and the tribal chiefs would now rival oil sheikhs
  and Japanese tycoons as the richest people in the
  world.

33

• Another popular example is that 1 received 1,992
  years ago, invested at 6 could now be used to
  purchase all the wealth in the world.
• Time value of money applies to day to day
  decisions.
• Understanding the effective rate on a business
  loan
• The mortgage payment in a real estate loan
• Distinction must be made on money received today
  and money received in the future.

34
Future value

• Assume that an investor has 1000 and wishes to
  know its worth after four years if it grows at 10
  percent per year. At the end of the first year,
  he will have 1000 X 1.10 or 1,100. By the end
  of the year two, the 1,100 will have grown to
  1,210 (1,100 X 1.10). The four-year pattern is
  indicated below.

35

• 1st year 1,000 X 1.10 1,100
• 2nd year 1,100 X1.10 1,210
• 3rd year 1,210 X1.10 1,331
• 4th year 1,331 X 1.10 1,464
• If
• FV Future value
• PV Present value
• i Interest rate
• n Number of periods
• The formula for calculation of FV PV(1i)n
• In this case PV 1,000, I 10, n4, so we
  have
• FV 1,000(1.10)4 or 1,000 X 1.464 1,464

36

• Future value of 1

37
Relationship of present value and future value
1,464 future value

10 interest
1000 Present value
0

• 2

1
3
4
Number of periods
38
Present value

• The formula for the present value is derived from
  the original formula for future value
• FV PV(1i)n -------Future Value
• PV FV1/(1i)n -----Present Value
• The present value of 1,464 in the previous
  example is 1,000 today that is it is calculated
  as follows
• PV FV X PVif (n 4, I 10) if interest
  factor as given in the chart
• PV 1,464 X 0.683 1,000

39

• Present value of 1

40
Compounding process of annuity
Period 4
Period 1
Period 2
Period 3
Period 0
1,000 X 1.000 1,000
1,000 for one period 10
1,000 X 1.100 1,100
1,000 for two periods 10
1,000 X 1.210 1.210
1,000 for three periods 10
1,000 X 1.331 1.331
4,641
To find the present value of annuity the process
is reversed.In theory, each individual payment is
discounted back to the present and then all of
the discounted payments are added up, yielding
the present value of annuity.
41
The relationship between the present value and
future value

• It would be noticed that the future value and the
  present value are the flip side of each other.
• Because you can earn a return on your money,
  1.00 received in the future is less than 1.00
  today, and the longer you have to wait to receive
  the dollar, the less it is worth.
• Because we want to avoid large mathematical
  rounding errors, we actually carry the decimal
  points 3 places. For example .683

42
Future value for say .68 at 10 Graphical
presentation
Value at the end of each period

• 1.00

1.00
.909
0.90
.826
0.80
.751
0.70
.683
0.60
0.00
Period 0
Period 1
Period 2
Period 3
Period 4
43

• Present value of 1.00 at 10
• Value at the beginning of each period

1.00
1.00
0.90
.909
0..80
.826
0.70
.751
.683
0.60
1.00
Period 0
Period 1
Period 2
Period 3
Period 4
44
The PV of a 2 year annuity is simply the present
value of one payment at the end of period 1 and
one payment at the end of Period 2

• 3.50

PV of a 4 year annuity
3.17
3.00
PV of 1.00 to be received In 1 year
.909
2.50
2.49
PV of 1.00 to be received In 2 years
.826
2.00
.909
1.74
1.50
.909
.826
.751
PV of 1.00 to be received In 3 years
1.00
.909
.909
0.50
.826
.751
.683
PV of 1.00 to be received In 4 years
0.00
Period 1
Period 2
Period 3
Period 4
45
Relationship between the PV of a single amount
and the present value of an annuity

• The relationship between the present value of
  1.00 and the present value of a 1.00 annuity.
  The assumption is that you will receive 1.00 at
  the end of each period. This is the same concept
  as a lottery, where you win 2 million over 20
  years and receive 100,000 per year for twenty
  years.

46
PV of a 4 year annuity
5.00
The PV of a 2 year annuity is simply the future
value of one payment at the end of period 1 and
one payment at the end of Period 2
4.641
4.50
PV of 1.00 invested at the end of Period 4

• 3.50

1.00
3.00
Future value of an annuity of 1.00 at 10
2.50
3.31
PV of 1.00 invested for 1 year
1.10
1.00
2.10
2.00
1.50
1.00
.1.10
1.21
PV of 1.00 invested for 2 years
1.00
1.00
1.00
1.10
.1.21
0.50
.1.33
PV of 1.00 invested For 3 years
0.00
Period 1
Period 2
Period 3
Period 4