CAPITAL BUDGETING

[savio13]

CAPITAL BUDGETING:

Capital budgeting is vital in decisions. Decisions on investment, which take time to mature, have to be based on the returns, which that investment will make. Unless the project is for social reasons only, if the investment is unprofitable in the long run, it is unwise to invest in it now.
Often, it would be good to know what the present value of the future investment is, or how long it will take to mature (give returns). It could be much more profitable putting the planned investment money in the bank and earning interest, or investing in an alternative project.
Capital budgeting is very obviously a vital activity in business. Vast sums of money can be easily wasted if the investment turns out to be wrong or uneconomic. The subject matter is difficult to grasp by nature of the topic covered and also because of the mathematical content involved. However, it seeks to build on the concept of the future value of money, which may be spent now. It does this by examining the techniques of net present value, internal rate of return and annuities. The timing of cash flows are important in new investment decisions and so the chapter looks at this "payback" concept. One problem which plagues developing countries is "inflation rates" which can, in some cases, exceed 100% per annum. The chapter ends by showing how marketers can take this in to account.

Capital budgeting versus current expenditures

A capital investment project can be distinguished from current expenditures by two features:

a) Such projects are relatively large
b) a significant period of time (more than one year) elapses between the investment outlay and the receipt of the benefits.
As a result, most medium-sized and large organizations have developed special procedures and methods for dealing with these decisions. A systematic approach to capital budgeting implies:
a) The formulation of long-term goals
b) The creative search for and identification of new investment opportunities
c) Classification of projects and recognition of economically and/or statistically dependent proposals
d) The estimation and forecasting of current and future cash flows
e) A suitable administrative framework capable of transferring the required information to the decision level
f) The controlling of expenditures and careful monitoring of crucial aspects of project execution
g) A set of decision rules, which can differentiate acceptable from unacceptable alternatives, is required.
The last point (g) is crucial and this is the subject of later sections of the chapter.

The classification of investment projects

a) By project size
Departmental managers may approve small projects. More careful analysis and Board of Directors' approval is needed for large projects of, say, half a million Rs. or more.
b) By type of benefit to the firm
• an increase in cash flow
• a decrease in risk
• an indirect benefit (canteen for workers, etc).
c) By degree of dependence
• mutually exclusive projects (can execute project A or B, but not both)
• complementary projects: taking project A increases the cash flow of project B.
• substitute projects: taking project A decreases the cash flow of project B.
d) By degree of statistical dependence
• Positive dependence
• Negative dependence
• Statistical independence.
e) By type of cash flow
• Conventional cash flow: only one change in the cash flow sign
e.g. -/++++ or +/----, etc
• Non-conventional cash flows: more than one change in the cash flow sign,
e.g. +/-/+++ or -/+/-/++++, etc.

 

[savio13]

Re: CAPITAL BUDGETING... contd..1

The economic evaluation of investment proposals
The time value of money

Recall that the interaction of lenders with borrowers sets an equilibrium rate of interest. Borrowing is only worthwhile if the return on the loan exceeds the cost of the borrowed funds. Lending is only worthwhile if the return is at least equal to that which can be obtained from alternative opportunities in the same risk class.

The interest rate received by the lender is made up of:

i) The time value of money: the receipt of money is preferred sooner rather than later. Money can be used to earn more money. The earlier the money is received, the greater the potential for increasing wealth. Thus, to forego the use of money, you must get some compensation.
ii) The risk of the capital sum not being repaid. This uncertainty requires a premium as a hedge against the risk; hence the return must be commensurate with the risk being undertaken.
iii) Inflation: money may lose its purchasing power over time. The lender must be compensated for the declining spending/purchasing power of money. If the lender receives no compensation, he/she will be worse off when the loan is repaid than at the time of lending the money.

a) Future values/compound interest
Future value (FV) is the value in Rs. at some point in the future of one or more investments.

FV consists of:

i) the original sum of money invested, and
ii) the return in the form of interest.
The general formula for computing Future Value is as follows:
FVn = Vo (l + r)n
Where
Vo is the initial sum invested
r is the interest rate
n is the number of periods for which the investment is to receive interest.
Thus we can compute the future value of what Vo will accumulate to in n years when it is compounded annually at the same rate of r by using the above formula.

Future values/compound interest

i) What is the future value of Rs.10 invested at 10% at the end of 1 year?
ii) What is the future value of Rs.10 invested at 10% at the end of 5 years?
We can derive the Present Value (PV) by using the formula:
FVn = Vo (I + r)n
By denoting Vo by PV we obtain:
FVn = PV (I + r)n
by dividing both sides of the formula by (I + r)n we derive:

Rationale for the formula:

As you will see from the following exercise, given the alternative of earning 10% on his money, an individual (or firm) should never offer (invest) more than Rs.10.00 to obtain Rs.11.00 with certainty at the end of the year.

b) Net present value (NPV)
The NPV method is used for evaluating the desirability of investments or projects.


where:
Ct = the net cash receipt at the end of year t
Io = the initial investment outlay
r = the discount rate/the required minimum rate of return on investment
n = the project/investment's duration in years.
The discount factor r can be calculated using:

Examples:

Decision rule:

If NPV is positive (+): accept the project
If NPV is negative(-): reject the project

Net present value Example

A firm intends to invest Rs.1,000 in a project that generated net receipts of Rs.800, Rs.900 and Rs.600 in the first, second and third years respectively. Should the firm go ahead with the project?

c) Annuities

A set of cash flows that are equal in each and every period is called an annuity.
Example:
Year Cash Flow (Rs.)
0 -800
1 400
2 400
3 400
PV = Rs.400(0.9091) + Rs.400(0.8264) + Rs.400(0.7513)
= Rs.363.64 + Rs.330.56 + Rs.300.52
= Rs.994.72
NPV = Rs.994.72 - Rs.800.00
= Rs.194.72
Alternatively,
PV of an annuity = Rs.400 (PVFAt.i) (3,0,10)
= Rs.400 (0.9091 + 0.8264 + 0.7513)
= Rs.400 x 2.4868
= Rs.994.72
NPV = Rs.994.72 - Rs.800.00
= Rs.194.72

d) Perpetuities
Perpetuity is an annuity with an infinite life. It is an equal sum of money to be paid in each period forever.

where:
C is the sum to be received per period
r is the discount rate or interest rate

Example:

You are promised a perpetuity of Rs.700 per year at a rate of interest of 15% per annum. What price (PV) should you be willing to pay for this income?
PV = 700/0.15
= Rs.4,666.67

A perpetuity with growth:

Suppose that the Rs.700 annual income most recently received is expected to grow by a rate G of 5% per year (compounded) forever. How much would this income be worth when discounted at 15%?
Solution:
Subtract the growth rate from the discount rate and treat the first period's cash flow as a perpetuity.

= 700(1.05)/(0.15-0.05)
= Rs.735/0.10

 

[savio13]

Re: CAPITAL BUDGETING... contd..1

The economic evaluation of investment proposals
The time value of money

Recall that the interaction of lenders with borrowers sets an equilibrium rate of interest. Borrowing is only worthwhile if the return on the loan exceeds the cost of the borrowed funds. Lending is only worthwhile if the return is at least equal to that which can be obtained from alternative opportunities in the same risk class.

The interest rate received by the lender is made up of:

i) The time value of money: the receipt of money is preferred sooner rather than later. Money can be used to earn more money. The earlier the money is received, the greater the potential for increasing wealth. Thus, to forego the use of money, you must get some compensation.
ii) The risk of the capital sum not being repaid. This uncertainty requires a premium as a hedge against the risk; hence the return must be commensurate with the risk being undertaken.
iii) Inflation: money may lose its purchasing power over time. The lender must be compensated for the declining spending/purchasing power of money. If the lender receives no compensation, he/she will be worse off when the loan is repaid than at the time of lending the money.

a) Future values/compound interest
Future value (FV) is the value in Rs. at some point in the future of one or more investments.

FV consists of:

i) the original sum of money invested, and
ii) the return in the form of interest.
The general formula for computing Future Value is as follows:
FVn = Vo (l + r)n
Where
Vo is the initial sum invested
r is the interest rate
n is the number of periods for which the investment is to receive interest.
Thus we can compute the future value of what Vo will accumulate to in n years when it is compounded annually at the same rate of r by using the above formula.

Future values/compound interest

i) What is the future value of Rs.10 invested at 10% at the end of 1 year?
ii) What is the future value of Rs.10 invested at 10% at the end of 5 years?
We can derive the Present Value (PV) by using the formula:
FVn = Vo (I + r)n
By denoting Vo by PV we obtain:
FVn = PV (I + r)n
by dividing both sides of the formula by (I + r)n we derive:

Rationale for the formula:

As you will see from the following exercise, given the alternative of earning 10% on his money, an individual (or firm) should never offer (invest) more than Rs.10.00 to obtain Rs.11.00 with certainty at the end of the year.

b) Net present value (NPV)
The NPV method is used for evaluating the desirability of investments or projects.


where:
Ct = the net cash receipt at the end of year t
Io = the initial investment outlay
r = the discount rate/the required minimum rate of return on investment
n = the project/investment's duration in years.
The discount factor r can be calculated using:

Examples:

Decision rule:

If NPV is positive (+): accept the project
If NPV is negative(-): reject the project

Net present value Example

A firm intends to invest Rs.1,000 in a project that generated net receipts of Rs.800, Rs.900 and Rs.600 in the first, second and third years respectively. Should the firm go ahead with the project?

c) Annuities

A set of cash flows that are equal in each and every period is called an annuity.
Example:
Year Cash Flow (Rs.)
0 -800
1 400
2 400
3 400
PV = Rs.400(0.9091) + Rs.400(0.8264) + Rs.400(0.7513)
= Rs.363.64 + Rs.330.56 + Rs.300.52
= Rs.994.72
NPV = Rs.994.72 - Rs.800.00
= Rs.194.72
Alternatively,
PV of an annuity = Rs.400 (PVFAt.i) (3,0,10)
= Rs.400 (0.9091 + 0.8264 + 0.7513)
= Rs.400 x 2.4868
= Rs.994.72
NPV = Rs.994.72 - Rs.800.00
= Rs.194.72

d) Perpetuities
Perpetuity is an annuity with an infinite life. It is an equal sum of money to be paid in each period forever.

where:
C is the sum to be received per period
r is the discount rate or interest rate

Example:

You are promised a perpetuity of Rs.700 per year at a rate of interest of 15% per annum. What price (PV) should you be willing to pay for this income?
PV = 700/0.15
= Rs.4,666.67

A perpetuity with growth:

Suppose that the Rs.700 annual income most recently received is expected to grow by a rate G of 5% per year (compounded) forever. How much would this income be worth when discounted at 15%?
Solution:
Subtract the growth rate from the discount rate and treat the first period's cash flow as a perpetuity.

= 700(1.05)/(0.15-0.05)
= Rs.735/0.10

 

[savio13]

Re: CAPITAL BUDGETING...contd...2

The internal rate of return (IRR)

• The IRR is the discount rate at which the NPV for a reject equals zero. This rate means that the present value of the cash inflows for the project would equal the present value of its outflows.
• The IRR is the break-even discount rate.
• The IRR is found by trial and error.
where r = IRR

IRR of an annuity:

where:
Q (n,r) is the discount factor
Io is the initial outlay
C is the uniform annual receipt (C1 = C2 =....= Cn).

Economic rationale for IRR:

If IRR exceeds cost of capital, project is worthwhile, i.e. it is profitable to undertake.
Net present value vs. internal rate of return
Independent vs dependent projects
NPV and IRR methods are closely related because:
i) both are time-adjusted measures of profitability, and
ii) their mathematical formulas are almost identical.
So, which method leads to an optimal decision: IRR or NPV?
a) NPV vs IRR: Independent projects

Independent project: Selecting one project does not preclude the choosing of the other.

With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to the same accept/reject decisions.
NPV vs IRR Independent projects
If cash flows are discounted at k1, NPV is positive and IRR > k1: accept project.
If cash flows are discounted at k2, NPV is negative and IRR < k2: reject the project.
Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e.

Similarly for the same project to be acceptable:

where R is the IRR.
Since the numerators Ct are identical and positive in both instances:
• implicitly/intuitively R must be greater than k (R > k);
• If NPV = 0 then R = k: the company is indifferent to such a project;
• Hence, IRR and NPV lead to the same decision in this case.
b) NPV vs IRR: Dependent projects

NPV clashes with IRR where mutually exclusive projects exist.
Example:

ABC Ltd is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a prime site. The following information is available:
Initial Investment Outlay Net Inflow at the Year End
Project A -9,500 11,500
Project B -15,000 18,000
Assume k = 10%, which project should ABC Ltd undertake?
NPVA = 11500/1.1 -9500
= Rs.954.55
NPVB = 18000/1.1 -15000
= Rs.1,363.64
Both projects are of one-year duration:
IRRA:
=11500/RA =9500
Rs.11,500 = Rs.9,500 (1 +RA)
RA = 11500/9500-1
= 1.21-1
therefore IRRA = 21%
IRRB:
Rs.18,000 = Rs.15,000(1 + RB)
RB = 18000/15000 -1
=1.2-1
therefore IRRB = 20%
Decision:
Assuming that k = 10%, both projects are acceptable because:
NPVA and NPVB are both positive
IRRA > k AND IRRB > k
Which project is a "better option" for ABC Ltd?
If we use the NPV method:
NPVB (Rs.1,363.64) > NPVA (Rs.954.55): ABC Ltd should choose Project B.
If we use the IRR method:
IRRA (21%) > IRRB (20%): ABC Ltd should choose Project A.
NPV vs IRR: Dependent projects

Up to a discount rate of ko: project B is superior to project A, therefore project B is preferred to project A.
Beyond the point ko: project A is superior to project B, therefore project A is preferred to project B
The two methods do not rank the projects the same.
Differences in the scale of investment
NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:
Years 0 1 2 3
Project A -2,500 1,500 1,500 1,500
Project B -14,000 7,000 7,000 7,000
Assume k= 10%.
NPVA = Rs.1,500 x PVFA at 10% for 3 years
= Rs.1,500 x 2.487
= Rs.3,730.50 - Rs.2,500.00
= Rs.1,230.50.
NPVB == Rs.7,000 x PVFA at 10% for 3 years
= Rs.7,000 x 2.487
= Rs.17,409 - Rs.14,000
= Rs.3,409.00.
IRRA = 36%
IRRB = 21%
Decision:
Conflicting, as:
• NPV prefers B to A
• IRR prefers A to B
NPV IRR
Project A Rs. 3,730.50 36%
Project B Rs.17,400.00 21%

i) the NPV prefers B, the larger project, for a discount rate below 20%

 

[savio13]

Re: CAPITAL BUDGETING...contd...3

Internal Rate of Return


Differences in the scale of investment

NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:
Years 0 1 2 3
Project A -2,500 1,500 1,500 1,500
Project B -14,000 7,000 7,000 7,000
Assume k= 10%.
NPVA = Rs.1,500 x PVFA at 10% for 3 years
= Rs.1,500 x 2.487
= Rs.3,730.50 - Rs.2,500.00
= Rs.1,230.50.
NPVB == Rs.7,000 x PVFA at 10% for 3 years
= Rs.7,000 x 2.487
= Rs.17,409 - Rs.14,000
= Rs.3,409.00.
IRRA = 36%
IRRB = 21%
Decision:
Conflicting, as:
• NPV prefers B to A
• IRR prefers A to B
NPV IRR
Project A Rs. 3,730.50 36%
Project B Rs.17,400.00 21%

i) the NPV prefers B, the larger project, for a discount rate below 20%
ii) the NPV is superior to the IRR
a) Use the incremental cash flow approach, "B minus A" approach
b) Choosing project B is tantamount to choosing a hypothetical project "B minus A".


0 1 2 3
Project B - 14,000 7,000 7,000 7,000
Project A - 2,500 1,500 1,500 1,500
"B minus A" - 11,500 5,500 5,500 5,500
IRR"B Minus A"
= 20%
c) Choosing B is equivalent to: A + (B - A) = B
d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of Rs.11,500 of which Rs.5,500 will be realized each year for the next 3 years.
e) The IRR"B minus A" on the incremental cash flow is 20%.
f) Given k of 10%, this is a profitable opportunity, therefore must be accepted.
g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.
i) If k = 20% (IRR of "B - A") the company should accept project A.
• This justifies the use of NPV criterion.
Advantage of NPV:
• It ensures that the firm reaches an optimal scale of investment.
Disadvantage of IRR:
• It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the IRR will prefer 500% of Rs.1 to 20% return on Rs.100. However, most companies set their goals in absolute terms and not in % terms, e.g. target sales figure of Rs.2.5 million.
The timing of the cash flow
The IRR may give conflicting decisions where the timing of cash flows varies between the 2 projects.

Note that initial outlay Io is the same.
0 1 2
Project A - 100 20 125.00
Project B - 100 100 31.25
"A minus B" 0 - 80 88.15
Assume k = 10%
NPV IRR
Project A 17.3 20.0%
Project B 16.7 25.0%
"A minus B" 0.6 10.9%
IRR prefers B to A even though both projects have identical initial outlays. So, the decision is to accept A, that is B + (A - B) = A
The horizon problem
NPV and IRR rankings are contradictory. Project A earns Rs.120 at the end of the first year while project B earns Rs.174 at the end of the fourth year.
0 1 2 3 4
Project A -100 120 - - -
Project B -100 - - - 174
Assume k = 10%
NPV IRR
Project A 9 20%
Project B 19 15%
Decision:
NPV prefers B to A
IRR prefers A to B.