Complex Investment Decisions

Complex Investment Decisions

Nature of Investment DecisionsThe investment decisions of a firm are generally known as the capital budgeting, or capital expenditure decisions.The firms investment decisions would generally include expansion, acquisition, modernisation and replacement of the long-term assets. Sale of a division or business (divestment) is also as an investment decision. Decisions like the change in the methods of sales distribution, or an advertisement campaign or a research and development programme have long-term implications for the firms expenditures and benefits, and therefore, they should also be evaluated as investment decisions.

Features of Investment Decisions The exchange of current funds for future benefits.The funds are invested in long-term assets.The future benefits will occur to the firm over a series of years.

Importance of Investment DecisionsGrowthRiskFunding IrreversibilityComplexity

Types of Investment DecisionsOne classification is as follows:Expansion of existing businessExpansion of new businessReplacement and modernisationYet another useful way to classify investments is as follows:Mutually exclusive investmentsIndependent investmentsContingent investments

Investment Evaluation CriteriaThree steps are involved in the evaluation of an investment:Estimation of cash flowsEstimation of the required rate of return (the opportunity cost of capital)Application of a decision rule for making the choice

Investment Decision RuleIt should maximise the shareholders wealth.It should consider all cash flows to determine the true profitability of the project.It should provide for an objective and unambiguous way of separating good projects from bad projects.It should help ranking of projects according to their true profitability.It should recognise the fact that bigger cash flows are preferable to smaller ones and early cash flows are preferable to later ones.It should help to choose among mutually exclusive projects that project which maximises the shareholders wealth.It should be a criterion which is applicable to any conceivable investment project independent of others.

Evaluation Criteria1.Discounted Cash Flow (DCF) CriteriaNet Present Value (NPV)Internal Rate of Return (IRR)Profitability Index (PI)2.Non-discounted Cash Flow CriteriaPayback Period (PB)Discounted Payback Period (DPB)Accounting Rate of Return (ARR)

Net Present Value MethodCash flows of the investment project should be forecasted based on realistic assumptions.Appropriate discount rate should be identified to discount the forecasted cash flows. The appropriate discount rate is the projects opportunity cost of capital. Present value of cash flows should be calculated using the opportunity cost of capital as the discount rate.The project should be accepted if NPV is positive (i.e., NPV > 0).

Net Present Value Method

Net present value should be found out by subtracting present value of cash outflows from present value of cash inflows. The formula for the net present value can be written as follows:

Acceptance RuleAccept the project when NPV is positive NPV > 0Reject the project when NPV is negative NPV < 0May accept the project when NPV is zero NPV = 0The NPV method can be used to select between mutually exclusive projects; the one with the higher NPV should be selected.

Internal Rate of Return MethodThe internal rate of return (IRR) is the rate that equates the investment outlay with the present value of cash inflow received after one period. This also implies that the rate of return is the discount rate which makes NPV = 0.

Acceptance RuleAccept the project when r > k.Reject the project when r < k.May accept the project when r = k.In case of independent projects, IRR and NPV rules will give the same results if the firm has no shortage of funds.

Profitability IndexProfitability index is the ratio of the present value of cash inflows, at the required rate of return, to the initial cash outflow of the investment.

Acceptance RuleThe following are the PI acceptance rules:Accept the project when PI is greater than one. PI > 1Reject the project when PI is less than one. PI < 1May accept the project when PI is equal to one. PI = 1The project with positive NPV will have PI greater than one. PI less than means that the projects NPV is negative.

Case of Ranking Mutually Exclusive ProjectsInvestment projects are said to be mutually exclusive when only one investment could be accepted and others would have to be excluded.Two independent projects may also be mutually exclusive if a financial constraint is imposed.The NPV and IRR rules give conflicting ranking to the projects under the following conditions:The cash flow pattern of the projects may differ. That is, the cash flows of one project may increase over time, while those of others may decrease or vice-versa.The cash outlays of the projects may differ.The projects may have different expected lives.

Timing of Cash Flows

Scale of Investment

Project Life Span

Reinvestment AssumptionThe IRR method is assumed to imply that the cash flows generated by the project can be reinvested at its internal rate of return, whereas the NPV method is thought to assume that the cash flows are reinvested at the opportunity cost of capital.

Complex Investment Decisions

ObjectivesShow the application of the NPV rule in the choice between mutually exclusive projects, replacement decisions, projects with different lives etc.Understand the impact of inflation on mutually exclusive projects with unequal lives.Make choice between investments under capital rationing.Illustrate the use of linear programming under capital rationing situation.

Complex Investment ProblemsHow shall choice be made between investments with different lives?Should a firm make investment now, or should it wait and invest later?When should an existing asset be replaced?How shall choice be made between investments under capital rationing?

Projects with Different LivesThe choice between projects with different lives should be made by evaluating them for equal periods of time.

Annual Equivalent Value (AEV) MethodThe method for handling the choice of the mutually exclusive projects with different lives, as discussed in last slide, can become quite cumbersome if the projects lives are very long. We can calculate the annual equivalent value (AEV) of cash flows of each project. We shall select the project that has lower annual equivalent cost.

AEV for Perpetuities When we assume that projects can be replicated at constant scale indefinitely, we imply that an annuity is paid at the end of every n years starting from the first period.

where NPV is the present value of the investment indefinitely, NPVn is the present value of the investment for the original life, n and k is the opportunity cost of capital.

Investment Timing and DurationThe rule is straightforward: undertake the project at that point of time, which maximizes the NPV.

Tree Harvesting ProblemThe maximisation of the investments NPV would depend on when we harvest trees. The net future value of trees increases when harvesting is postponed; but the opportunity cost of capital is incurred by not realising the value by harvesting the trees. The NPV will be maximised when the trees are harvested at the point where the percentage increase in value equals the opportunity cost of capital.Suppose the net future value obtained over the years from harvesting the trees is At and if the opportunity cost of capital is k, then the net present value (NPV) of the net realisable value of trees is given by:

Replacement of an Existing Asset Compare the annual equivalent value (AEV) of the old and new equipment as given below.It is indicated that a chain of new machines is equivalent to an annuity of Rs 9,630 3.605 = Rs 2,671 a year for the life of the chain. The existing machine is still capable of providing an annuity of: Rs 7,390 2.402 = Rs 3,076. So long as the existing machine generates a cash inflow of more than Rs 2,671 there does not seem to be an economic justification for replacing it.

Investment Decisions Under InflationExecutives generally estimate cash flows assuming unit costs and selling price prevailing in year zero to remain unchanged. They argue that if there is inflation, prices can be increased to cover increasing costs; therefore, the impact on the projects profitability would be the same if they assume rate of inflation to be zero.This line of argument, although seems to be convincing, is fallacious for two reasons.First, the discount rate used for discounting cash flows is generally expressed in nominal terms. It would be inappropriate and inconsistent to use a nominal rate to discount constant cash flows. Second, selling prices and costs show different degrees of responsiveness to inflation:The depreciation tax shield remains unaffected by inflation since depreciation is allowed on the book value of an asset, irrespective of its replacement or market price, for tax purposes.

Nominal Vs. Real Rates of ReturnFor a correct analysis, two alternatives are available:either the cash flows should be converted into nominal terms and then discounted at the nominal required rate of return, orthe discount rate should be converted into real terms and used to discount the real cash flows.Always remember: Discount nominal cash flows at nominal discount rate; or discount real cash flows at real discount rate.

Investment Decisions Under Capital RationingCapital rationing refers to a situation where the firm is constrained for external, or self-imposed, reasons to obtain necessary funds to invest in all investment projects with positive NPV. Under capital rationing, the management has not simply to determine the profitable investment opportunities, but it has also to decide to obtain that combination of the profitable projects which yields highest NPV within the available funds.

Types of Capital Rationing There are two types of capital rationing:External capital rationing.Internal capital rationing.

Profitability IndexThe NPV rule should be modified while choosing among projects under capital constraint. The objective should be to maximise NPV per rupee of capital rather than to maximise NPV. Projects should be ranked by their profitability index, and top-ranked projects should be undertaken until funds are exhausted.The Profitability Index does not always work. It fails in two situations:Multi-period capital constraints.Project indivisibility.

Programming Approach to Capital RationingLinear Programming (LP)Integer Programming (IP)Dual variable

Cash Flows (Rs)NPV

ProjectC0C1C2C3at 9%IRR

M 1,6801,40070014030123%

N 1,6801408401,51032117%

Cash Flow (Rs)NPV

ProjectC0C1at 10%IRR

A-1,0001,50036450%

B-100,000120,0009,08020%

Cash Flows (Rs)

ProjectC0C1C2C3C4C5NPV at 10%IRR

X 10,00012,000 90820%

Y 10,000000020,1202,49515%

Cash Flows (Rs 000)

01234NPV, 10%

Y160404000129.42

Y200604040106.96

Y = Y1 + Y260401004040236.38

X12030303030215.10

Project Undertaken

at PeriodNPV

0100 + 150 0.909= 36.35

1120 0.909 + 180 0.826= 39.60

2140 0.826 + 205 0.751= 38.32

EquipmentC0C1C2C3C4C5NPV at 12%

New12666669.63

Old4327.39

AEV, New2.672.672.672.672.679.63

AEV, Old3.083.083.087.39