FINANCIALMATHEMATICS

CAPITAL BUDGETING

• Capital budgeting –Investment decisions of a firm.• Investment decision rules –Capital budgeting

techniques.• Grouped under 2 categories:

1.DISCOUNTED CASHFLOW• Net present value(NPV)• Internal rate of return(IRR)• Profitability index(PI)• Discounted payback period

2.NON-DISCOUNTED• Payback period (PB)

NPV

• Net present value – NPV is defined as the worth of an investment after taking into account all the cash flows associated with it.

• Steps to calculate NPV– The first step is to estimate the expected future cash flows.– The second step is to estimate the required return for projects of this

risk level.– The third step is to find the present value of the cash flows and

subtract the initial investment.

FORMULAE

NPV – Decision Rule• If the NPV is positive, accept the project

• A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.

• Accept if NPV >0• Reject if NPV <0• May accept if NPV=0

MERITS & DE-MERITS OF NPV

MERITS DE-MERITS

Considers all cash flows Requires estimates of cash flows-tedious

True measure of profitability Requires computation of opportunity cost of capital

Based on the concept of time value of money

Satisfies the value additivity principle

Consistent with wealth maximization principle.

IRR• Internal rate of return is the interest rate at which

the project cash flows give a zero NPV• If IRR > cost of capital ,proceed with the project• It takes into account the magnitude and timing of

cash flows.• It is also known as yield on an investment.• To calculate the rate of return on a project:

1. Setting the NPV of the project to zero.2. Solving for “r”.

• Value of “r” by trial and error

MERITS & DE-MERITS OF IRR

MERITS DE-MERITS

Considers all cash flows Requires estimates of cash flows-tedious

True measure of profitability Does not hold the value additivity principle

Based on the concept of time value of money Relatively difficult to compute.

Generally, consistent with wealth maximization principle

PROFITABILITY INDEX • It is defined as, the ratio of present values of cash

inflows, at the required rate of return, to the initial cash outflow of the investment.

PI= PV of cash inflows Initial cash outlay• Measures the benefit per unit cost, based on the

time value of money.• Acceptance Rule:• Accept if PI > 1• Reject if PI < 1• May accept if PI = 1

MERITS & DE-MERITS OF PI

MERITS DE-MERITS

Considers all cash flows Requires estimates of cash flows-tedious

Recognizes the time value of money

Relative measure of profitability

Consistent with wealth maximization principle

PAYBACK • It is defined as the number of years required to

recover the original cash outlay that is invested in a project.

Payback = Initial Investment Annual cash inflow• Computation

– Estimate the cash flows– Subtract the future cash flows from the initial cost until the initial

investment has been recovered

• Decision Rule – Accept if the payback period is less than some preset limit(Standard payback)

MERITS & DE-MERITS OF PAYBACKMERITS DE-MERITS

Easy to understand and compute Ignores the time value of money

It ranks projects Ignores cash flows occurring after the payback period

Easy and crude way to cope with risk Not a measure of profitability

Uses cash flows information No objective way to determine standard payback

No relation with wealth maximization principle

DISCOUNTED PAYBACK• One of the serious objections to the payback method-It

does not discount cash flows.

• It is defined as the time period it takes for the discounted cash flows generated by the project to cover the initial investment in the project.

• It still fails to consider the cash flows after the payback period.

• Decision Rule - Accept the project if it pays back on a discounted basis within the specified time

MERITS & DE-MERITS OF DISCOUNTED PAYBACK

MERITS DE-MERITS

Includes time value of money Requires an arbitrary cutoff point

Easy to understand Ignores cash flows beyond the cutoff point

Weighted Average Cost of Capital(WACC)• It is defined as the average cost of raising finance for the business

• Depends on the financing mix of the company’s capital (depends on the level of debt and equity)

• It is used as the discount rate in project appraisal

• Formulae: WACC = MV of debt/MV of debt +equity *net cost of debt+ MV of equity/MV of debt +equity *cost of equity

WHY WACC?

• Advantages of WACC:

• Flexibility and simplicity

• Disadvantages of WACC:

• While the relative debt and equity values can be easily determined, calculating the costs of debt and equity can be problematic.

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