Value and Capital Budgeting

Time Value of Money, Techniques for Capital Budgeting Decisions, Valuation

of Cash Flow, Term Structure of Interest Rate

Capital BudgetingCapital Budget can be dissected into two parts –

a) Capital – refers to operating assets in production.b) Budget – is a plan that details projected cash flows

during some future period.

Therefore, • Capital budgeting is the whole process of analyzing the

projects and deciding which one to include in the capital budget.

• It is a process of evaluating specific investment decisions.

Capital Budgeting

Need for Capital Budgeting – • A firm’s capital budgeting decisions must define its

strategic direction. Planning is essential because launching of a new products, services or markets is preceded by capital expenditure.

• Results of capital budgeting decisions may be achieved in many years to come.

• Poor investments can lead to non-optimal utilisation of financial resources.

Capital Budgeting

Consider a hypothetical scenario –

Sales representative reporting to his sales manager about the demand for a product of a particular type and quality.

How would the sales manager go about tackling this new market potential ?

Sales ManagerMarketing Research

Production

Accounts

Capital Budgeting

Capital Expenditure – Types, classifications and decisions.

• Replacement: Maintenance of business (Should we carry on ?).

• Replacement: Cost reduction (Cut cost through alternatives).

• Expansion into existing and new markets (How can we ?).• Expenditure on product quality and quantity enhancement.• Safety and/or Environment Projects (Social responsibility).• Research and Development (Product enhancement).• Long term contracts (Securing market deals).

Capital Budgeting

Techniques for Capital Budgeting –

a) Payback.

b) Discounted Payback.

c) Net Present Value.

d) Internal Rate of Return.

e) Modified Internal Rate of Return.

f) Profitability Index.

Capital Budgeting

Expected After – Tax

Net Cash Flow, CFt

Year (t) Project S Project T

0 ($1000) ($1000)

1 500 100

2 400 300

3 300 400

4 100 600

Project S has higher cash flows at the beginning of operation.

For Project T, higher cash flows comes as years pass on.

Which of these two options are optimal from investment and revenue point of you ?

Capital Budgeting

Payback Period – is the number of years required to recover the original investment.

Initial Investment - $1000

Net Cash Flow -1000 500 400 300 100

Cumulative NCF -1000 -500 -100 200 300

0 1 32 4

Project S

0 321 4

Net Cash Flow -1000 100 300 400 600

Cumulative NCF -1000 -900 -600 200 400

Project T

Capital BudgetingUnrecovered cost at

the start of year

Cash flow during the year

Year before full recovery +Pay back period =

Payback Short Term = 2 + (100/300)

= 2.33 years.

Payback Long Term = 3 + (200/600)

= 3.33 years

Capital Budgeting

Discounted Payback Period –

• How realistic is the Payback Period method ?• Does it account for inflation factor & time vale of money ?

DPP method allows for discounting of cash flows. The discount rate used is the project’s cost of capital.

Therefore, the discounted payback period is defined as the number of years required to recover the investment from the discounted cash flows.

Capital Budgeting

Net Cash Flow -1000 500 400 300 100

Cumulative NCF 10% -1000 455 331 225 68

0 1 2 3 4

Project S

C. discounted NCF -1000 -545 -214 11 79

Discounted Payback Period = 2 + (214/225)

= 2.95 years.

Capital Budgeting

Net Cash Flow -1000 100 300 400 600

Cumulative NCF 10% -1000 91 248 301 410

0 1 2 3 4

Project T

C. discounted NCF -1000 -909 -661 -360 50

Discounted Payback Period = 3 + (360/410)

= 3.87 years.

Capital Budgeting

Net Present Value – In principle, similar to the discounted cash flow method.

Projects with positive NPV should be accepted. If not, the project must be rejected. If two projects have positive NPV, then the one with higher NPV must be accepted.

Link: Net Present Value

Capital Budgeting

Internal Rate of Return – is the discount rate that equates the present value of the projects cash inflows to the present value of the projects costs.

Link: Bond’s Yield to Maturity

Significance of IRR – • The IRR on a project is its expected rate of return.• If the IRR exceeds the cost of the funds used to finance the

project, a surplus will remain after paying for the capital.A surplus indicates that there is an increase in shareholder wealth

Capital Budgeting

Modified Internal Rate of Return –

In MIRR, the cash flows from each projects are reinvested at the cost of capital.

Recall, MIRR is the rate at which all the future cash flows are reinvested. Any rate above the MIRR is beneficial.

Link: MIRR

Σ CIFt ( 1 + r ) n - tt = 0

n

( 1 + MIRR ) n

=COFt

( 1 + r )t

Σ t = 0

n

Capital Budgeting

Probability Index – shows the relative profitability of any project or the present value per dollar of initial cost.

Numerator – PV of the Cash Flow.

Denominator – Initial Cost.

Therefore,

PI = 1078.82 / 1,000 = 1.078

CF t / ( 1 + r )tΣt = 1

n

n

CF 0

PI =

Net Present Value, In detail

Calculating NPV based on –

• Perpetuity.

• Uneven Cash Flow Perpetuity.

• Annuity.

a) Ordinary Annuities.

b) Annuities Due.

Perpetuities and NPV’sIt is the constant stream of cash flows without end.

In contrast to finite number of cash flows called annuities, perpetuities provide for an infinite unending stream of cash flows over an un-measurable period of time.

Can this happen ?

Consol Bonds issued in the UK entitles the owner to receive yearly interest from the British government “forever”.

Now the obvious question ? How to value the consol ??

Perpetuities and NPV’s

PV of the Consol –

Link: Perpetuities

PV Consol @ 10 % = 100 / 0.10 = $1000

PV Consol @ 8 % = 100 / 0.08 = $1250

PV Consol @ 11.75 % = 100 / 0.1175 = $851.07

Cash Flow

Interest RatePV Consol =

Perpetuities and NPV’s

Perpetuities and Uneven Cash Flows –

Talking of annuities, the term constant payment is always referred to. In other words, annuities involve payments that are the same in every period.

• Are there any scope of uneven cash flow ?• If yes, Could you think of any asset that will generate,

hypothetically, a variable cash flow ??

Common Stocks and its uneven cash flow – dividends.

Perpetuities and NPV’s

100 200 225 170 300 0 100

0 1 32 54 76

Present and Future Value of an uneven Cash flow –

Link - Perpetuities

Perpetuities and NPV’s

Growing Perpetuities – Similar to perpetuities in terms of its application , in growing perpetuities, the cash flows are expected to grow at some constant rate “g”.

C – cash flow received one period.r – discount rate.g – rate of growth per period.

PV = C + C (1 + g) + C(1 + g)2 …. + ….. C(1 + g)N – 1

(1 + r) (1 + r)2 (1 + r)3 (1 + r)N

Perpetuities and NPV’s

Example:

Year 1 Cash Flow: $100,000.

Rate of Interest: 11% (assumed constant).

TTM: Indefinite.

Growth Rate: 5% (assumer constant).

PV = 100,000 + 100,000 (1.05) + 100,000 (1.05)2 + 100,000 (1.05) N-1 +…

1.11 (1.11)2 (1.11)3 (1.11)N

Annuities and FVA’sAn annuity is a level stream of regular payments that lasts for

a “fixed” number of periods.Examples:1) Pensions.2) Unspecified time based leases.

In other words, an annuity is a series of equal payments made at fixed intervals for a specified number of period.

Payments made at the end of one accounting period – Ordinary or Deferred Annuity.

Payments made typically on the 1st day of the accounting period – Annuity Due.

Annuities and FVA’s

(1 + i) n – 1

iPMTFVA n =

FVA n = 100 ((1 + 0.05)10 – 1)/0.05)

FVA n = $ 552.56

Link: Annuities

( )

Ordinary Annuities

Annuities and FVA’s

Annuities Due

Link: Annuities

100 100 100 100

5%

( )(1 + i) n – 1

iPMTDue FVA n = (1 + i)

Amortized Loans

One of the most important applications of compound interest involves loans that are paid off in instalments over time.

1. Automobile Loans.

2. Home Mortgage Loans.

3. Student Loans.

If the Loans is said to be paid in equal periodic ($374.11) amounts, it is called amortized loans .

Link: Amortized Loans

Amortized Loans

Mathematically, we can calculate the payment due each period from the following equation.

( )1 – ( 1 / 1 + i )n

iPMTPVA n =

PVAn = £1000

i = 6%

n = 3

PMT = ?

( )1 – ( 1 / 1 + 0.06 )3

0.06PMT£1000 =

£1000 = PMT(2.6730)

PMT = £1000 / 2.6730 = £374.11

Cash Flow and Risk Estimation

Capital Budgeting and its estimation begins with the identification of the relevant cash flow.

Relevant cash flow can be defined as the specific set of cash flows that should be considered in the decision in hand.

Capital budgeting begins with the estimation of project’s cash flows – investment outlays and annual net cash flow after a project goes into operation.

Scope for errors:- • Capital budgeting decisions must be based on cash flows

and not on accounting income.

Cash Flow and Risk Estimation

Free Cash Flow is the cash available to all investors in the company – both shareholders and bondholders after consideration for taxes, capital expenditure and working capital investment.

Free Cash Flow =

How do you value a firm or a project ??

Firm’s / Project’s value depends on its free cash flows

NOPAT + Depreciation – Capital Expenditure – (+) Increase (Decrease)in Working Capital Investments

Cash Flow and Risk Estimation

Project Cash Flow Vs Accounting Income –

CAPEX - is incurred when a business spends money either to buy fixed assets or to add to the value of an existing fixed asset with a useful life that extends beyond the taxable year.

• Project Cash Flow – projects require assets and asset purchase leads to negative capital outflow.

• Accounting Income – do not show purchase of fixed assets as a deduction from accounting income.

Cash Flow and Risk Estimation

Non Cash Charges – Depreciation expenses are deducted to arrive at revenues. Accountants do not subtract the purchase price of fixed asset but deduct depreciation on a yearly basis. Depreciation itself is not a cash flow. Therefore it must be added back to NOPAT.

Net Operating Working Capital – New operations and project require additional capital. New operations will bring in additional account receivables, payables and accruals. The difference between the required increase in operating current assets and increase in operating current liabilities is the change in NOWC.

Cash Flow and Risk Estimation

Interest expenses are not included in the Project Cash Flow – Reasons:1) Project cash flow is discounted by its cost of capital.2) Cost of Capital is the weighted average of cost of debts,

preferred stocks & common equity adjusted for project’s risks.

3) WACC is the rate of returns expected / necessary to satisfy all of the project’s investors – Debt holders, Stock holders.

Therefore, the value of the projects by discounting those cash flows at the average rate required by all investors.

Note: We do NOT subtract interest when estimating project cash flow.

Cash Flow and Risk Estimation

Incremental Cash Flow – all those cash flows that occur, if and only, if we accept the project. These cash flows represent the firm’s total cash flow that occur as a direct result of accepting the project.

Sunk Costs – Sunk costs are cost that are incurred or occurred and the money invested is never recovered. Sunk costs are no incremental cost therefore it must not be included in the cash flow analysis.