Corporate Finance

CORPORATE FINANCE FICHES

TOPIC 1 : REVIEW OF FINANCIAL MATHEMATICS

Investment project : series of future cash flows/out flows

2 pbs:

• mesure the value of series
• decide whether it is worth (valoir/mériter) its price/cost/investment and should be adopted (or not)=  a decision criterion is needed

1. Value

PV= Present Value = the value of a series of future cash-flows + the maximum price to pay for the series.

E(CFt)= Expented cash flow

R= discount rate[pic 1]

[pic 2]

PV= [pic 3]

The higher the risk, the larger the discount rate, the lower the PV.

1. Decision Criterion

In order to obtain the project and transform it into an activity, a price must be paid= a CASH OUTFLOW now, at time 0. Often called “the investment” or I0.

NPV= Comparison of the PV with the necessary investment

NPV= NPV = - I0 + PV

Decision criterion:

• adopt if NPV ≥0
• reject if NPV < 0

1. Nature And Meaning Of NPV

1. NPV=0

NPV = - I0 + = 0[pic 4]

I0 (1+r)2 = E(CF1) x (1+r) + E(CF2) = Final Value (FV) of the investment

The FV shows that, through the future CFs, you can expect to recover your initial investment (I0) and earn, on average, the required yearly return.

1. NPV is expressed in terms of a specific currency (monnaie spécifique). What does this quantity represent?

It is the PV of the “excess” or “abnormal” portion of future expected cash flows.

1. Two words of caution

• NPV is based on expectations. Reality may differ ex-post (be better or worse than expected)
• Large positive NPVs should not be frequent and should appear only if the business enjoys a long-term advantage which competitors cannot obtain.

1. Projects With Long Lives

Discounting over 30 years or more? Shortcuts may be needed. (Un rabais sur 30 ans ou plus? Des raccourcis peuvent être nécessaires.)

Called final value, horizon value, resale value… Shortcuts to choose from:

• Perpetual annuity (flat perpetuity)

Vn = [pic 5]

• Growing/decreasing perpetuity

Vn = [pic 6]

1. Alternative Criterion: The IRR

IRR: Internal rate of return

IRR= the discount rate that will bring NPV to 0

Decision criterion: if IRR ≥ required rate of return (cost of capital), go ahead

                         if  IRR < required rate of return (cost of capital), don’t

The IRR is a popular decision criterion, easy to understand, but it presents several problems:

• Problem 1: a dubious reinvestment assumption (reinvesting at exceptional rates) une hypothèse de réinvestissement douteuse
• Problem 2: there may exist multiple IRRs for the same project, all mathematically correct. Potentially as many IRRs as there are sign reversals in the series of cash-flows.
• Problem 3: when comparing mutually exclusive projects, the IRR tends to unduly favor

• small scale projects over larger scale ones
• projects with early relatively large cash-flows over projects with more progressive cash-flows

(The NPV criterion should be preferred)

1. Alternative Criterion: The Payback Period

Calculation: How many periods does it take to recover the original investment through future expected cash-flows?

Limit: arbitrary decision criterion, ignores the cost of capital and the time value of money, ignores the other cash-flows and may lead to wrong decisions when projects are mutually exclusive.( critère de décision arbitraire, ignore le coût du capital et la valeur temporelle de l'argent, ignore les autres flux de trésorerie et peut conduire à de mauvaises décisions lorsque les projets sont mutuellement exclusifs.)

TOPIC 2 : CAPITAL BUDGETING

Capital budgeting=  the process through which firms analyze alternative projects and decide which ones to accept.

A capital budget lists the projects and investments that a company plans to undertake during the coming year.

• To evaluate projects, firms need to forecast the projects’ future consequences for the firm.

• Main lines of reasoning (principaux axes de réfléxions) 

Any well-advised investment decision must respect the following principles:

• consider cash flows (flux de trésorerie) rather than accounting data
• reason in terms of incremental cash flows, considering only those associated with the project
• reason in terms of opportunity
• disregard the type of financing
• consider taxation
• be consistent

1. Reason in terms of cash flows

Return on an investment is assessed in terms of the resulting cash flows.( Le rendement d'un investissement est évalué en fonction des flux de trésorerie qui en résultent.)

Accounting income or expenses are not actual cash flows, because : Les produits ou les charges comptables ne sont pas des flux de trésorerie réels, car

• they do not take into account the time lags between accounting recognition in the income statement and what really happens in the cash account (revenue is not = cash inflow, cost are not = cash outflows); influence of commercial credit policies and of inventory policy. (ils ne tiennent pas compte des délais entre la comptabilisation dans le compte de résultat et ce qui se passe réellement dans le compte de trésorerie (les recettes ne sont pas = entrées de trésorerie, les coûts ne sont pas = sorties de trésorerie) ; influence des politiques de crédit commercial et de la politique des stocks.)

• they include depreciation which is a non-cash item. (ils comprennent l'amortissement qui est un élément non monétaire.)

As a result, only cash flows are relevant in the financial analysis of investments.

1. Reason in terms of incremental cash flows

Incremental flows= the flows by which the firm’s cash flows are expected to change as a result of investment decisions. (Les flux incrémentiels sont les flux par lesquels les flux de trésorerie de l'entreprise sont censés changer à la suite des décisions d'investissement.)

When estimating cash flows on an incremental basis, one only considers the future cash flows arising from the investment.

Sunk costs= are costs that have been or will be paid regardless of the decision whether or not the investment is undertaken. Sunk costs should not be included in the incremental earnings analysis

Project externalities are indirect effects of the project that may increase or decrease the cash-flows of other business activities of the firm. They should be taken into account in capital budgeting. One example of externalities is cannibalization, when sales of an existing product displace sales of an existing product.

1. Reason in terms of opportunity costs

Opportunity cost is the value an existing resource could have provided in its best alternative use (Le coût d'opportunité est la valeur qu'une ressource existante aurait pu fournir dans sa meilleure utilisation alternative)