Corporate finance

CORPORATE FINANCE

I. Firm and financial markets

Corporations make decisions by investing in real assets (tangible and intangible) used to produce goods and services.

Corporations finance assets in 3 ways:

• Borrowing
• Retaining and reinvesting cash flow
• By selling additional shares to shareholders

However investments and financial decision lead to capital structure choices :

• Investment decisions ⇒ purchase of real assets. Capital budgeting, choices on how to allocate capital to investments projects.
• Financing decisions ⇒ sale of financial assets. Capital structure, choice between debt and equity financing.

Shareholders desire wealth maximization. Agency problems : conflicts between management and owners of the corporation.

II. Time value of money

Having one dollar today is worth more than having the same dollar two years in the future.

Future value : future value of a cash flow of C$ in T years when invested at a rate-of-return r.

FV(C) = $C x (1+r)t

Present value : present value of a cash flow of C$ to be received in T years when the interest rate is r.

PV(C) = $C / (1+r)t  = $C x [discount factor at r, maturity T]

1° Value additivity

Financial assets have cash flows that span many periods. To assess the desirability of an investments, have to calculate the PV of the total series of cash flows and add them together.

Net present value : present value of the cash inflows minus the present value of the cash outflows.

NPV = Cf0 + Cf1 / (1+r) + Cf2 / (1+r)2 + … + CfT / (1+r)t

2° Perpetuities

A perpetuity is a constant stream of cash flows, C, that occur every unit period and continues forever.

Present value of a stream of cash flows : cash flows C starting in one period and lasting forever.

PV (perpetuity) = C / (1+r) + C / (1+r)2 + … + C / (1+r)t

                                                                 = C / r

3° Growing perpetuities

A growing perpetuities is a stream of cash flows, Ct which occur every unit period and continues forever. Cash flows are equal at the end of the first year and grow at a constant rate, g every unit period after.

Present value of growing perpetuities :

PV (growing perpetuities) = C / r - g

4°Annuities

Constant stream of cash flows, that occurs every year for a fixed number of unit period.

Present value of an annuity : annuity with a maturity of T can be replicated with two perpetuities.

PV (annuity) = C / r - 1 / (1+r)t x C / r

                                                                          = C x [annuity factor at r, maturity T]

                                                                          = C x 1 / r x (1 - 1 / (1+r)t)

5° Growing annuities

Stream of cash flows that occurs every unit period for a fixed number of period.

PV (growing annuities) = C / (r - g) - 1 / (1+r)t x C(1+g)t / (r - g)

                                           = C / (r - g) x (1 - (1+g)t / (1+r)t)

III. The equivalent annual cost

Good to know the NPV, but sometime useful to reverse the calculation and determine the value of the cash flow (equivalent annual cost).

EAC = (NPVproject * r) / 1 - 1 / (1+r)t

IV. Bonds

A bond is a loan issued with specific conditions by an issuer subscribed or purchased by a counterparty called subscriber or purchaser.

Each bond is determined by a series of parameters :

• The coupon ⇒ % of the nominal value paid at specific dates.
• Start and maturity date ⇒ life of the bond.
• Issue price ⇒ percentage of the nominal value.
• Redemption price ⇒ percentage of the nominal value.

Future cash flows are fixed so risk is much lower in comparison to shares. The present value of a bond is the summation of two discounted cash flows :

PV = CA + CB

CA = PV of annual interests payments.

CB = PV of final payment.

PV = C1 / (1+r) + C2 / (1+r)2 + … + 1000 + CT / (1+r)T

V. Share

A share represents a piece of ownership in the firm, give the right of vote and is entitle to receive dividends.

The value of a share is equal to the sum of the present value of future dividends :

Value = Σ Dividends t / (1+k)t

VI. Project appraisal

1° The Net Present Value

NPV = the present value of the cash inflows minus the present value of the cash outflows.

• If NPV < 0 ⇒ project decreases the value of the firm by the amount of the NPV.
• If NPV > 0 ⇒ project is worthwhile, it increases the value of the firm.

2° Alternative methods

• Payback, discounted payback ⇒ period which elapses until the initial outlay has been recouped.

• Internal rate of return ⇒ rate at which the project cash flows have a zero NPV. The IRR is the rate for which the NPV is equal to 0.

C0 + C1 / (1+IRR) + C2 / (1+IRR)2 + … + CT / (1+IRR)T = 0

• Profitability Index ⇒ ratio of the present value of the project cash flows divided by the initial investment C0.

Profitability Index : PV / ⎮C0⎮

VII. Risk and return

1° Characterizing assets returns

Two steps to determine the expected rate of return on a risky asset :

• Consider all the possible outcomes and attach a probability to each outcome.
• Compute the return corresponding to each outcome and compute the weighted average.

Example :

IBM initial value = 1,000

Possible future value = 860 with probability 0.20, 1,035 with probability 0.60 and 1,170 with probability 0,20.

Corresponding returns =

• (860 - 1,000) / 1,000 = -14%,
• (1,035 - 1,000) / 1,000 = 3.5%
• (1,170 - 1,000) / 1,000 = 17%

Expected return on asset : sum of probability * associated return.

⇒ E(rIBM) = rIBM = p1.r1 + p2.r2 + p3.r3

Variance : measure how much the actual return is likely to differ from the expected return.

⇒ Var(rIBM) = σ2IBM = p1(r1 - rIBM)2 + p2(r2 - rIBM)2 + p3(r3 - rIBM)2

 Standard deviation : square root of the variance. It measures the total risk of the asset.

⇒ STD [rIBM] = √VAR(rIBM) = σIBM

Covariance : a measure of the degree to which two assets returns “vary together”.

⇒ Cov(rIBM,rGE) = σIBM,GE