Finance 1

Module 1: Objectives of a Firm, Financial Statement Analysis, and Accounting Returns

Book Value vs. Market Value

Book Value

\[Assets=Liabilities+Equity\]

\[Cash+AR+PPE=AP+Debt+Equity\]

\[Business\,Assets = Invested\,Capital\]

\[LHS=RHS\]

\[AR+PPE-AP=Debt+Equity-Cash\]

Debt(D): the amount of money invested by debtholders

Market capitalization (E): the market value of the company’s shares

Book Value of the Firm: the amount of many invested by all capital providers

\[V=D+BVE\]

Invested Capital / Book Value of the Business / Book Value of Business Assets:

\[IC=D+BVE-Cash=AR+PPE-AP\]

Market Value

Why Enterprise Value is different from Invested Capital?

1. Not all assets appear on the balance sheet. The company may have intangible capital that it has developed. GAAP accounting conventions prohibit this capital from appearing on the balance sheet.
2. Book value accounting records assets and liabilities are acquisition cost, not market value.
3. The company may have made NPV > 0 investments. The market value of AAPL will reflect the present value of the future cash flows that the asset is expected to generate. If this present value is different from the acquisition cost, then book value <> market value.

Market Capitalization (E): the market value of the company's share:

\[MVE = MktCap = Share Price * No. of Shares\]

Market Value of the Firm / $ to “Buy” the Firm:

\[V=D+MVE\]

Enterprise Value / $ to “Buy” the Business / Market Value of Business Assets: Business assets exlude Cash, include Operating Liabilities

\[EV=D+MVE-Cash=AR+PPE+Brand-AP\]

Market-to-Book Ratio

Market-to-Book Equity Shareholders only

\[Market-to-Book\,Ratio=\frac{Market\,Capitalization(MVE)}{Book\,Value\,of\,Equity(BVE)}\]

Market-to-Book Invested Capital All the capital providers (Debtholder+Shareholder)

\[Market-to-Book\,Invested\,Capital=\frac{Enterprise\,Value(EV)}{Invested\,Captital(IC)}=\frac{MVE+D-Cash}{BVE+D-Cash}\]

Market Value Added vs. Economic Value Added

\[Market\,Value\,Added=Enterprise\,Value(EV)-Invested\,Capital(IC)\]

An important difference between Market Value Added and Economic Value Added is that the latter takes into account the opportunity cost of capital. This might have happened over a long period of time. (Always equal to "plug")

\[Economic\,Value\,Added= (ROIC - OCC) * Capital\]

This is "how much profit the company earned PER UNIT capital (ie, the "return on capital"), minus how much they were "supposed to earn," multiplied by the total amount of capital that was deployed. We'll call the first part the ROIC ("Return on Invested Capital"). It is primarily about what happened last year not over many years.

Opportunity Cost of Capital (OCC): the return (or expected return) that the owners of the firm could earn on their money if they invested it elsewhere, in their "next best alternative."

Balance Sheet -> "Stock","as at a date" Income Statement -> "Flows","over the period of..."

Accounting Returns

Accounting Returns

\[Accounting\,Return=\frac{Accounting\,Profit}{Book\,Value\,of\,Capital}\]

• Measures of how much income was earned per-unit of capital required to earn this income.
• Measures of previous performance.
• Profit per dollar of capital.
• Standaized measure of profitability

Drawbacks associated with Accounting Rates of Return:

• The fact that they don't incorporate various intangible assets in the denominator.
• The fact that they do not incorporate investors beliefs about a company's future prospects.
• The fact that they are susceptible to a company's ability to manipulate it's published earnings to some degree.

Stock Returns: what I made / what I paid

\[Stock\,Return=\frac{Dividend+Current\,Stock\,Price-Purchase\,Price}{Purchase\,Price}=Dividend\,Yield+Capital\,Gain\]

Return on Invested Capital (ROIC)

accounting returns for the business (all capital providers)

\[Operating Profit - Sales Expenses = Net Income (NI) + Interest + Tax\]

Shareholders get NI; Debtholders get Interest; Government gets Tax.

ROIC assess financial performance for the whole firm, mesasure profit associated with all capital providers as a ratio of all capital invested. The ROIC is partly a reflection of how well the firm did this year.

\[ROIC=\frac{Net\,Operating\,Profit\,After\,Tax(NOPAT)}{D+BVE-Cash}=\frac{NOPAT}{IC}\]

\[ROIC=\frac{NOPAT}{Sales}*\frac{Sales}{IC}=Operating\,Efficiency*Capital\,Efficiency\]

• ROIC drives by profit margin or operating efficiency(NOPAT/Sales) and capital efficiency(Sales/IC).

Profit Margin: a measure of "operating efficiency", how much profit is generated by each dollar of sales.

\[\frac{NOPAT}{Sales}\]

Capital Efficiency: a measure of "capital efficiency", how many dollars of sales are generated by each dollar of capital.

\[\frac{Sales}{Invested\,Capital}\]

Return on Equity (ROE)

accounting returns for shareholders

\[ROE=\frac{Net\,Income(NI)}{Book\,Value of Equity(BVE)}\]

Net Operating Profit After Tax (NOPAT)

profit for the business

• NOPAT measures the profit generated by the business operations; measures profit going to all capital providers both debt and equity holders.
• Interest expense is a financing expense, not an operating expense. So we need to add interest expense back to Net Income to get to NOPAT.
• NOPAT is usually not provided on Income Statement.

\[NOPAT=Net\,Income+(1-Tax\,Rate)*Interest\,Expense=ROIC*IC\]

\[Tax\,Rate=\frac{Tax\,Expense}{Taxable\,Income}\]

NOPAT(Net Operating Profit After Tax) - Earning Before Interest (EBIT - TAX)

Net Income

profit for shareholders (owners) Revenue earnings after taking out all the expenses (including interest and tax).

Hurdle Rate

The Hurdle Rate(r) is the ROIC you could have earned on your next-best investment.

• Must have the same risk.
• Provide a benchmark to compare investments.
• Often use Industry Average.
• Benchmark to compare returns, evaluate whether a "good" return.
• Can express in dollars as "economic profit".

Opportunity Cost of Capital (OCC)

"If I invest elsewhere, what rate of return would I expect to receive?"

Break Even Profit: the amount of profit that the firm's owners could have earned by investing their capital in their "next best alternative".

\[Breakeven\,Profit=r*Invested\,Capital(IC)\]

Economic Profit

\[Economic\,Profit=NOPAT-Breakeven\,Profit=(ROIC-r)*IC\]

• if negative: under-performning the benchmark
• if positive: out performing the benchmark

Module 2: Tools for Investment Decision Making

Rates of Return and the Cost of Capital

Rates of Return

Riskless Return:

\[Return (irr)=\frac{Future\,Value-Today's\,Cost}{Today's\,Cost}=\frac{Future\,Value}{Today's\,Cost}-1\]

Expected Return:

\[Expected(Return)=\frac{Expected(Future\,Value)}{Today's\,Cost}-1\]

• Riskless rate of return or “interest rate” (future value is known).
• Risky rate of return (future value is a random variable).
• Expected return (based on expected value of the random variable).
• Realized return (possible outcome of the random variable).

Opportunity Cost of Capital

• The opportunity cost of capital provides a hurdle rate to evaluate investment opportunities of equivalent risk.
• The expected return on your investment is called the internal rate of return and denoted irr
• The opportunity cost of capital (or “cost of capital”) is denoted r
• Invest if irr > r (Rule #1)

irr (internal return rate) vs r:

• irr is specific to the project in question, and the project is typically not an asset that is traded in a liquid market.
• In contrast, the opportunity cost of capital is a rate from a traded investment, such as a U.S. T-bill or the S&P500 index*.

The Time Value of Money

Time Value of Money

Compute FV by multiplying today’s investment by \((1+r)^T\):

\[FV=PV(1+r)^T\]

Compute PV by dividing future value by \((1+r)^T\):

\[PV=\frac{FV}{(1+r)^T}\]

• irr typically refers non traded investments
• r => cost of capital / discount rate
• discount factor: 1/(1+r)
• If investment is riskless, r is an interest rate
• If the investment is risky, r is an expected return on traded investments of equivalent risk, e.g., the expected return on the S&P500.

Observations:

• A dollar today is worth more than a dollar tomorrow.
• A riskless dollar tomorrow is worth more than a risky dollar tomorrow. Why? Because the discount rate, r, is higher for risky investments.
• Dollars in different time periods are not directly comparable unless they are converted to present value OR future value using an appropriate discount rate.

Net Present of Value

A project’s net present value is the difference between the present value of its future payments and its cost:

\[NPV = PV - Cost\]

If NPV > 0, should invest, results in value creation for a company (Rule #2 - better and more flexible)

1. Riskier projects have a higher cost of capital
2. Cash flows that are further in the future, where T is larger, will be discounted more.

\[Share\,Price = \frac{MktCap+NPV}{Number\,of\,Shares}\]

The Capital Asset Pricing Model (CAPM)

A project's cost of capital is the rate of return on a traded asset of equivalent risk.

2 types of investment opportunities:

• traded, such as stock, bonds, real estate, etc (next best alternatives come from outside of the corporation; assume MV=PV)
• non-traded, such as internal investments made by firms (where we are focused in this course; no "market value")

Use the expected return from a traded asset of equivalent risk as the cost of capital when coming up with our estimate of the value of the non-traded asset

Arbitrage Example

• Buy the relatively underpriced bond. As many as you can.
• Pay for the bonds by borrowing from the bank at 2%.
• In one year, receive $100 for each bond and pay off the loan. The difference is known as an “arbitrage profit.”

Expected Return and Risk

\(r_i\) = return on the stock of firm i

\(E(r_i)\)= expected return on the stock of firm i

\(r_m\) = return on the stock market

\(E(r_m)\) =expected return on the stock market

\(r_f\) = riskless return

Risk Premium - the difference between the risky asset’s expected return and the risk-free return

\[ Risk\,Premium = Expected\,Return\,on\,Ricky\,Asset - Riskless\,Return\]

\[Risk\,Premium = E(r_i) - r_f\]

In the U.S., the equity market risk premium is 5-6%:

Equity Market Risk Premium

\[E(rm)=\frac{E(Future\,Price\,and\,Dividends)}{Today's\,Price}=\frac{E(P_t+D_t)}{P_0}\]

The CAPM

• Firm specific risk can be eliminated by “diversifying” or increasing the number of investments in your portfolio.
• Diversification reduces portfolio risk, but only to the level of non diversifiable or market risk.
• Returns on an individual firm are driven in part by market or systematic risk and in part by firm-specific or idiosyncratic risks.The latter type of risk may be eliminated with diversification, while market risk is non-diversifiable.
• Since investors can eliminate idiosyncratic risk, they only care about non-diversifiable risk.

Non-diversifiable risk is measured by the covariance of the returns on an individual asset with the returns on the market. We call this an asset’s “beta”:

Beta: market increase $1, asset increase by $beta / the sensitivity of the investment return to the market return

CAPM:

\[E(R_i)-r_f = β_i[E(r_m)-r_f]\]

\[E(R_i) = r_f+β_i[E(r_m)-r_f]\]

\[Equity\,Cost\,of\,Capital = Risk\,Free\,Rate + Beta * Equity\,Market\,Risk\,Premium\]

Estimated Beta:

• From a regression

• Use a high-quality 3rd party data

Module 3: Discounted Cash Flows

Multiple-Period Cash Flows

Multiple-Period Cash Flows

\[PV=\sum_{t=1}^{T} \frac{EV_t}{(1+r)^t}\]

Discount Rate

Excel Formula: irr()

Discount Factors

\[DF_t=\frac{1}{(1+r)^t}\]

\[PV = FV_t*DF_t=FV_t*\frac{1}{(1+r)^t}\]

Compounding and Annualization

5% interest every 6 months

Annual Percentage Rate(APR)=5%*2=10%

Effective Annual Rate =(1+5%)^2-1=10.25%

\[Effective Annual Rate =((1+\frac{r}{m})^n)-1\]

• r: annual rate
• m: number of compounding periods per year
• n: number of time periods

Perpetuities and Annuities

Perpetuities

A "perpetuities" is a constant payment, $c per-period forever.

\[PV=\frac{c}{r}\]

• c: cash receives per period
• r: cost of capital per period

Delayed Perpetuities

A delayed perpetuity starts t-periods after the next period.

\[PV=\frac{1}{(1+r)^t}\frac{c}{r}\]

• t: number of periods delayed

Growing Perpetuities

A growing perpetuity grows at rate g every period after the first payment.

\[PV=\frac{c}{r-g}\]

Delayed Growing Perpetuities

\[PV=\frac{1}{(1+r)^t}\frac{c}{r-g}\]

Annuities

An annuity is a series of constant periodic payments that start in the next period, and end after t periods.

A t-period annuity is a perpetuity less a t-period delayed perpetuity.

\[PV=\frac{c}{r}-\frac{1}{(1+r)^t}\frac{c}{r}=\frac{c}{r}(1-\frac{1}{(1+r)^t})=c*AF(r,t)\]

AF(r,t): Annuities Factor

Delayed Annuities

\[PV=\frac{c}{r}=\frac{1}{(1+r)^T}\frac{c}{r}(1-\frac{1}{(1+r)^t})=\frac{1}{(1+r)^T}*c*AF(r,t)\]

• T: number of periods delated

Module 4: Discounted Cash Flows

Free Cash Flow

Free Cash Flow: The amount of after-tax cash flow generated by a firm’s business operations.

Like NOPAT:

• Ignore interest expense, dividends and other payments to capital providers.

Unlike NOPAT:

• Excludes non-cash expenses, such as deprecation and amortization.
• Includes capital expenditures.
• Cash measure, so we must adjust accrual measures (revenue and expenses) for working capital changes.

To compute free cash flows we:

1. Start with NOPAT.

2. Subtract depreciation, depletion and amortization (DDE) expense.

3. Add CAPEX (Capital Expenditures: funds used by a company to acquire, upgrade, and maintain physical assets)

4. Adjust for changes in working capital: subtract the increase or add the reduction in WC.

Incremental Free Cash Flow

Only look at what changes based on the investment decision.

Working Capital

Working capital are assets and liabilities that support the operations of the business. * “Operating” assets and liabilities. * Includes accounts receivable, inventory, accounts payable, unearned income, etc. * These all have implications for cash flows.

Steps: 1. Compute working capital balance: WC = AR + Inventory - AP - Unearned Revenue 2. Compute the increase in WC: This periods WC – last period’s WC 3. Subtract the increase in WC from NOPAT

• Unearned Revenue: Custmer Pay Advance
• Accounts Receivable
• Accounts Payable
• Inventories

Why does unearned revenue (eg. gift card) increase enterprise value?

• Getting cash receipt upfront
• Customer may not use
• Discounted Cashflow (value of $1 today is worth more than $1 in the future) Getting cash sooner than later

Module 5:Valuing a Firm

The Dividend Discount Model

The firm's share price P_t is equal to the present value of all the expected future dividend payments:

\[P_t=\frac{d_t+1}{1+r}+\frac{d_t+2}{(1+r)^2}+\frac{d_t+3}{(1+r)^3}+...\]

Multiple of Comparables

\[Value = f(Earnings)= M * Earnins\]

price/dividend ratio -> not often used in practice as some firms don't pay devidends

price/earnings(P/E) ratio -> a better ratio

Discounted Cash Flow Valuation

\[EV_t=\frac{FCF_t+1}{1+r}+\frac{FCF_t+2}{(1+r)^2}+\frac{FCF_t+3}{(1+r)^3}+...\]

\[E=EV+Cash-D\]

Module 6:Leverage and Capital Structure

Step 1: Expected Return for both scenarios (irr_1; irr_2)

Step 2: Expected Return Overall: p_1x_1+p_2x_2

\[E(x)=p_1*x_1+p_2*x_2\]

\[Var(x)=E[x-E(x)^2]=E(x^2)-(E(x))^2=p_1*x_1^2+p_2*x_2^2-(p_1*x_1+p_2*x_2)^2\]

x_1 - expected return scenario 1 (irr_1)

x_2 - expected return scenario 2 (irr_2)

"Volatility" -> Stand Deviation / Risk

\[Stdev(x)=\sqrt[2]Var(x)\]

Project with Multiple Scenarios:

Step 1: Cost of Capital

\[Equity\,Cost\,of\,Capital = Risk\,Free\,Rate + Beta * Equity\,Market\,Risk\,Premium\]

Step 2: Expected Future Value (Payoff_1 * Probability_1 + Payoff_2 * Probability_2)

Step 3: Expected Present Value (discount back using r - cost of capital)

Step 4: NOPAT (PV-Cost)

Step 5: Internal Rate of Return (irr)

\[Expected(Return)=\frac{Expected(Future\,Value)}{Today's\,Cost}-1\]

Portfolio returns are value-weighted averages of the returns of the stocks that are in the portfolio:

\[r_p = w(AEO) * r(AEO) + w(GPS) * r(GPS) = w(AEO) * r(AEO) + (1 - w(AEO)) * r(GPS)\]

\[R_AEO = \frac{P(AEO,Jun)}{P(AEO,Mar)} - 1\]

\[R_GPS = \frac{P(GPS,Jun)}{P(GPS,Mar)} - 1\]

\[w_AEO = \frac{P(AEO,Mar)}{P(P,Mar)}\]

\[w_GPS = 1 - w(AEO)\]

The financial structure of the project doesn't change the payoff and the return of the project but it change how the return will be split among the equity and debt providers. Adding debt makes equity much riskier.

Risky Debt - higher counpon rate (higher than the risk-free rate) for the up-state

Example:

Capital Structure

All Cash = 100% Equity Financing

What is Leverage

Leverage arises from the relationship between variable revenues and expenses, and fixed costs.

Operating leverage means that a percentage change in sales revenue will result in a higher percentage change in earnings if the firm has fixed costs.

Financial leverage is determined by the firm's financing decisions. Debt creates interest expense, which is like another a fixed cost impacting the returns to equity holders.

Financial leverage increases volatility and expected return of equity in an investment.

100% Cash (Equity):

50% Cash(Equity) + 50% Debt:

Leverage and Beta

• A levered firm is not necessarily riskier than an unlevered firm, but the equity is riskier.
• Shareholders can manage this risk through diversification.
• Debt increases the risk to equity holders but not the business. Financing decisions do not impact risk and return generated by business assets.
• Debt increases the value of the firm because of tax shields.
• Firms should find the “optimal” amount of debt by trading off the benefits of debt (e.g. tax shields, flexibility) against the costs of debt (e.g. bankruptcy).
• Leverage doesn't affect the value of the firm, and therefore, it doesn't affect the firm's optimal investment policies.

\[V=Cash+Business\,Assets=Debt+Equity\]

\[E(rV)=\frac{CASH}{V}E(rCASH)+\frac{BA}{V}E(rBA)=\frac{D}{V}E(rD) + \frac{E}{V}E(rE)\]

\[β_v=\frac{CASH}{V}β_CASH + \frac{BA}{V}β(BA) = \frac{D}{V}β_D + \frac{E}{V}β_E\]

β_CASH = 0; β_D often = 0

\[β(BA) = β_D * \frac{D}{BA} + β_E * \frac{E}{BA}\]

AEO (No Debt):

GPS (Debt):

Cash lowering down the risk of the firm, β(v) < β(BA)

Debt increasing the risk of the equity relative to the firm, β(E) > β(v)

In the end, β(BA) = β(E)

With Debt In downstream, if project value < debt amount + interest, the debt holders only get the project value.

Bond is a debt security.

Convertible Bond is a hybrid debt/equity.

Capital Structure and Firm Value

Miller-Modigliani Theorem ((M&M)

In frictionless capital markets, capital structure does not change the value of the firm.

• Capital structure is about dividing up the cash flows between debt and equity providers.
• How cash flows are divided does not change the magnitude or present value of the cash flows.
• The division of cash flows does however affect the value of debt and equity.

Miller-Modigliani Theorem ignores frictions (eg. tax).

Debt Policy (Certainty):

Debt Policy (Uncertainty):

Capital Structure and Taxes

\[V_L≈V_U+τ*D\]

V_L = Value of the levered firm

V_U = Value of the firm if it had no debt

D = Value of debt

τ = tax rate

Tax Shield: Debt reduces a company’s taxes, which creates value.

Implication? PV(FCF) will understate the value of a levered firm! Two Fixes:

• Adjust the cash flows (Adjusted Present Value, APV)
• Adjust the discount rate (WACC)

levered recapitalization - issuing new debt and paying out the proceeds to shareholders

Issue Debt to Pay Devidend

1. Announcement of the levered recapitalization (Tax Shield)
2. Company Value Increase = τ*D
3. Since debt doesn't change (yet), this results in an increase in the value of equity.
4. Equity Value Increase = τ*D ; Share Price Increase = Equity Value Increase / No. of Shares
5. Issuance of the debt and payment of the dividend
   1. Now the value of debt increases, but the value of the company doesn't change.
   2. Equity Value Decrease, Share Price Decrease

Weighted Average Cost of Capital

Value of the Firm = Sum of PV(FCF)

Problem: FCF Analysis based on NOPAT ignores the impace of Capital Structure; it will value a leveraged company too low

WACC is a discount rate for discounted cash flow analysis that incorporates the value of tax shield.

Assume the following:

1. A constant after-tax expected free cash flow, c, in perpetuity for an unlevered firm.
2. Constant, riskless debt, D, in perpetuity with an interest rate r_f.
3. Opportunity cost of capital, r. (assciated with the business assets)

\[WACC=r_D(1-τ)\frac{D}{V}+r_E\frac{E}{V}\]

Value of Tax Shields:

\[PV(Tax\,Shields)=τD\]

Levered Firm Value:

\[V=\frac{c}{r}+τD\]

Weighted Average Cost of Capital:

\[WACC=r(1-τ\frac{D}{V})\]

Bankruptcy

1. Failure to pay part or all of a coupon to debt providers. This is a liquidity problem.

2. Inability to repay the principal of the debt. For example, the value of the debt is larger than the present value of the free cash flows (i.e., the enterprise value.) This is insolvency.

3. Violation of debt covenants, which may include maintaining various financial ratios. These can be specific to the company and the debt issue. This is not necessarily a cash flow issue but can trigger default.

\[V_L=V_U + Value\,of\,tax\,saving\,of\,interest - Value\,of\,bankruptcy\,costs\]