Finance Final (Chapter 4,5,6,7,8,9,11,13)
Term Structure
The relationship between time to maturity and yields, all else equal - The effect of default risk, different coupons, etc. has been removed.
The security market line (SML) is the representation of ___________ equilibrium
The security market line (SML) is the representation of market equilibrium The slope of the SML = reward-to-risk ratio:
M&M Proposition I with Taxes
The value of the firm increases because of the interest tax shield. This is the basis of the M&M Proposition I with taxes.
How does Leverage effect variability in Return on Equity (ROE) and EPS (Earnings Per Share)?
The variability in both ROE and EPS increases when financial leverage is increased Variability in ROE Current: ROE ranges from 6.25% to 18.75% Proposed: ROE ranges from 2.50% to 27.50% Variability in EPS Current: EPS ranges from $1.25 to $3.75 Proposed: EPS ranges from $0.50 to $5.50
How do you find the discount rate?
To find the implied interest rate, rearrange the basic PV equation and solve for r: FV = PV(1 + r)^t r = (FV / PV)^1/t - 1 If using formulas with a calculator, make use of both the yx and the 1/x keys
Returns
Total Return = Expected return + unexpected return R = E(R) + U Unexpected return (U) = Systematic portion (m) + Unsystematic portion (ε) Total Return = Expected return E(R)+ Systematic portion (m) + Unsystematic portion ε = E(R) + m + ε
Treasury Quotations 5/15/2030 6.250 149.4063 149.4688 -0.0938 2.353 When does the bond mature? What is the coupon rate on the bond? What is the bid price? What does this mean? What is the ask price? What does this mean? How much did the price change from the previous day? What is the YTM based on Ask price?
Treasury Quotations 5/15/2030 6.250 149.4063 149.4688 -0.0938 2.353 - Maturity = May 15, 2030 - Coupon rate = 6.250% per year - Bid price = 149.4063 % of par + Price at which dealer is willing to buy from you - Ask price = 149.4688 % of par + Price at which dealer is willing to sell to you - Bid-Ask Spread = Dealer's profit (.0625) - Change = ask price is down 0.0938 % since the previous day - Asked Yield = 2.353%
What are Treasury Securities? Government Bonds
Treasury Securities = Federal government debt - Treasury Bills (T-bills) + Pure discount bonds + Original maturity of one year or less - Treasury notes + Coupon debt + Original maturity between one and ten years - Treasury bonds + Coupon debt + Original maturity greater than ten years
What is Reinvestment Rate Risk?
Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds
"Leverage"
Use of debt in capital structure
Valuing a Premium Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 20 years YTM = 8%
Using the calculator: 20 N 8 I/Y 100 PMT 1000 FV CPT PV = -1196.36 Using the formula: B = PV(annuity) + PV(lump sum) B = 981.81 + 214.55 = 1196.36
Valuing a Discount Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 5 years YTM = 11%
Using the calculator: 5 N 11 I/Y 100 PMT 1000 FV CPT PV = -963.04 Using the formula: B = PV(annuity) + PV(lump sum) B = 369.59 + 593.45 = 963.04
What do variance and standard deviation measure?
Variance and standard deviation measure the volatility of returns Variance = Weighted average of squared deviations Standard Deviation = Square root of variance
What is the equation for WACC?
WACC = RA = (E/V) x RE + (D/V) x RD RE = RA + (RA - RD) x (D/E) RA = the "cost" of the firm's business risk (i.e., the risk of the firm's assets) (RA - RD)(D/E) = the "cost" of the firm's financial risk (i.e., the additional return required by stockholders to compensate for the risk of leverage)
When the YTM is greater than the coupon rate and the par is greater than the price, than the bond is a _________ bond.
When the YTM is greater than the coupon rate and the par is greater than the price, than the bond is a discount bond. When YTM > Coupon rate Price < Par = "Discount Bond"
What is a par bond? Bond Prices: Relationship Between Coupon and Yield
When the coupon rate is equal to the YTM or when price is equal to par. Coupon rate = YTM Price = Par
What is a discount bond? Bond Prices: Relationship Between Coupon and Yield
When the yield to maturity is greater than the coupon rate and the price is less than par. Coupon rate < YTM Price < Par
What is a premium bond?
When the yield to maturity is less than the coupon rate and the price is greater than par. Coupon rate > YTM Price > Par
Whenever there is a conflict between NPV and another decision rule, always use ______ Conflicts Between NPV and IRR
Whenever there is a conflict between NPV and another decision rule, always use NPV NPV directly measures the increase in value to the firm IRR is unreliable in the following situations: - Non-conventional cash flows - Mutually exclusive projects
Maturity
Years until bond must be repaid
You ALWAYS need to make sure that the interest rate and the ____________ match.
You ALWAYS need to make sure that the interest rate and the time period match. Annual periods -> annual rate. Monthly periods -> monthly rate.
You can afford $632 per month. Going rate = 1%/month for 48 months. How much can you borrow? Annuity Example 5.5
You borrow money TODAY so you need to compute the present value.
How do you develop a model to price a stock?
You could continue to push back when you would sell the stock You would find that the price of the stock is really just the present value of all expected future dividends
Capital restructuring
changing the amount of leverage without changing the firm's assets
Annuity
finite series of *equal* payments that occur at *regular* intervals If the first payment occurs at the end of the period, it is called an *ordinary annuity* If the first payment occurs at the beginning of the period, it is called an *annuity due*
Perpetuity
infinite series of equal payments.
What is Financial leverage?
the use of debt Leverage amplifies the variation in both EPS and ROE
List of Relevant Cash Flows
"Sunk" Costs ..................... N Opportunity Costs ............... Y Side Effects/Erosion............ Y Net Working Capital....................... Y Financing Costs....................... N Tax Effects .................................. Y
Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? Zero Growth Dividend
$20
Coupon rate
(risk characteristics of the bond when issued) Usually about equal to the Yield at issue Usually ≈ yield at issue
IRR & Non-Conventional Cash Flows
*"Non-conventional"* - Cash flows change sign more than once - Most common: + Initial cost (negative CF) + A stream of positive CFs + Negative cash flow to close project. + For example, nuclear power plant or strip mine. - More than one IRR .... - Which one do you use to make your decision?
What is the decision rule for IRR?
*Accept the project if the IRR is greater than the required return*
Interest Tax Shield
*Annual interest tax shield:* - Tax rate times interest payment - $1,000 in 8% debt = $80 in interest expense - Annual tax shield = .30($80) = $24 *Present value of annual interest tax shield* - Assume perpetual debt - PV = $24 / .08 = $300 - PV = D(RD)(TC) / RD = D*TC = $1,000(.30) = $300
Bankruptcy can be _________ and slow
*Bankruptcy can be expensive and slow* - Prepacks: pre-packaged filings - Cram-downs: court-ordered plan acceptance - Section 363: auction-like bankruptcy - Workouts: negotiated extensions or payments
What are the Three Special Cases of the Capital Structure Theory?
*Case I - Assumptions:* - No corporate or personal taxes - No bankruptcy costs *Case II - Assumptions:* - Corporate taxes, but no personal taxes - No bankruptcy costs *Case III - Assumptions:* - Corporate taxes, but no personal taxes - Bankruptcy costs
What are the conclusions we can draw from each of the three cases?
*Case I - no taxes or bankruptcy costs:* - No optimal capital structure *Case II - corporate taxes but no bankruptcy costs* - Optimal capital structure = 100% debt - Each additional dollar of debt increases the cash flow of the firm *Case III - corporate taxes and bankruptcy costs* - Optimal capital structure is part debt and part equity - Occurs where the benefit from an additional dollar of debt is just offset by the increase in expected bankruptcy costs
The Capital Structure Question Figure 13.6
*Case I:* With no taxes or bankruptcy costs, the value of the firm and its weighted average cost of capital are not affected by capital structures. *Case II* With corporate taxes and no bankruptcy cots, the value of the firm increases and the weighted average cost of capital, WACC, decreases as the amount of debt goes up. *Case III* With corporate taxes and bankruptcy costs, the value of the firm, VL, reaches a maximum as D*, the optimal amount of borrowing. At the same time, the weighted cost of average capital, WACC, is minimized at D*/E*.
Dealers vs. Brokers
*Dealer*: Maintains an inventor Ready to buy or sell at any time Think "Used car dealer" *Broker*: Brings buyers and sellers together Think "Real estate broker"
*Decision Rule: ___________ the project if the AAR is greater than target rate.*
*Decision Rule: Accept the project if the AAR is greater than target rate.*
What is another bankruptcy cost?
*Financial distress* - Significant problems meeting debt obligations - Most firms that experience financial distress do not ultimately file for bankruptcy
Changes in NWC
*GAAP requirements:* - Sales recorded when made, not when cash is received + Cash in = Sales - ΔAR - Cost of goods sold recorded when the corresponding sales are made, whether suppliers paid yet or not + Cash out = COGS - ΔAP - Buy inventory/materials to support sales before any cash collected
Independent versus Mutually Exclusive Projects
*Independent:* The cash flows of one project are unaffected by the acceptance of the other. *Mutually Exclusive* The acceptance of one project precludes accepting the other.
What are two disadvantages of sensitivity and scenario analysis?
*Neither provides a decision rule.* - No indication whether a project's expected return is sufficient to compensate for its risk. *Ignores diversification.* - Measures only stand-alone risk, which may not be the most relevant risk in capital budgeting.
What is the equation for Net Salvage Cash Flow? Tax Effect on Salvage
*Net Salvage Cash Flow = SP - (SP-BV)(T)* *Where:* SP = Selling Price BV = Book Value T = Corporate Tax Rate
What are some Features of Preferred Stock?
*Preferred Stock Dividends:* - Must be paid before dividends can be paid to common stockholders - Not a liability of the firm - Can be deferred indefinitely - Most preferred dividends are cumulative + Missed preferred dividends have to be paid before common dividends can be paid Preferred stock generally does not carry voting rights
Primary vs. Secondary Markets
*Primary Market*: New-issue market *Secondary Market:* Existing shares traded among investors
Pro Forma Statements and Cash Flow
*Pro Forma Financial Statements:* Projects future operations *Operating Cash Flow:* OCF = EBIT + Depr - Taxes OCF = NI + Depr if no interest expense *Cash Flow From Assets:* CFFA = OCF - NCS -ΔNWC NCS = Net capital spending
Case I - Propositions I and II
*Proposition I: The Pie Model* - The value of the firm is NOT affected by changes in the capital structure - The cash flows of the firm do not change; therefore, value doesn't change *Proposition II: WACC* - The WACC of the firm is NOT affected by capital structure
What is a Managerial Recommendation regarding risk of financial distress?
*Risk of financial distress:* - The greater the risk of financial distress, the less debt will be optimal for the firm - The cost of financial distress varies across firms and industries
What are two reasons why NPV Profiles Cross?
*Size (scale) differences:* - Smaller project frees up funds sooner for investment. - The higher the opportunity cost, the more valuable these funds, so high discount rate favors small projects. *Timing differences:* - Project with faster payback provides more CF in early years for reinvestment. - If discount rate is high, early CF especially good
What is a Managerial Recommendation regarding taxes?
*Taxes:* - The tax benefit is only important if the firm has a large tax liability - Higher tax rate → greater incentive to use debt
The right to file bankruptcy has __________ value
*The right to file bankruptcy has strategic value* - Immediate "stay" on creditors - Ability to terminate labor agreements - Ability to lay off large numbers of workers - Ability to reduce wages
What are four Factors Affecting Required Return?
- *Default risk premium* - bond ratings - *Taxability premium* - municipal versus taxable - *Liquidity premium* - Bonds that have more frequent trading will generally have lower required returns - *Maturity premium* - Longer term bonds will tend to have higher required returns. *Anything else that affects the risk of the cash flows to the bondholders will affect the required returns*
Modigliani and Miller Capital Structure Theory
- *Modigliani and Miller:* + M&M Proposition I - The Pie Model + M&M Proposition II - WACC - The value of the firm is determined by the cash flows to the firm and the risk of the firm's assets - Changing firm value + Change the risk of the cash flows + Change the cash flows
What are three features of common stock?
- *Voting Rights* + Stockholders elect directors + Cumulative voting vs. Straight voting + Boards are often staggered, or "classified" + Proxy voting - *Classes of stock* + Founders' shares + Class A and Class B shares - *Other Rights* + Share proportionally in declared dividends + Share proportionally in remaining assets during liquidation + Preemptive right ++ Right of first refusal to buy new stock issue to maintain proportional ownership if desired
Capital Budgeting
- Analysis of potential projects - Long-term decisions - Large expenditures - Difficult/impossible to reverse - Determines firm's strategic direction
Announcements, News, and Efficient Markets
- Announcements and news contain both expected and surprise components - The surprise component affects stock prices - Efficient markets result from investors trading on unexpected news + The easier it is to trade on surprises, the more efficient markets should be - Efficient markets involve random price changes because we cannot predict surprises
What are some conclusions we can make about portfolios?
- As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio + σp falls very slowly after about 40 stocks are included + The lower limit for σp ≈ 20% = σM. - Forming well-diversified portfolios can eliminate about half the risk of owning a single stock
The Bond Indenture Loan Agreement Contract between issuing company (BORROWER) and bondholders (LENDERS) includes what six aspects?
- Basic terms of the bonds - Total amount of bonds issued - Secured versus Unsecured - Sinking fund provisions - Call provisions - Deferred call - Call premium - Details of protective covenants
What is financial distress?
- Business failure - business terminated with a loss to creditors - Legal bankruptcy - petition filed in federal court for bankruptcy - Technical insolvency - firm unable to meet debt obligations - Accounting insolvency - book value of equity is negative
What are some Disadvantages of IRR?
- Can produce multiple answers - Cannot rank mutually exclusive projects - Reinvestment assumption flawed
Capital Rationing
- Capital rationing occurs when a firm or division has limited resources + Soft rationing - the limited resources are temporary, often self-imposed + Hard rationing - capital will never be available for this project - The profitability index is a useful tool when faced with soft rationing
How long does it take to recover the initial cost of a project? Payback Period
- Computation + Estimate the cash flows + Subtract the future cash flows from the initial cost until initial investment is recovered + A "break-even" type measure *Decision Rule: Accept if the payback period is less than some preset limit*
What are three main problems with scenario analysis?
- Considers only a few possible outcomes - Assumes perfectly correlated inputs + All "bad" values occur together and all "good" values occur together - Focuses on stand-alone risk, although subjective adjustments can be made
What are some Managerial Options regarding Capital Investment Decisions?
- Contingency planning - Option to expand - Expansion of existing product line - New products - New geographic markets - Option to abandon + Contraction + Temporary suspension - Option to wait - Strategic options
What are floating rate bonds?
- Coupon rate floats depending on some index value - Examples - adjustable rate mortgages and inflation-linked Treasuries - Less price risk with floating rate bonds - Coupon floats, so is less likely to differ substantially from the yield-to-maturity - Coupons may have a "collar" - the rate cannot go above a specified "ceiling" or below a specified "floor"
What is the principle of diversification?
- Diversification can substantially reduce risk without an equivalent reduction in expected returns + Reduces the variability of returns + Caused by the offset of worse-than-expected returns from one asset by better-than-expected returns from another - Minimum level of risk that cannot be diversified away = systematic portion
What are three weaknesses of sensitivity analysis?
- Does not reflect diversification. - Says nothing about the likelihood of change in a variable. - Ignores relationships among variables.
Decision Criteria Test Payback
- Does the payback rule: + Account for the time value of money? + Account for the risk of the cash flows? + Provide an indication about the increase in value? + Permit project ranking? - Should we consider the payback rule for our primary decision rule?
Advantages of AAR
- Easy to calculate - Needed information usually available
Par value
- Face amount - Re-paid at maturity - Assume $1,000 for corporate bonds
Constant dividend/Zero Growth
- Firm will pay a constant dividend forever - Like preferred stock - Price is computed using the perpetuity formula
IRR assumes reinvestment at ________ Reinvestment Rate Assumption
- IRR assumes reinvestment at IRR - NPV assumes reinvestment at the firm's weighted average cost of capital (opportunity cost of capital) + More realistic + NPV method is best - NPV should be used to choose between mutually exclusive projects
Disadvantages of Payback
- Ignores the time value of money - Requires an arbitrary cutoff point - Ignores cash flows beyond the cutoff date - Biased against long-term projects, such as research and development, and new projects
Relevant Cash Flows
- Include only cash flows that will *only* occur if the project is accepted - *Incremental cash flows* - The *stand-alone principle* allows us to analyze each project in isolation from the firm simply by focusing on incremental cash flows
Case II - Corporate Taxes
- Interest on debt is tax deductible - When a firm adds debt, it reduces taxes, all else equal - The reduction in taxes increases the cash flow of the firm - The reduction in taxes reduces net income
What are five indirect bankruptcy costs?
- Larger than direct costs, but more difficult to measure and estimate - Stockholders wish to avoid a formal bankruptcy - Bondholders want to keep existing assets intact so they can at least receive that money - Assets lose value as management spends time worrying about avoiding bankruptcy instead of running the business - Lost sales, interrupted operations, and loss of valuable employees, low morale, inability to purchase goods on credit
What are direct costs of bankruptcy?
- Legal and administrative costs + Enron = $1 billion; WorldCom = $600 million - Bondholders incur additional losses - Disincentive to debt financing
How do you maximize stockholder wealth?
- Maximizing firm value - Minimizing WACC
What are some benefits of the NPV Method?
- Meets all desirable criteria + Considers all CFs + Considers TVM + Adjusts for risk + Can rank mutually exclusive projects - Directly related to increase in VF - Dominant method; always prevails
Internal Rate of Return
- Most important alternative to NPV - Widely used in practice - Intuitively appealing - Based entirely on the estimated cash flows - Independent of interest rates
NASDAQ
- NASDAQ OMX (merged 2007) - Computer-based quotation system - Multiple market makers - Electronic Communications Networks - Three levels of information + Level 1 - median quotes, registered representatives + Level 2 - view quotes, brokers & dealers + Level 3 - view and update quotes, dealers only - Large portion of technology stocks
Evaluating NPV Estimates
- NPV estimates are only estimates - Forecasting risk: + Sensitivity of NPV to changes in cash flow estimates ++ The more sensitive, the greater the forecasting risk - Sources of value + Be able to articulate why this project creates value
Disadvantages of AAR
- Not a true rate of return - Time value of money ignored - Uses an arbitrary benchmark cutoff rate - Based on accounting net income and book values, not cash flows and market values
What are six aspects of debt?
- Not an ownership interest - No voting rights - Interest is tax-deductible - Creditors have legal recourse if interest or principal payments are missed - Excess debt can lead to financial distress and bankruptcy
What are five aspects of equity?
- Ownership interest - Common stockholders vote to elect the board of directors and on other issues - Dividends are not tax deductible - Dividends are not a liability of the firm until declared. - Stockholders have no legal recourse if dividends are not declared - An all-equity firm cannot go bankrupt
What are some Advantages of IRR?
- Preferred by executives + Intuitively appealing + Easy to communicate the value of a project - If the IRR is high enough, may not need to estimate a required return - Considers all cash flows - Considers time value of money - Provides indication of risk
What are three strengths of a sensitivity analysis?
- Provides indication of stand-alone risk. - Identifies dangerous variables. - Gives some breakeven information.
Quoted Price vs. Invoice Price
- Quoted bond prices = "clean" price + Net of accrued interest - Invoice Price = "dirty" or "full" price + Price actually paid + Includes accrued interest - Accrued Interest + Interest earned since last coupon payment is owed to bond seller at time of sale
Nominal rate of interest
- Quoted rate of interest - Change in purchasing power and inflation
What are the three different bond classifications?
- Registered vs. Bearer Bonds - Security + Collateral - secured by financial securities + Mortgage - secured by real property, normally land or buildings + Debentures - unsecured + Notes - unsecured debt with original maturity less than 10 years - Seniority + Senior versus Junior, Subordinated
Which bonds will have the higher coupon, all else equal?
- Secured debt versus a debenture - Subordinated debenture versus senior debt - A bond with a sinking fund versus one without - A callable bond versus a non-callable bond
Sensitivity Analysis
- Shows how changes in an input variable affect NPV or IRR - Each variable is fixed except one + Change one variable to see the effect on NPV or IRR - Answers "what if" questions
What are four other types of bonds?
- Structured notes - Convertible bonds - Put bonds - Many types of provisions can be added to a bond + Important to recognize how these provisions affect required returns + Who does the provision benefit?
If you own a share of stock, you can receive cash in which two ways?
- The company pays dividends - You sell your shares, either to another investor in the market or back to the company
What is the market risk for individual securities?
- The contribution of a security to the overall riskiness of a portfolio - Relevant for stocks held in well-diversified portfolios - Measured by a stock's beta coefficient, j - Measures the stock's volatility relative to the market
What is the Systematic Risk Principle?
- There is a reward for bearing risk - There is no reward for bearing risk unnecessarily The expected return (market required return) on an asset depends only on that asset's systematic or market risk.
Total Risk = Stand-Alone Risk
- Total risk = Systematic risk + Unsystematic risk + The standard deviation of returns is a measure of total risk - For well-diversified portfolios, unsystematic risk is very small + Total risk for a diversified portfolio is essentially equivalent to the systematic risk
Depreciation & Capital Budgeting
- Use the schedule required by the IRS for tax purposes - Depreciation = non-cash expense + Only relevant due to tax affects - Depreciation tax shield = DT - D = depreciation expense - T = marginal tax rate
What is the APR if the monthly rate is .5%?
.5%(12) = 6%
What is the APR if the semiannual rate is .5%?
.5%(2) = 1%
What are the six conditions for the constant growth model?
1. Dividend expected to grow at g forever 2. Stock price expected to grow at g forever 3. Expected dividend yield is constant 4. Expected capital gains yield is constant and equal to g 5. Expected total return, R, must be > g 6. Expected total return (R): = expected dividend yield (DY) + expected growth rate (g) = dividend yield + g
What are three Conclusions we can draw from the Trans Am Corp Example?
1. The effect of leverage depends on EBIT - When EBIT is higher, leverage is beneficial 2. Under the "Expected" scenario, leverage increases ROE and EPS 3. Shareholders are exposed to more risk with more leverage - ROE and EPS more sensitive to changes in EBIT
$1,000 due on credit card Payment = $20 month minimum Rate = 1.5% per month The sign convention matters!!!
1.5 I/Y 1000 PV -20 PMT 0 FV CPT N = 93.111 months = 7.75 years
What are the three methods to calculate Modified Internal Rate of Return? (MIRR)
1.Discounting Approach = Discount future outflows to present and add to CF0 2. Reinvestment Approach = Compound all CFs except the first one forward to end 3. Combination Approach - Discount outflows to present; compound inflows to end MIRR will be unique number for each method Discount (finance) /compound (reinvestment) rate externally supplied
What is the monthly rate if the APR is 12% with monthly compounding?
12% / 12 = 1%
What is the present value of $500 to be received in 5 years? 10 years? The discount rate is 10% Present Value: Important Relationship I
5 yrs: PV = 500/(1.10)5 = -310.46 (1.10)^5 =1.6105 10 yrs: PV = 500/(1.10)10= -192.77 (1.10)^10 = 2.5937
Each payment covers the interest expense plus reduces principal Consider a 4-year loan with annual payments. The interest rate is 8% and the principal amount is $5000. What is the annual payment? Amortized Loan with Fixed Payment Example
5,000 = PMT[1 - 1 / 1.084] / .08 PMT = 1,509.60 =PMT(0.08,4,5000,0) = 1509.60 4 N; 8 I/Y; 5000 PV, 0 FV, CPT PMT = 1509.60
Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? What is the price expected to be in year 4? *What is the implied return given the change in price during the four year period?* Gordon Growth Company - II
50.50 = 40(1+return)^4 return = 6% 4 N -40 PV 50.50 FV 0 PMT CPT I/Y = 6% The price grows at the same rate as dividends
A taxable bond has a yield of 8% and a municipal bond has a yield of 6% If you are in a 40% tax bracket, which bond do you prefer?
8%(1 - .4) = 4.8% The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal
A taxable bond has a yield of 8% and a municipal bond has a yield of 6% At what tax rate would you be indifferent between the two bonds?
8%(1 - T) = 6% T = 25%
Unsystematic Risk
= Diversifiable risk Risk factors that affect a limited number of assets Risk that can be eliminated by combining assets into portfolios "Unique risk" "Asset-specific risk" Examples: labor strikes, part shortages, etc.
Average Accounting Return
AAR = Average Net Income / Average Book Value Average book value depends on how the asset is depreciated. Requires a target cutoff rate *Decision Rule: Accept the project if the AAR is greater than target rate.*
Without a financial calculator or Excel, this becomes a trial-and-error process Calculator Enter the cash flows as for NPV Press IRR and then CPT IRR = 16.13% > 12% required return Do we accept or reject the project?
Accept the project because IRR is greater than the required rate of return.
Optimal Capital Structure Figure 13.5
According to the static theory, the gain from the tax shield on debt is offset by financial distress costs. An optimal capital structure exists that just balances the additional gain from leverage against the added financial distress costs.
Good Decision Criteria
All cash flows considered? TVM considered? Risk-adjusted? Ability to rank projects? Indicates added value to the firm?
Interest rate and time period must ________!
Annual periods -> annual rate Monthly periods -> monthly rate
Any stockholder who prefers leverage can create their own ____________ and replicate the payoffs
Any stockholder who prefers leverage can create their own "homemade" and replicate the payoffs Trans Am's capital structure is irrelevant to shareholders
As interest rates increase present values ____________
As interest rates increase present values decrease
AAR Summary
Average Accounting Return= - Average net income/Average book value - Accept if AAR > Some specified target - Needed data usually readily available - Not a true rate of return - Time value of money ignored - Arbitrary benchmark - Based on accounting data not cash flows
Portfolio Beta
Beta p = Weighted average of the Betas of the assets in the portfolio Weights (wj) = % of portfolio invested in asset j
Bond Value
Bond Value = PV(coupons) + PV(par) Bond Value = PV(annuity) + PV(lump sum)
What must members of NYSE historically have to do to get onto the exchange?
Buy a trading license (own a seat) Designated market makers, DMMs (formerly known as "specialists") Floor brokers Supplemental liquidity providers (SLPs)
Suppose you have a 1-year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5,000 to invest. What interest rate must you earn to have the $75,000 when you need it? Discount Rate - Example 3
Calculator: 17 N -5000 PV 0 PMT 75000 FV CPT I = 17.27%
Capital structure_________ by industries
Capital structure differs by industries Differences according to Cost of Capital 2010 Yearbook by Ibbotson Associates, Inc. *Lowest levels of debt:* Computer equipment = 9.09% Drugs = 7.80% debt *Highest levels of debt:* Pay television = 63.56% Airlines = 63.92% debt
What is the sign convention?
Cash inflows are positive Cash outflows are negative
What is Price Risk? Interest Rate Risk
Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds
Real rate of interest
Change in purchasing power
What is The Bankruptcy Process regarding Reorganization?
Chapter 11 of the Federal Bankruptcy Reform Act of 1978 *Process:* - Petition filed by firm or creditors - Usually, firm continues operation as "debtor-in-possession" - Firm submits reorganization plan - If accepted by classes of creditors, then confirmed by court - Firm makes payments to creditors and operates under plan for some fixed time
What is The Bankruptcy Process regarding Liquidation?
Chapter 7 of the Federal Bankruptcy Reform Act of 1978 *Process:* - Petition filed in federal court - Trustee elected by creditors to take over firm's assets - Trustee attempts to sell assets - Proceeds distributed according to the absolute priority rule (APR)
What is the objective of a capital structure?
Choose the capital structure that will minimize WACC and maximize stockholder wealth
What are some advantages to the profitability index?
Closely related to NPV, generally leading to identical decisions - Considers all CFs - Considers TVM Easy to understand and communicate Useful in capital rationing
Portfolio Variance
Compute portfolio return for each state: RP,i = w1R1,i + w2R2,i + ... + warm,i Compute the overall expected portfolio return using the same formula as for an individual asset Compute the portfolio variance and standard deviation using the same formulas as for an individual asset
Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends. Nonconstant Growth
Compute the dividends until growth levels off D1 = 1(1.2) = $1.20 D2 = 1.20(1.15) = $1.38 D3 = 1.38(1.05) = $1.449 Find the expected future price at the beginning of the constant growth period: P2 = D3 / (R - g) = 1.449 / (.2 - .05) = 9.66 Find the present value of the expected future cash flows P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
Capital Budgeting in Practice
Consider all investment criteria when making decisions NPV and IRR are the most commonly used primary investment criteria Payback is a commonly used secondary investment criteria All provide valuable information
Modified Internal Rate of Return (MIRR)
Controls for some problems with IRR
Incremental Cash Flow for a Project Relevant Cash Flows
Corporate cash flow *with* the project *Minus* Corporate cash flow *without* the project
Semiannual Bonds Coupon rate = 14% - Semiannual YTM = 16% (APR) Maturity = 7 years Number of coupon payments? Semiannual coupon payment? Semiannual yield?
Coupon rate = 14% - Semiannual YTM = 16% (APR) Maturity = 7 years Number of coupon payments? (2t or N) 14 = 2 x 7 years Semiannual coupon payment? (C/2 or PMT) $70 = (14% x Face Value)/2 Semiannual yield? (YTM/2 or I/Y) 8% = 16%/2
Computing Straight line Depreciation
D = (Initial cost - salvage) / number of years Straight Line -> Salvage Value
Projected Dividends Stock
D0 = $2.00 and constant g = 6% D1 = D0(1+g) = 2(1.06) = $2.12 D2 = D1(1+g) = 2.12(1.06) = $2.2472 D3 = D2(1+g) = 2.2472(1.06) = $2.3820
Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? DGM - Example 1
D0= $0.50 g = 2% R = 15% P0 = D0 (1+g)/ R-g JUST PAID A DIVIDEND P0 = 0.50 (1+.02) / .15 - .02 = $3.92
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. - You expect it to pay a $2 dividend in one year which will grow at 5% annually. - You believe you can sell the stock for $14 at that time. - You require a return of 20% on investments of this risk - What is the maximum you would be willing to pay? One Period Example
D1 = $2 dividend expected in one year R = 20% P1 = $14 CF1 = $2 + $14 = $16 Compute the PV of the expected cash flows P0 = (2+14)/1.20 = 13.33
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. - You expect it to pay a $2 dividend in one year which will grow at 5% annually. - You believe you can sell the stock for $14 at that time. - You require a return of 20% on investments of this risk - What is the maximum you would be willing to pay? What if you decide to hold the stock for two years? Two Period Example
D1 = $2.00 D2 = $2.10 (2 x .05 = $2.10) P2 = $14.70 (14 x .05 = $0.70 and $14 + $14.70) CF1 = $2.00 CF2 = $2.10 + $14.70 = $16.80 (You will receive dividend and sell stock in Year 2) P0 = 2 / 1.20 + (2.10 + 14.70) / (1.20)^2 = 13.33
Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? DGM - Example 2
D1 = $2.00 g = 5% r = 20% P0 = D1 / R-g EXPECTED DIVIDEND P0 = 2.00/.20 - .05 = $13.33
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. - You expect it to pay a $2 dividend in one year which will grow at 5% annually. - You believe you can sell the stock for $14 at that time. - You require a return of 20% on investments of this risk - What is the maximum you would be willing to pay? What if you decide to hold the stock for three years? Three Period Example
D1 = $2.00 D2 = $2.10 D3 = $2.205 P3 = $15.435 ($14.70 x .05 = 0.735 and $14.70 + 0.735 = $15.435 CF1 = $2.00 CF2 = $2.10 CF3 = $2.205 + $15.435 = $17.640 (2.10 x .05 = .1050 and 2.10 + .1050 = 2.205) Now how much would you be willing to pay? $13.33
What are municipal securities? Government Bonds
Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level Interest usually exempt from state tax in issuing state
Computing MACRS Depreciation
Depreciate -> 0 Recovery Period = Class Life 1/2 Year Convention Multiply percentage in table by the initial cost
Chapter 5
Discounted Cash Flow Valuation
P0 = $10.50 D0 = $1 g = 5% per year What is the dividend yield? What is the capital gains yield?
Dividend Yield 1(1.05) / 10.50 = 10% Capital Gains Yield g = 5%
Supernormal growth
Dividend growth is not consistent initially, but settles down to constant growth eventually
Dividend Characteristics
Dividends are not a liability of the firm until declared by the Board of Directors - A firm cannot go bankrupt for not declaring dividends Dividends and Taxes - Dividends are *not* tax deductible for firm - Taxed as ordinary income for individuals - Dividends received by corporations have a minimum 70% exclusion from taxable income
Zero Growth
Dividends expected at regular intervals forever = perpetuity P0 = D / R
As with bonds, the price of the stock is the present value of these expected cash flows
Dividends → cash income Selling → capital gains
Advantages of Payback?
Easy to understand Adjusts for uncertainty of later cash flows Biased towards liquidity but... *ASKS THE WRONG QUESTION!*
ECNs
Electronic Communications Networks provide direct trading among investors Developed in late 1990s ECN orders transmitted to NASDAQ Observe live trading online at Batstrading.com
Chapter 7
Equity Markets and Stock Valuation
Shark Attractant Project
Estimated sales 50,000 cans Sales Price per can $4.00 Cost per can $2.50 Estimated life 3 years Fixed costs $12,000/year Initial equipment cost $90,000 100% depreciated over 3 year life Investment in NWC $20,000 Tax rate 34% Cost of capital 20%
Scenario Analysis
Examines several possible situations: - Worst case - Base case or most likely case - Best case Provides a range of possible outcomes
MIRR in Excel
Excel = Method 3 MIRR = discount rate which causes the PV of a project's terminal value (TV) to equal the PV of costs (outflows) MIRR assumes CFs reinvested at WACC Function: =MIRR(Range, FR, RR) FR = Finance rate (discount) RR = Reinvestment rate (compound)
Expected Returns
Expected returns are based on the probabilities of possible outcomes
Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years? Future Value: Multiple Cash Flows Example
FV = $ 500 x (1.09)2 = $ 594.05 + $ 600 x (1.09) = $ 654.00 = $1,248.05
Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%? Future Value: Multiple Cash Flows Example 3 - Formula
FV = $100(1.08)4 + $300(1.08)2 = $136.05 + $349.92 = $485.97
Suppose you can earn 1% per month on $1 invested today. What is the APR? 1(12) = 12% How much are you effectively earning?
FV = 1(1.01)12 = 1.1268 Rate = (1.1268 - 1) / 1 = .1268 = 12.68%
What is the general formula for Future Value?
FV = PV(1+r)^t FV = future value PV = present value r = period interest rate, expressed as a decimal t = number of periods Future value interest factor = (1 + r)^t Note: "yx" key on your calculator
Systematic Risk
Factors that affect a large number of assets "Non-diversifiable risk" "Market risk" Examples: changes in GDP, inflation, interest rates, etc.
Finding PVs is discounting, and it's the ____________ of compounding.
Finding PVs is discounting, and it's the reverse of compounding.
Constant dividend growth
Firm will increase the dividend by a constant percent every period
For stocks that don't pay dividends (or have erratic dividend growth rates), we can value them using the _________ ratio and/or the _________ ratio: Valuation Using Multiples
For stocks that don't pay dividends (or have erratic dividend growth rates), we can value them using the price-earnings (PE) ratio and/or the price-sales ratio Price at time t = Pt = Benchmark PE ratio X Earnings per sharet Price at time t = Pt = Benchmark price-sales ratio X Sales per share - The price-sales ratio can be especially useful when earnings are negative.
Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today? Future Values - Example 3
Formula Solution: FV = PV(1+r)^t = 10(1.055)200 =10(44718.984) =447,189.84 Calculator Solution 200 N 5.5 I/Y 10 PV 0 PMT CPT FV = -447,189.84
Suppose you invest the $100 from the previous example for 5 years. How much would you have? Future Values - Example 2
Formula Solution: FV =PV(1+r)t =100(1.10)5 =100(1.6105) =161.05 Calculator Solution PV= 100 i= 10 n= 5 FV = 161.05
Second: Find discount rate that equates PV and TV (continued)
Formula: R = (186 / 129.444)1/2 - 1 = .1987 = 19.87% Calculator - the sign convention matters!!! 2 N -129.444 PV 0 PMT 186 FV CPT I/Y = 19.87% Excel: =RATE(2,0,-129.444,186) = 0.1987 =MIRR(Range, FR, RR) 19.87%
Yield Curve
Graphical representation of the term structure Normal = upward-sloping L/T > S/T Inverted = downward-sloping L/T < S/T
What is the definition of IRR?
IRR = discount rate that makes the NPV = 0
Interpretation of Beta
If Beta is equal to 1, the stock has average risk If Beta = 1.0, stock has average risk If Beta is greater than 1, the stock is riskier than average. If Beta > 1.0, stock is riskier than average If Beta is less than 1, the stock is less risky than average. If Beta < 1.0, stock is less risky than average Most stocks have betas in the range of 0.5 to 1.5. Beta of the market = 1.0 Beta of a T-Bill = 0 (essentially no risk)
If NPV is _________, accept the project
If NPV is positive, accept the project *NPV > 0 (or greater than zero) means:* - Project is expected to add value to the firm - Will increase the wealth of the owners NPV is a direct measure of how well this project will meet the goal of increasing shareholder wealth.
After-Tax Salvage
If the salvage value is different from the book value of the asset, then there is a tax effect Book value = initial cost - accumulated depreciation After-tax salvage = salvage - T(salvage - book value)
If we expect EBIT to be greater than the break-even point, then leverage is ____________ to our stockholders If we expect EBIT to be less than the break-even point, then leverage is _____________ to our stockholders Break-Even EBIT Table
If we expect EBIT to be greater than the break-even point, then leverage is beneficial to our stockholders If we expect EBIT to be less than the break-even point, then leverage is detrimental to our stockholders
If you have an APR based on monthly compounding, you have to use _________ periods for lump sums or adjust the interest rate accordingly.
If you have an APR based on monthly compounding, you have to use monthly periods for lump sums or adjust the interest rate accordingly.
In equilibrium, all assets and portfolios must have the same _________ ratio Market Equilibrium
In equilibrium, all assets and portfolios must have the same reward-to-risk ratio Each ratio must equal the reward-to-risk ratio for the market
How does one increase and decrease leverage?
Increase leverage by issuing debt and repurchasing outstanding shares Decrease leverage by issuing new shares and retiring outstanding debt
Chapter 6
Interest Rate and Bond Valuation
IRR Summary
Internal rate of return = - Discount rate that makes NPV = 0 - Accept if IRR > required return - Same decision as NPV with conventional cash flows Unreliable with: - Non-conventional cash flows - Mutually exclusive projects MIRR = better alternative
Leverage amplifies the ___________ in both EPS and ROE
Leverage amplifies the variation in both EPS and ROE
Chapter 13
Leverage and Capital Structure
What are low grade bonds? Bond Ratings - Speculative
Low Grade - Moody's Ba, B, Caa and Ca - S&P BB, B, CCC, CC - Considered speculative with respect to capacity to pay. The "B" ratings are the lowest degree of speculation.
Graph of Proposition II
M&M Proposition I with taxes implies that a firm's WACC decreases as the firm relies more heavily on debt financing. WACC = (E/V) x RE + (D/V) x RD x (1 - TC) M&M Proposition II with taxes implies that a firm's cost of equity RE, rises as the firm relies more heavily on debt financing. RE = RU + (RU - RD) x (D/E) x (1 - TC)
How does MIRR compare with IRR?
MIRR correctly assumes reinvestment at opportunity cost = WACC MIRR avoids the multiple IRR problem Managers like rate of return comparisons, and MIRR is better for this than IRR
What are Zero Coupon Bonds?
Make no periodic interest payments (coupon rate = 0%) Entire yield-to-maturity comes from the difference between the purchase price and the par value (capital gains) Cannot sell for more than par value Sometimes called zeroes, or deep discount bonds Treasury Bills and U.S. Savings bonds are good examples of zeroes
Chapter 9
Making Capital Investment Decisions
What is the primary goral of financial managers?
Maximize stockholder wealth
What is an disadvantage to the profitability index?
May lead to incorrect decisions in comparisons of mutually exclusive investments (can conflict with NPV)
What does the Profitability Index measure?
Measures the benefit per unit cost, based on the time value of money A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value Can be very useful in situations of capital rationing *Decision Rule: If PI > 1.0 Accept*
New York Stock Exchange (NYSE)
Merged with Euronext in 2007 NYSE Euronext merged with the American Stock Exchange in 2008
What are medium grade bonds? Bond Ratings - Investment Quality
Moody's A and S&P A - capacity to pay is strong, but more susceptible to changes in circumstances Moody's Baa and S&P BBB - capacity to pay is adequate, adverse conditions will have more impact on the firm's ability to pay
What are high grade bonds? Bond Ratings - Investment Quality
Moody's Aaa and S&P AAA - capacity to pay is extremely strong Moody's Aa and S&P AA - capacity to pay is very strong
What are very low grade bonds? Bond Ratings
Moody's C and S&P C - income bonds with no interest being paid Moody's D and S&P D - in default with principal and interest in arrears
Can you divide the above APR by 2 to get the semiannual rate?
NO. You need an APR based on semiannual compounding to find the semiannual rate.
Rationale for the NPV Method NPV=0 → Project's inflows are "__________ sufficient to repay the invested capital and provide the required rate of return"
NPV = PV inflows - Cost NPV=0 → Project's inflows are "exactly sufficient to repay the invested capital and provide the required rate of return"
NPV = _____ gain in shareholder wealth
NPV = net gain in shareholder wealth
- Suppose an investment will cost $90,000 initially and will generate the following cash flows: + Year 1: 132,000 + Year 2: 100,000 + Year 3: -150,000 - The required return is 15%. - Should we accept or reject the project? Non-Conventional Cash Flows
NPV > 0 at 15% required return, so you should Accept IRR =10.11% (using a financial calculator), which would tell you to Reject Recognize the non-conventional cash flows and look at the NPV profile
NPV and IRR will generally give the ______ decision
NPV and IRR will generally give the same decision Exceptions include: *Non-conventional cash flows* - Cash flow sign changes more than once *Mutually exclusive projects* - Initial investments are substantially different - Timing of cash flows is substantially different - Will not reliably rank projects
Chapter 8
Net Present Value and Other Investment Criteria
Net Present Value is the _____ of the PVs of all cash flows
Net Present Value is the Sum of the PVs of all cash flows Initial cost is often CF0 and is an outflow.
NPV Summary
Net present value = Difference between market value (PV of inflows) and cost - Accept if NPV > 0 - No serious flaws - Preferred decision criterion
The Tax Shield Approach to Operating Cash Flow (OCF)
OCF = (Sales - costs)(1 - T) + Deprec*TC OCF=(200,000-137,000) x 66% + (30,000 x .34) OCF = 51,780 - Particularly useful when the major incremental cash flows are the purchase of equipment and the associated depreciation tax shield + i.e., choosing between two different machines
Constant Dividend Growth Stock
One whose dividends are expected to grow forever at a constant rate, g. D1 = D0(1+g)^1 D2 = D0(1+g)^2 Dt = D0(1+g)^t D0 = Dividend JUST PAID D1 to Dt = Expected dividends
NYSE Operations
Operational goal = attract order flow NYSE DMMs: - Assigned broker/dealer + Each stock has one assigned DMM + All trading in that stock occurs at the "DMM's post" - Trading takes place between customer orders placed with the DMMs and "the crowd" - "Crowd" = Floor brokers and SLPs
Why is present value worth less than face value?
Opportunity cost Risk & Uncertainty Discount Rate = ƒ (time, risk)
Dividend Growth Model
P0 = D0 (1+g) / R-g JUST PAID DIVIDEND P0 = D1/R-g EXPECTED DIVIDED
Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? Gordon Growth Company - I
P0 = D1 / R - g EXPECTED DIVIDEND P0 = 4.00 / .16 - .06 = $40
Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? *What is the price expected to be in year 4?* Gordon Growth Company - II
P4 = D4 (1+g) / R-g P4 = D5 / R-g D5 = D1(1+g)^4 P4 = 4.00 (1 + .06)^4 / .16 - .06 = $50.50
You are considering an investment that will pay you $1,000 in one year, $2,000 in two years and $3,000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? Present Value: Multiple Cash Flows Another Example - Formula Solution
PV = $1,000 / (1.1)1 = $ 909.09 PV = $2,000 / (1.1)2 = $1,652.89 PV = $3,000 / (1.1)3 = $2,253.94 PV = $4,815.92
What is the equation for Present Value?
PV = FV / (1+r)^t PV = FV(1+r)^-t
What is the formula for a perpetuity?
PV = PMT / r
Payback Summary
Payback period = - Length of time until initial investment is recovered - Accept if payback < some specified target - Doesn't account for time value of money - Ignores cash flows after payback - Arbitrary cutoff period - Asks the wrong question
Capital structure
Percent of debt and equity used to fund the firm's assets
Perpetuity Example 5.7
Perpetuity formula: PV = PMT / r Current required return: 40 = 1 / r r = .025 or 2.5% per quarter Dividend for new preferred: 100 = PMT / .025 PMT = 2.50 per quarter
Portfolios
Portfolio = collection of assets An asset's risk and return impact how the stock affects the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
Portfolio standard deviation is _______ a weighted average of the standard deviation of the component securities' risk Portfolio Risk Variance & Standard Deviation
Portfolio standard deviation is NOT a weighted average of the standard deviation of the component securities' risk - If it were, there would be no benefit to diversification.
What are four aspects of bond markets?
Primarily over-the-counter transactions with dealers connected electronically Extremely large number of bond issues, but generally low daily volume in single issues Getting up-to-date prices difficult, particularly on small company or municipal issues Treasury securities are an exception
Treasury bills are excellent examples of pure discount loans.
Principal amount is repaid at some future date No periodic interest payments
Profitability Index Summary
Profitability Index = - Benefit-cost ratio - Accept investment if PI > 1 - Cannot be used to rank mutually exclusive projects - May be used to rank projects in the presence of capital rationing
Computing AAR for the Project Sample Project Data: Year 0: CF = -165,000 Year 1: CF = 63,120 NI = 13,620 Year 2: CF = 70,800 NI = 3,300 Year 3: CF = 91,080 NI = 29,100 Average book value = $72,000 Required average accounting return = 25% Average Net Income: ($13,620 + 3,300 + 29,100) / 3 = $15,340 AAR = $15,340 / 72,000 = .213 = 21.3% Do we accept or reject the project?
Reject before the AAR is less than the target rate.
Reward-to-Risk Ratio
Reward-to-Risk Ratio = Slope of line on graph In equilibrium, ratio should be the same for all assets When E(R) is plotted against β for all assets, the result should be a straight line
What are three factors affecting required return?
Rf measures the pure time value of money RPM = (E(RM)-Rf) measures the reward for bearing systematic risk Beta j measures the amount of systematic risk
Chapter 11
Risk and Return
If NPV > 0 (greater than zero) do you accept or reject the project?
Rule: Accept project if NPV > 0
Finding the Required Return A firm's stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?
Start with DGM P0 = D0(1+g)/R-g = D1 / R-g Rearrange and Solve for R R = D0 (1+g) / P0 + g = D1 / P0 + g
Calculating IRR with Excel
Start with the cash flows as you did to solve for NPV Use the IRR function - Enter the range of cash flows, beginning with the initial cash flow (Cash flow 0) - You can enter a guess, but it is not necessary - The default format is a whole percent
Coupon interest rate
Stated interest rate Usually = YTM at issue Multiply by par value to get coupon payment
MIRR Method 2 Reinvestment Approach
Step 1: Compound ALL cash flows (except CF0) to end of project's life Step 2: Zero out all cash flows which have been added to the last year of the project's life. Step 3: Compute IRR normally
MIRR Method 3 Combination Approach
Step 1: Discount all outflows (except CF0) to present and add to CF0. Step 2: Compound all cash inflows to end of project's life Step 3: Compute IRR normally
MIRR Method 1 Discounting Approach
Step 1: Discount future outflows (negative cash flows) to present and add to CF0 Step 2: Zero out negative cash flows which have been added to CF0. Step 3: Compute IRR normally
How much value is created from undertaking an investment? Net Present Value
Step 1: Estimate the expected future cash flows. Step 2: Estimate the required return for projects of this risk level. Step 3: Find the present value of the cash flows and subtract the initial investment to arrive at the Net Present Value.
What is an alternative method to calculating Expected Portfolio Return?
Steps: 1. Calculate expected portfolio return in each state. 2. Apply the probabilities of each state to the expected return of the portfolio in that state. 3. Sum the result of Step 2.
Stock Value = __ of Dividends
Stock Value = PV of Dividends
YTM with Semiannual Coupons Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $1197.93. Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?
Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93. 40 N 1197.93 PV (negative) 1000 FV 50 PMT CPT PV 4% (= ½ YTM) YTM = 4%*2 = 8% when semiannual coupons, multiply answer by 2.
Computing EAR and APR
Suppose if you put it in another account, you earn 3% per quarter. What is the APR? 3(4) = 12% How much are you effectively earning? FV = 1(1.03)4 = 1.1255 Rate = (1.1255 - 1) / 1 = .1255 = 12.55%
Future Values: Example 1
Suppose you invest $100 for one year at 10% per year. What is the future value in one year? Interest = 100(.10) = 10 Value in one year = Principal + interest = 100 + 10 = 110 Future Value (FV) = 100(1 + .10) = 110 Or calculator PV: 100 n: 1 i: 10 FV: 110
Future Values - Example 1 (continued)
Suppose you leave the money in for another year. How much will you have two years from now? FV = 100(1.10)(1.10) = 100(1.10)2 = 121.00 Or calculator PV: 100 n: 2 i: 10 FV: 121.00
Proposition II: the systematic risk of the stock depends on what two factors?
Systematic risk of the assets, RA, (business risk) Level of leverage, D/E, (financial risk)
Suppose we are trying to value the company Inactivision, a video game developer that does not pay dividends. If the appropriate industry PE for this type of company is 20 and you predict earnings to be $2.50 per share for the coming year, then the forecasted stock price for a year from now, or target price, is the following: Valuation Using Multiples
Target price = 20 x $2.50 = $50
The Security Market Line (SML) is part of the Capital __________ Pricing Model (CAPM)
The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM)
With the sign convention cash inflows are _____________ and cash outflows are ______________.
The Sign Convention - Cash inflows are positive - Cash outflows are negative
Future Value (FV)
The amount an investment is worth after one or more periods. "Later" money on a time line
Annual Percentage Rate (APR) "Nominal"
The annual rate quoted by law APR = periodic rate X number of periods per year Periodic rate = APR / periods per year
Capital Asset Pricing Model (CAPM) defines the relationship between risk and __________.
The capital asset pricing model (CAPM) defines the relationship between risk and return E(RA) = Rf + (E(RM) - Rf)βA If an asset's systematic risk (B) is known, CAPM can be used to determine its expected return
M&M Propositions I & II Figure 13.3
The change in the capital structure weights (E/V and D/V) is exactly offset by the change in the cost of equity (RE), so the WACC stays the same.
Present Value (PV)
The current value of future cash flows discounted at the appropriate discount rate Value at t=0 on a time line
The ex ante ___________ rate of interest includes our desired real rate of return plus an adjustment for expected inflation
The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation
The expected return of a portfolio is the weighted average of the _______ returns for each asset in the portfolio Portfolio Expected Returns
The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio Weights (wj) = % of portfolio invested in each asset
Case III With Bankruptcy Costs
The higher the Debt Equity (D/E) ratio → the higher the probability of bankruptcy The higher the probability of bankruptcy → the greater expected bankruptcy costs At some point, the additional value of the interest tax shield will be offset by the expected bankruptcy costs At this point, the value of the firm will start to decrease and the WACC will start to increase as more debt is added
The higher the beta, the _____________ the risk premium should be Beta and the Risk Premium
The higher the beta, the greater the risk premium should be Risk premium = E(R ) - Rf Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES!
For a given time period.... Present Value Important Relationship II
The higher the interest rate, The smaller the present value PV = FV / (1+r)^t
Effective Annual Rate (EAR)
The interest rate expressed as if it were compounded once per year. Used to compare two alternative investments with different compounding periods
Yield to maturity (YTM)
The market required rate of return for bonds of similar risk and maturity The discount rate used to value a bond Return if bond held to maturity Usually = coupon rate at issue Quoted as an APR
Present Value: Multiple Cash Flows You are offered an investment that will pay $200 in year 1, $400 the next year, $600 the following year, and $800 at the end of the 4th year. You can earn 12% on similar investments. What is the most you should pay for this one? Example 5.3
Find the PV of each cash flow and add them: Year 1 CF: $200 / (1.12)1 = $ 178.57 Year 2 CF: $400 / (1.12)2 = $ 318.88 Year 3 CF: $600 / (1.12)3 = $ 427.07 Year 4 CF: $800 / (1.12)4 = $ 508.41 Total PV = $1,432.93
You think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest. You currently have $7,000 in the account. How much will you have in 3 years? How much in 4 years? Future Value: Multiple Cash Flows
Find the value at year 3 of each cash flow and add them together. Year 0: FV = $7,000(1.08)3 = $ 8,817.98 Year 1: FV = $4,000(1.08)2 = $ 4,665.60 Year 2: FV = $4,000(1.08)1 = $ 4,320.00 Year 3: value = $ 4,000.00 Total value in 3 years = $21,803.58 Calculator Solution: PV = $7,000 n = 3 i = 8 PMT = $4,000 Total value in 3 years = $21,803.58 Value at year 4 = $21,803.58(1.08)= $23,547.87
Discounting
Finding the present value of one or more future amounts.
Which savings accounts should you choose: 5.25% with daily compounding. 5.30% with semiannual compounding.
First account: EAR = (1 + .0525/365)365 - 1 = 5.39% ICONV: NOM=5.25; C/Y=365 EFF=5.3899 Excel: =EFFECT(0.525,365) = 5.39% Second account: EAR = (1 + .053/2)2 - 1 = 5.37% ICONV: NOM=5.3; C/Y=2 EFF=5.3702 Excel: =EFFECT(0.53,2) = 5.37%
How much will you have in 5 years if you make no further deposits? Future Value: Multiple Cash Flows Example (continued)
First way: FV = $500(1.09)5 + $600(1.09)4 = $1,616.26 Second way - use value at year 2: FV = $1,248.05(1.09)3 = $1,616.26
For a given interest rate.... Future Value: Important Relationship I
For a given interest rate: The longer the time period The higher the interest rate The higher the future value FV= PV (1+r)^t
For a given interest rate: The longer the time period, The _________ the present value
For a given interest rate: The longer the time period, The lower the present value PV = FV / (1+r)^t
For a given r, as t increases, FV ______________. Future Value: Important Relationship I
For a given r, as t increases, FV increases THIS IS THE TIME VALUE OF MONEY
For a given r, as t increases, PV _________________ Present Value: Important Relationship I
For a given r, as t increases, PV decreases
For a given t, as r increases, PV ___________________ Present Value Important Relationship II
For a given t, as r increases, PV decreases PV = FV / (1+r)^t
Suppose your company expects to increase unit sales of widgets by 15% per year for the next 5 years. If you currently sell 3 million widgets in one year, how many widgets do you expect to sell in 5 years? Future Value: General Growth Formula
Formula Solution: FV =PV(1+r)t =3(1.15)5 =3(2.0114) =6.0341 million Calculator Solution 5 N 15 I/Y 3 PV 0 PMT CPT FV = -6.0341
You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today? Present Values: Example 2 Multi-Periods
Formula Solution: PV =FV(1+r)-t =150,000(1.08)-17 =150,000/(1.08)17 =40,540.34 Calculator Solution: 17 N 8 I 0 PMT 150000 FV CPT PV = -40,540.34
Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today? Present Value: Example 1 Single Period
Formula Solution: PV =FV/(1+r)t =10,000/(1.07)1 =10,000/1.07 =9,345.79 Calculator Solution 1 N 7 I 0 PMT 10000 FV CPT PV = -9345.79
Interest rate (r)
- *Discount rate* - Cost of capital - Opportunity cost of capital - Required return - Terminology depends on usage
If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market?
1 N 10,000 FV 7 I/Y CPT PV = -9345.79 =PV(.07,1,0,10000)
Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest? Discount Rate - Example 2
6 N -10000 PV 0 PMT 20000 FV CPT I = 12.25%
APR - Example Suppose you want to earn an effective rate of 12% and you are looking at an account that compounds on a monthly basis. What APR must they pay?
APR = 12 [(1+.12)^1/12 - 1 = .1138655 = 11.39% ICONV: EFF = 12 C/Y = 12 NOM = 11.3866 Excel: =NOMINAL(0.12,12)
As interest rates increase, bond prices ___________ and vice versa
As interest rates increase, bond prices decrease and vice versa
You are ready to buy a house and you have $20,000 for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000. The bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house? Buying a House
Bank loan Monthly income = 36,000 / 12 = 3,000 Maximum payment = .28(3,000) = 840 360 N (30*12) 0.5 I/Y -840 PMT CPT PV = 140,105 Total Price Closing costs = .04(140,105) = 5,604 Down payment = 20,000 - 5604 = 14,396 Total Price = 140,105 + 14,396 = 154,501
Effects of Compounding Example
Consider the previous example FV w/simple interest = 100 + 10 + 10 = 120 FV w/compound interest =100(1.10)2 = 121.00 The extra 1.00 comes from the interest of .10(10) = 1.00 earned on the first interest payment
Bond
Debt contract Interest-only loan
EAR Formula
EAR = (1 + APR/m)^m - 1 APR = the quoted rate m = number of compounds per year
Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest? Present Values: Example 3 Multi-Periods
Formula Solution: PV =FV/(1+r)t =19,671.51/(1.07)10 =19.671.51/(1.07)10 =-10,000 Calculator Solution: 10 N 7 I 0 PMT 19671.51 FV CPT PV = -10000
You are looking at an investment that will pay $1200 in 5 years if you invest $1000 today. What is the implied rate of interest? Discount Rate - Example 1
Formula: r = (1200 / 1000)1/5 - 1 = .03714 = 3.714% Calculator - the sign convention matters!!! 5 N -1000 PV (you pay $1,000 today) 0 PMT 1200 FV (you receive $1,200 in 5 years) CPT I = 3.714%
What's the PV of $100 due in 3 Years if r = 10%?
Formula: PV = FV(1+r)-t = 100(1.10)-3 = $75.13 Calculator: 3 N 10 I/Y 0 PMT 100 FV CPT PV = -75.13
If you deposit $100 in one year, $200 in two years and $300 in three years. How much will you have in three years at 7 percent interest? How much in five years if you don't add additional amounts?
Future Value: Multiple Uneven Cash Flows Year 1 CF: 2 N; -100 PV; 7 I/Y; CPT FV = 114.49 Year 2 CF: 1 N; -200 PV; 7 I/Y; CPT FV = 214.00 Year 3 CF: 0 N; -300 PV; 7 I/Y; CPT FV = 300.00 Total FV3 = 628.49 Total FV5 = 628.49 * (1.07)2 = 719.56
Compound interest
Interest earned on principal and on interest received "Interest on interest" - interest earned on reinvestment of previous interest payments
Simple interest
Interest earned only on the original principal
Interest rate and time period must _________!
Interest rate and time period must match! - Annual periods -> annual rate - Monthly periods -> monthly rate
Chapter 4
Introduction to Valuation: The Time Value of Money
Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15% return on investments of this risk, should you take the investment?
No - the broker is charging more than you would be willing to pay.
Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today? Annuity - Sweepstakes Example
PV = $333,333.33[1 - 1/1.0530] / .05 = $5,124,150.29
What is the Basic PV Equation?
PV = FV / (1 + r)^t There are four parts to this equation: - PV, FV, r and t - Know any three, solve for the fourth Be sure and remember the sign convention +CF = Cash INFLOW -CF = Cash OUTFLOW
What is the present value of $500 received in 5 years if the interest rate is 10%? 15%? Present Value: Important Relationship II
Rate = 10% Calculator Solution: 5 N 10 I 0 PMT 500 FV CPT PV = -310.46 Rate = 15% Calculator Solution: 5 N 15 I 0 PMT 500 FV CPT PV = -248.59
What is Present Value? (PV)
The current value of future cash flows discounted at the appropriate discount rate or The current value of an amount to be received in the future Value at t=0 on a time line Answers the questions: How much do I have to invest today to have some amount in the future? What is the current value of an amount to be received in the future?
When YTM is less than the coupon rate and the price is greater than par, than the bond is a _________________ bond.
When YTM is less than the coupon rate and the price is greater than par, than the bond is a premium bond. When YTM < Coupon rate Price > Par = "Premium Bond"
