Module 43: Financial Risk Management and Capital Budgeting Flashcards
What type of relationship does risk and return have?
Inverse relationship
Avoidable costs
Costs that will not continue to be incurred if a particular course of action is taken
Cash flow hedge
A hedge of the variability in the cash flows of a recognized asset or liability or of a forecasted transaction that is attributable to a particular risk
Committed costs
Costs related to the company’s basic commitment to open its doors (e.g., depreciation, property taxes, management salaries, etc.)
Credit (default) risk
The risk that a firm will default on payment of interest or principal of a debt
Currency swaps
Forward-based contracts in which two parties agree to exchange an obligation to pay cash flows in one currency for an obligation to pay in another currency
Differential (incremental) cost
The difference in cost between two alternative courses of action
Discretionary costs
Fixed costs whose level is set by current management decisions (e.g. advertising, research and development)
Fair value hedge
A hedge of the changes in fair value of a recognized asset or liability, or of an unrecognized firm commitment
Forwards
Negotiated contracts to purchase and sell a specific quantity of a financial instrument, foreign currency, or commodity at a price specified at the origination of the contract, with delivery and payment at a specified future date
Futures
Forward-based standardized contracts to take delivery of a specified financial instrument, foreign currency, or commodity at a specified future date or during a specified period generally at the then market price
Interest rate risk
The risk that the value of a debt instrument will decline due to an increase in prevailing interest rates
Interest rate swaps
Forward-based contracts in which two parties agree to swap streams of payments over a specified period of time. These contracts are often used to trade variable-rate instruments for fixed-rate instruments
Internal rate of return method
Uses the rate of return that equates investment with future cash flows to evaluate investment alternatives
Market risk
The risk that the value of a debt instrument will decline due to a decline in the aggregate value of all assets in the economy
Net present value method
Uses the present value of future cash flows to evaluate investment alternatives
Opportunity cost
Maximum income or savings (benefit) foregone by rejecting an alternative
Options
An instrument that allows, but does not require, the holder to buy (call) or sell (put) a specific or standard commodity or financial instrument, at a specified price during a specified period of time or at a specified date
Outlay cost
Case disbursement associated with a specific project
Payback method
Evaluates investment alternatives based on the length of time until the investment is recaptured
Relevant costs
Future costs that will change as a result of a specific decision
Sensitivity analysis
Exploring the importance of various assumptions to forecasted results
Sunk (unavoidable) costs
Committed costs that are not avoidable and are therefore irrelevant to future decisions
Swaption
Option of a swap that provides the holder with the right to enter into a swap at a specified future date with specified terms
Systematic risk
The risk related to market factors which cannot be diversified away
Unsystematic risk
Risk that exists for one particular investment or a group of like investments. This risk can be diversified away
Equity risk premium
Real return minus risk-free real return
Risk averse
Compensated for taking risk
Risk-neutral
Investors that prefer investments with higher returns whether or not they have risk; disregard risk
Risk-seeking investors
Investors that prefer to take risks and would invest in a higher-risk investment despite the fact that a lower-risk investment might have the same return
Return on a single asset
Investment return is total gain or loss on an investment for a period of time
Change in asset’s value (either gain or loss) plus any cash distributions (e.g. cash flow, interest, dividends)
Investment return equation
Rt+1 = Pt+1 - Pt + CFt+1 / Pt
Rt+1 = investment return from time t tp t+1 Pt+1 = asset's price (market value) at t+1 Pt = asset's price (market value) at t CFt+1 = cash flow received from the asset from t to t+1
This formula measures return on an ex post basis (after the fact) - does not consider risk
How should investors evaluate investments?
Ex ante basis (before the fact)
Use expected returns and estimates of risk
Arithmetic average return
Computer by simply adding the historical returns for a number of periods and dividing by number of periods
Used for short holding periods
Geometric average return
Depicts compound annual return earned by an investor who bought the asset and held it for the number of historical periods examined. If returns vary through time, geometric return will always fall below the arithmetic average.
Used for longer holding periods
Normal distribution
Pattern of historical returns of large numbers (bell curve shaped)
Normal distribution
About 95% of returns will fall within the range created by expected return +/- two standard deviations
Subjective estimates of risk
When management does not have significant historical data on returns to calculate the mean and variance
Expected returns of a portfolio
E(Rp) = w1E(R1) + w2E(R2) + w3E(R3) …
E(Rp) = expected return on the portfolio w1,2,3 = weight of each of the assets E(R1,2,3) = expected return of each of the assets
What does the variance of portfolio returns depends on (3 factors)
- Percentage of the portfolio invested in each asset (the weight)
- Variance of returns of each individual asset
- Covariance among the returns of assets in the portfolio
Covariance
Captures the degree to which the asset returns move together over time
If the individual assets move together, little benefit to holding portfolio
What do portfolios allow investors to do?
Diversify away unsystematic risk
What are examples of systematic risk
Fluctuations in GDP, inflation, interest rates
Cannot be diversified away
What does the variance of an individual investment capture?
Total risk of the investment, both systematic and unsystematic)
Standardized measure to estimate an investment’s systematic risk
Beta
Beta = Bi = covariance of investment’s returns with returns of overall portfolio / portfolio’s variance
Measures how the value of the investment moves with changes in the value of the total portfolio
Risk preference function
Describes the investor’s trade-off between risk and return
Falling on the line is an efficient portfolio
What does interest represent?
Cost of borrowing funds
What are the two parts of credit/default risk?
- Individual firm’s creditworthiness (or risk of default)
2. Sector risk - risk related to economic conditions in firm’s economic sector
Interest rate risk
Risk that the value of the loan or bond will decline due to an increase in interest rates
Systematic risk
Market risk
Risk that the value of the loan or bond will decline due to a decline in the aggregate value of all the assets in the economy
Systematic risk
What type of risk is credit risk?
Unsystematic risk; unique to particular loan or investment
Stated interest rate
Contractual rate charged by the lender
Effective annual rate
True annual return to the lender
Why do the effective annual rate and stated interest rate differ?
Interest is compounded more often than annually
What is the formula for calculating the effective annual rate from the stated rate?
EAR = (1 + r/m)^4 -1
r = stated interest rate m = compounding frequency
Term structure of interest rates
Describes the relationship between long-and short-term rates
Important in determining whether to use long-term fixed or variable rate financing
How are term structure of interest rates depicted?
A yield curve
Normal yield curve
Upward sloping curve in which short-term rates are less than intermediate-term rates which are less than long-term rates
Inverted (abnormal) yield curve
A downward-sloping curve in which short-term rates are greater than intermediate-term rates which are greater than long-term rates
Flat yield curve
Curve in which short-term, intermediate-term and long-term rates all about the same
Humped yield curve
A curve in which intermediate-term rates are higher than both short-term and long-term rates
Why are long-term rates usually higher?
They involve more interest rate risk so require higher maturity risk premiums for long-term lending
Liquidity preference (premium) theory
Long-term rates should be higher than short-term rates, because investors have to be offered a premium to entice them to hold less liquid and more price-sensitive securities
If interest rates increase and an investor holds a fixed-rate long-term security, the value of the security will decline
Market segmentation theory
This theory states that treasury securities are divided into market segments by the various financial institutions investing in the market.
What type of securities do commercial banks prefer?
Short-term securities to match their short-term lending strategies
What types of securities do savings and loans prefer?
Intermediate-term securities
What types of securities do insurance companies prefer?
Long-term securities because of the nature of their commitments to policy holders
Expectations theory
Explains yields on LT securities as a function of ST rates
States that LT rates reflect average of ST expected rates over the time period that the LT security will be outstanding
When LT rates are lower than ST rates…
Market is expecting ST rates to fall
How are interest rates tied to inflation rates?
Directly
If LT rates are lower than ST rates…
Market is indicating a belief that inflation will decline
Derivative
Financial instrument or contract whose value is derived from some other financial measure (underlyings, such as commodity prices, stock prices, interest rates, etc.) and includes payment provisions
Examples of derivatives
- Options
- Forwards
- Futures
- Currency swaps
- Interest rate swaps
- Swaption
Options
Allow, but do not require, the holder to buy (call) or sell (put) a specific or standard commodity of financial instrument, at a specified price during a specified period of time (American option) or a specified date (European option)
Forwards
Negotiated contracts to purchase and sell a specified quantity of a financial instrument, foreign currency, or commodity at a price specified at origination of the contract, with delivery and payment at a specified future date
Futures
Forward-based standardized contracts to take delivery of a specified financial instrument, foreign currency, or commodity at a specified future date or during a specified period generally at the then market price
Currency swaps
Forward-based contracts in which two parties agree to exchange an obligation to pay cash flows in one currency for an obligation to pay in another currency
Interest rate swaps
Forward-based contracts in which two parties agree to swap streams of payments over a specified period of time
Example of interest rate swap
One party agrees to make payments based on a fixed rate of interest and other party agrees to make payments based on a variable rate of interest
Swaption
Option of swap that provides the holder with the right to enter into a swap at a specified future date with specified terms, or to extend or terminate the life of an existing swap. Characteristics of an option and an interest rate swap
Examples of financial intermediaries
- Commercial banks
- Insurance companies
- Pension funds
- Savings and loan associations
- Mutual funds
- Finance companies
- Investment bankers
- Money market funds
- Credit unions
Counterparty
Other party to the contract or agreement
Credit risk in using derivative
Risk of loss as a result of the counterparty to a derivative agreement failing to meet its obligation
Market risk in using derivative
The risk of loss from adverse changes in market factors that affect the fair value of a derivative, such as interest rates, foreign exchange rates, and market indexes for equity securities
Basis risk in using derivative
Risk of loss from ineffective hedging activities
Difference between fair value (or cash flows) of the hedged item and the fair value (or cash flows) of the hedging derivative
Entity is subject to the risk that FVs (or cash flows) will change so that the hedge will no longer be effective
Legal risk in using derivative
Risk of loss from a legal or regulatory action that invalidates or otherwise precludes performance by one of both parties to the derivative agreement
Speculation
As an investment to speculate on price changes in various markets
Hedging
To mitigate a business risk that is faced by a firm. Protects the entity against the risk of adverse changes in the FV or CF of assets, liabilities, or future transactions. Defensive strategy
Financial statement effects of derivative transactions governed by who
Statement of Financial Accounting Standards 133 (SFAS 133)
Fair value hedge
Hedge of the changes in the FV of a recognized asset or liability, or of an unrecognized firm commitment, that are attributable to a particular risk
Cash flow hedge
A hedge of the variability in the CF of a recognized asset or liability, or of a forecasted transaction, that is attributable to a particular risk
Foreign currency hedges
- FV hedge of an unrecognized firm commitment or a recognized asset or liability valued in a foreign currency (a foreign currency fair value hedge)
- A CF hedge of a forecasted transaction, an unrecognized firm commitment, the forecasted functional-currency-equivalent cash flows associated with a recognized asset or liability, or a forecasted intercompany transaction
- Hedge of a net investment in a foreign operation
What does SFAS 133 require an entity to do about derivatives?
Report all derivatives as assets and liabilities in the statement of financial position, measured at fair value
Accounting for a FV hedge
Change in the FV of a derivative designated and qualifying as a FV hedge is recognized in earnings and is offset by the portion of the change in the FV of the hedged asset or liability that is attributable to the risk being hedged
If hedge is completely effective, change in the derivative’s FV will equal change in hedge item’s fair value = no effect on earnings
If hedge is not completely effective, earnings will be increased or decreased for the difference between the changes in the FV of the derivative and hedged item
Accounting for CF hedge
Effective portion of the change in the FV of a derivative designated and qualifying as a CF hedge is reported in other comprehensive income and the ineffective portion is reported in earnings
How are derivatives valued?
Valued on financial statements at FV, which is the current market price of the derivative
Quoted market prices in active markets are the best source of fair value and may be used for many derivatives
Black-Scholes option-pricing model
Mathematical model for estimating the price of stock options, using the following five variables
- Time to expiration of the option
- Exercise or strike price
- Risk-free interest rate
- Price of the underlying stock
- Volatility of the price of the underlying stock
Other methods include: Monte-Carlo simulation and binomial trees
Zero-coupon method
Used to determine the fair value of interest rate swaps
Present value model in which the net settlements from the swap are estimated and discounted back to their current value
Key variables:
- Estimated net settlement cash flows
- Timing of the cash flows as specified by contract
- Discount rate
Example of agreement to swap payments on fixed-rate liability for a variable rate
If interest rates decline, the firm will receive a net positive cash flow from the swap because the amount received on the fixed rate will be greater than the amount due on the variable rate; opposite is true if rates increase
Zero coupon method estimates future cash flows by calculating the net settlement that would be required if future interest rates are equal to the rates implied by the current yield curve; amount is discounted to determine the current fair value of the swap for financial reporting purposes
Short position
When a firm is committed to sell something it does not own
LIBOR rate
London Interbank Offered Rate
Example: Firm entered into a $20,000,000, 10 year noncallable debt agreement
- Variable interest payments tied to LIBOR rate (4.5%)
- Firm enters into an interest rate swap to pay 7% fixed interest for the remaining term of loan instead of variable LIBOR rate
- Financial statement effects of this transaction would be recognition of a 7% fixed rate of interest over the life of the loan as opposed to the variable rate
Example: short position and futures
Firm carries ~$200k in ST financing at variable interest rates and management concerned about current instability of ST interest rates.
Mgmt decides to see on futures market $200k in Treasury notes to be delivered one year from today
Sale gives firm a short position
If interest rates rise, the firm will pay more interest on its ST debt but it will also experience a gain on the futures contract because the price of Treasury notes will decline
Near end of contract, firm purchases Treasury note contracts to close its short position
If hedge was completely effective, $20k gain on futures contracts will offset the increase in interest expense experienced by the firm due to increase in ST interest rates
Gain on the contracts would be used to reduce interest expense in operating income
Future value (FV) of an amount
Future value of an amount is the amount that will be available at some point in the future if an amount is deposited today and earns compound interest for “n” periods
E.g. savings deposits
Example of future value of an amount
Deposited $100 today at 10%
[100 + (100 x 10%)] = $110 at end of first year
[100 + (110 x 10%)] = $121 at end of second year
Present value of a future amount
The present value of a future amount is the amount you would pay now for an amount to be received n periods in the future given an interest rate of “i”
Example of PV of a future amount
Money you would lend today for a noninterest-bearing note receivable in the future
Lending money at 10%, lend $100 for a $110 note due in one year or for a $121 note due in two years
Trick for PV v. FV
PV of $1 is the inverse of the FV of $1
E.g. The future value of $1 at 10% in five years is 1.611. Thus, the PV of $1 in 5 years would be 1.00 / 1.611 = 6.21
Conversely, the FV of $1 is found by dividing the PV of $1 into 1.00. 1.00 / 6.21 = 1.611.
Compounding
When interest is compounded more than once a year, 2 extra steps are needed:
- Multiply “n” by the # of times interest is compounded annually. Gives you total number of interest periods
- Divide “i” by # of times interest is compounded annually. Gives you appropriate interest rate for each interest period
Example of compounding
if 10% was compounded semiannually, the amount of $100 at the end of one year would be $110.25 [(1.05)^2].
Future value of an ordinary annuity
Amount available “n” periods in the future as a result of the deposit of an amount (A) at the end of every period 1 through “n”
E.g. bond sinking fund; deposit is made at the end of the first period and earns compound interest for n-1 periods (not during the first period)
Next to the last payment earns one period’s interest; n-(n-1) = 1; last payment earns no interest, because it is deposited at the end of the last (nth) period
Present value of an ordinary annuity
Value today, given a discount rate, of a series of future payments
E.g. capitalization of lease payments by either lessors or lessees
Payments “1” through “n” are assumed to be made at the end of years “1” through “n” and are discounted back to the present
Distinguishing a future value of an annuity from a present value of an annuity
Distinguished by determining whether the total dollar amount in the problem comes at the beginning (e.g. cost of equipment acquired for leasing) or at the end (e.g. amount needed to retire bonds) of the series of payments
PV of annuity = beginning
FV of annuity = end
Annuities due
E.g. payments might be made at the beginning of each of the five years instead of at the end of each year (aka annuity in advance in contrast to an ordinary annuity (annuity in arrears)).
How to convert either a FV of an ordinary annuity or PV of an ordinary annuity factor to an annuity due factor
Multiply the ordinary annuity factor times (1+i)
Interest rates
Usually given in problems
Made up of 2 components:
- Expected inflation/deflation rate (affects relative value of the currency)
- Inflation adjusted return for the particular investment (determined by risk of the investment)
TVMF Applications
Basic formula:
FV or PV = TVMF x Amount
If an annuity is involved, what is the amount?
Periodic payment or deposit; if not, it is a single sum
What three variables determines an FV or PV?
- Time
- Interest rate
- Payment
What two variables determines TVMF?
- Time
2. Interest rate
Bonds
Provide for periodic fixed interest payments at a coupon (contract) rate of interest
Bonds: What happens if the market rate exceeds the coupon rate of a bond?
Book value will be less than the maturity value. Difference (discount) will make up for the coupon rate being below the market rate
Bonds: What happens if the coupon rate exceeds the market rate?
Bond will sell for more than maturity value to bring the effective rate to the market rate. Difference (premium) will make up for the coupon rate being above the market rate.
Bonds: What happens if the coupon rate equals the market rate?
The bond will sell for the maturity value
What is the market value of a bond?
Equal to the maturity value and interest payments discounted to the present
Bond Valuation Example
$10K in bonds; semi-annual interest at 6% coupon rate, maturing in 6 years, and market rate of 5%
Find PV of maturity value; PV of $1 factor. Discount $10k back 12 periods at 2 1/2% interest (Factor = .7436)
$10k x .7436 = $7,436
- Find the PV of the annuity of 12 $300 interest payments. Use PV of an ordinary annuity of $1 factor for 12 periods at 2 1/2 % interest (Factor = 10.26)
$300 x 10.26 = $3,078
Today’s value of bond: $10,514
Capital budgeting
Technique to evaluate and control LT investments. There are six stages
Capital budgeting stage 1: Identification stage
Management determines the type of capital projects that are necessary to achieve mgmt’s objectives and strategies
Capital budgeting stage 2: Search stage
Mgmt attempts to identify alternative capital investments that will achieve mgmt’s objectives
Capital budgeting stage 3: Information-acquisition stage
Mgmt attempts to revaluate the various investments in terms of their costs and benefits
Capital budgeting stage 4: Selection stage
Mgmt chooses the projects that best meet the criteria established
Capital budgeting stage 5: financing stage
Mgmt decides on the best source of funding for the project
Capital budgeting stage 6: implementation and control stage
Mgmt undertakes the project and monitors the performance of the investment
How are capital budgeting alternatives typically evaluated?
Using discounted cash flow techniques
Sunk, past or unavoidable costs
Committed costs that are not avoidable and therefore irrelevant to the decision process
Avoidable costs
Costs that will not continue to be incurred if a department or product is terminated
Committed costs
Arise from a company’s basic commitment to open its doors and engage in business (depreciation, property taxes, management salaries)
Discretionary costs
Fixed costs whose level is set by current management decisions (e.g. advertising, R&D)
Relevant costs
Future costs that will change as a result of a specific decision
Differential (incremental) cost
Difference in cost between two alternatives
Opportunity cost
Maximum income or savings foregone by rejecting an alternative
Outlay (out of pocket) cost
Cash disbursement associated with a specific project
Examples of capital budgeting models
- Payback or discounted payback
- Accounting rate of return
- Net present value
- Excess present value index
- Internal (time-adjusted) rate of return
Capital budgeting mode: payback method
Evaluates investments on the length of time until recapture (return) of the investment
E.g. if a $10K investment were to return a cash flow of $2.5k a year for 8 years, the payback period is 4 years.
Depreciation and cash flow
Depreciation does not consume cash
Payback example (computed after income taxes)
8 year life with no salvage value and a 404 income tax rate:
Cash flow: $2,500 x (1-40%) = $1,500
Tax savings from depreciation: $1,250 x 40% = $500
Cash flow after tax: $1,500 + $500 = $2,000
$10,000 / $2,000 = 5 years
What are the limitations of the payback method?
- Ignores total project profitability and has little or no connection to maximization of shareholder value
- Method is not really effective in taking into account the time value of money
Discounted payback method
Essentially the same as the payback method except that in calculating the payback period, cash flows are first discounted to their present value
Disadvantages of discounted payback method
-Ignores any cash flows after the cutoff period and therefore does not consider total project profitability
Accounting rate of return (ARR)
Computes an approximate rate of return which ignores the time value of money
Accounting rate of return (ARR) formula
ARR = Annual net income / average (or initial) investment
Example of accounting rate of return (ARR)
(cash flow - depreciation) / (average or initial investment)
What are the limitations of the accounting rate of return?
- Results are effected by the depreciation method used
- ARR makes no adjustment for project risk
- ARR makes no adjustment for the time value of money
Net present value (NPV)
discounted cash flow method which calculates the PV of the future cash flows of a project and compares this with the investment outlay required to implement the project
What is the formula of the net present value?
NPV = (PV of future cash flows) - (Required investment)
What does the calculation of the present value of the future cash flows?
Requires the selection of a discount rate (aka target or hurdle rate)
Use minimum rate of return that management is willing to accept on capital investment projects
Rate used should be no less than the cost of capital - the rate management currently must pay to obtain funds
Excess present value (profitability) index
Computes the ratio of the PV of the cash inflows to the initial cost of a project
Used to implement the net present value method when there is a limit on funds available
Formula for the excess present value index
PV of future net cash inflows / initial investment
X
100
If the excess PV index is equal to or greater than 100%
Project will generate a return equal to or greater than the required rate of return
What is the most widely accepted methods of evaluating a capital expenditure?
Net present value methods
Advantages of net present value methods
- Presents results in dollars which are easily understood
- Adjusts for the time value of money
- Considers the total profitability of the project
- Provides a straightforward method of controlling for the risk of competing projects - higher-risk cash flows can be discounted at a higher interest rate
- Provides a direct estimate of the change in shareholder wealth resulting from undertaking a project
What are the limitations of net present value methods?
- May not be considered as simple or intuitive as some other methods
- Does not take into account the management flexibility with respect to a project - mgmt may be able to adjust the amount invested after the first year or two depending on the actual returns
Internal (time-adjusted) rate of return (IRR)
Discounted cash flow method; determines the rate of discount at which the PV of the future CF will exactly equal the investment outlay
TVMF formula
PV (investment today) / Cash flows
Relationship between NPV method and the IRR method
- NPV > 0; IRR > Discount rate
- NPV = 0; IRR = Discount
- NPV
Advantages of the internal rate of return method
- Adjusts for the time value of money
- Hurdle rate is based on market interest rates for similar investments
- Results tend to be a little more intuitive than the results of the net present value method
Limitations of the internal rate of return method
- Depending on the CF pattern, there may be no unique IRR for a particular project - there may be multiple
- Occasionally, there may be no real discount rate that equates the project’s NPV to zero
- Technique also has limitations when evaluating mutually exclusive investments
Capital rationing
Deciding on one of serveral projects that are all acceptable; decide on the best project
Net present value profile
Allows the portrayal of the net present value of projects at different discount rates
What works better when a choice must be made among a group of investments?
Net present value works better than internal rate of return
Example of choosing between IRR and NPV
Company must choose between projects C and D.
IRR on project C is 15% with life of 5 years
IRR on project D is 13% with life of 10 years
-Project C selected under IRR criteria (assumes that cash inflows can be reinvested at 15%)
If cash inflows can be reinvested at only 9%, project B may be better alternative
Examples of relevant cash flows
- Initial investment in LT tabgible or intangible assets for each investment alternative
- Any initial investment in working capital for each investment alternative (e.g. inventories, AR)
- Cash flow from sale of any assets being replaced
- Differences in cash flows from operations under the alternatives
What should be considered when determining future cash flows?
- Focus on cash flows not accounting income
- Payments for incremental income taxes should be included
- Depreciation expense does not affect cash flows but the firm receives a tax savings (shield) from depreciation expense; reduces taxable income and therefore reduces tax payments; note that this is tax depreciation that generates the tax shield
What happens if the tax basis is expected to be different from the disposal price?
Tax basis (initial cost - tax depreciation taken)
-Tax gain or loss will generate tax inflow or outflow
Recovery of any working capital investment
investment recovered at the end of project by liquidation of inventories, accounts receivable; generally no tax implications of this recovery because it is assumed that the cash received will be equal to the book value (tax basis) of the WC items
Risk in capital bugeting?
Cash flows are not known with certainty
Probability analysis
Provide mathematical way of expressing uncertainty about the outcomes
Probability distribution
Set of all possible outcomes from an investment with a probability assigned to each outcome
Can be discrete or continuous
Discrete probability distribution
Identifies a limited number of potential outcomes and assigns probabilities to each of the outcomes
Continuous probability distribution
Theoretically defines an infinite number of possible outcomes
E.g. normal distribution (bell-shaped curve)
Why is the normal distribution useful?
Approximates many real-world situations can be completely described with only two statistics; mean and standard deviation
Distances and curve areas under the normal distribution
- 00 = 68.3%
- 64 = 90.0%
- 96 = 95.0%
- 00 = 95.4%
- 57 = 99.0%
Expected return formula
k^ = summation kipi
k^ = expected value of the returns k = returns from various possible outcomes p = probabilities assigned to possible outcomes
Standard deviation formula
Summation (k^-k)^2pi
What does the standard deviation provide?
Rough estimate of how far each outcome falls away from the mean
The larger the standard deviation..
The greater the risk
What is the significant limitation of standard deviation as a measure of risk?
Size depends on the size of investment
How to eliminate the size difficulty analysts have with standard deviation as a measure of risk?
Coefficient of variation
Coefficient of variation formula
Standard deviation / expected return
Measure of risk that is normalized for the size of the investment
Risk-adjusted discount rates
Using different discount rates for proposals with different levels of risk
Sensitivity analysis
Management makes many assumptions before arriving at the investment’s net present value; recompute with different variables, management can determine how sensitive the net present value is to changes in each major assumption
Explore “what if” situations to determine the variables to which the outcomes are particularly sensitive
Scenario analysis
More complex variation of sensitivity analysis
Instead of exploring the effects of a change in one variable, management develops a scenario that might happen if a number of related variables change
Simulation models
Computer simulation software makes it possible to model the effects of even more economic conditions on the results of an investment project
Decision trees
Visual representation of decision points and potential decisions
Real options
Assumes that once management makes an initial investment, it has an option to take a number of future actions that will change the value of the investment
Expansion options
Mgmt may receive an option to expand the investment
Abandonment options
Management almost always has an option to abandon a project
Follow-up investment options
Management may receive other investment opportunities when investing in the project
Flexibility options
Management may be provided with the ability to take advantages of changes in economic circumstances
Lease versus Buy
Mgmt will often compare the two alternatives using discounted cash flow
Why is a lease attractive?
- Tax advantages
- Require less initial investment
- Less formal borrowing which may be restricted by loan covenants tied to the company’s other debt
- Certain leases do not have to be capitalized and therefore will not require recognition of debt on the company’s balance sheet
Risk preference function
Illustrates the efficient frontier for portfolio investments
Any portfolio of investments that falls on the line is efficient
Highly correlated investments do nothing to diversify risk
Negatively correlated investments do reduce overall risk (investments move in opposite directions with changing economic conditions)
Coefficient of correlation
Measure that is used to express the extent of the correlation between a set of investments
Value from +1 to -1
Positive is little risk reduction and negative is significant risk reduction
