FINA3000Test 2

Single asset investment

Volatiltiy of single asset is standalone risk. Invest in one asset. Select stock w/ highest return for any level of risk. Compare using coefficient of variation

CV_i=standard dev_i/E(r_i)

Or sharpe ratio

Sharpe_i=(E(r_i)-r_f)/standard dev_i

(E(r_i)-r_f)

Expected risk premium for investing in stock. It is extra return beyond risk free return rf

Portfolio w/ more than one asset

Portfolio could have stocks, bonds, commodities, real estate, firm projects, measurable assets. Any investment has return and standard dev. Investors build portfolios w/ more than one asset to manage risk (reduce avg overall risk)

Systemic risk/non diversifiable risk

risk from external macroecon factors that impact entire market (ex. interest, inflation, recession) cant be eliminated from diversification are considered systematic.

Specific risk/unsystematic risk/diversifiable risk

Eliminated by investing in multiple assets leaving market risk for assets

One period return

% earned over defined time (holding period)

Holding period return: r_t=(price gain+income)/initial price

In general/over time period: investment cashflow/initial price

In stock terms: (P_t-P_t-1+D_t)/P_t-1

P_t-1=price of investment last period

P_t=price today at end of period

D_t=dividend

Average return

Sum of all holding period returns divided by total num returns

r_avg=sum of r_t/N

Provides baseline to compare how individual returns behave and assess their volatility

Problem of average return

Time value ignored as each return is treated as separate entity. Value should be linked together

Standard dev return

Variability of individual returns from avg returns, indicating investment risk level. Larger SD, greater range of outcomes and higher volatility. Can help with diversification and risk tolerance. Measure volatility or dramatic increase/decrease in return

Compounded returns

returned linked together. PV=initial investment and r_t will not be constant every year

FV_N= PV (1+r₁)(1+r₂)…(1+r_N)

Yearly value/geometric return/annual compounded return also example

Geometric return

finding equivalent annual compounded interest rates

1. r_hp=(1+r₁)(1+r₂)…(1+r_N)-1

2. Geometric is yearly interest rate lets present value to future value after N years. r_geo=(1+r_HP)^1/N-1

Smaller than arithmetic return. W/ compounded interest and returns. Truer measure of earned

Total compounded return

Total compounded return is wealth factor (total multiplier)

holding period of return of r_hp. Holding period return (r_hp)-Total percentage change of wealth over entire duration (percentage gain (actual profit/loss)

Expected return w/ discrete distribution

Count possible outcomes of forecast. Need to find probability of outcome happening. All possible outcomes =100%. Chance of event multiplied by return. Expected return= E(r)=sum (p_i*r_i)

Arithmetic vs expected return

Expected→ looks forward at possible outcomes. Arithmetic→ looks backward w/ equally likely events b/c they happened

Discrete distribution

count possible outcomes in forecast b/c it is finite

Continuous

Typically used in finance w/ investments w/ large amt of outcomes. Also called normal distributions. Infinite outcomes

Positive ocrrelation

returns on two assets vary together. Degree of correlation described what % of time two assets returns move together relative to their avg. 0<P<=1. If 1, assets perfectly correlated

Negative correlation

Returns of two assets move in opposite directions relative to avg. -1<=P<0. If returns moving in same direction, not hedging risk. Return is either really up or really down

Removing risk

Can’t remove all risk w/ diversification. Market risk is portion of portfolio volatility can’t remove or diversify. Can remove all diversifiable risk/unsystematic risk

Beta

Compares systematic risk of individual assets vs. systematic risk of market portfolio. How risk investment compared to avg investment. Used to increase or decrease return to match risk in investment. Beta_i=(P_im*standard dev_i)/standard dev_m

If beta>1 asset has greater systematic/rewardable risk than market portfolio. Higher required return than avg asset

If beta<1 less rewardable risk in portfolio. lower required return than avg

If beta=1, asset same rewardable risk than market. asset has same required return as avg

Driven by stock’s total volatility and relation w/ econ.

Assets can have small beta if large volatility but small correlation and vice versa

Another way to calc is regressive coeff (slope between returns on market portfolio and individual asset

Beta_i=covariance (r_i,r_m)/variance (r_m)=standard dev_i,m/standard dev²_m=(P_i,m*standard_i*standard_m)/standard²_m

Risk free rate

opportunity of investing. Return we want on guaranteed investment, r_f. No volatility, min return required before considering riskier investment. Would want a higher return from riskier investment to compensate for additional risk (wouldn’t want to take on risk for same amount of return as risk free rate)

CAPM

r_i=r_f+beta_i(E(r_m)-r_f). Investors want fixed return plus bonus return for assets risk. Bonus is

beta_i(E(r_m)-r_f). Beta determines size of bonus return for risk.

Challenges: Hard to apply b/c no absolutely risk-free security, so we use yield to maturity on US gov debt issue. But split on which to use. Difficult to also measure market portfolio, use return on index that tracks US stock market. Can be used to measure required return of portfolio

1. Beta_p=sum w_i+beta_i→ weighted avg of each asset in portfolio based on dollars invested

2. Then CAPM becomes: r_p=r_f+beta_p(r_m-r_f). Calc required return to hold mutual fund or other portfolio. Evaluate risk of portfolio before commit capital

Capital budgeting process

1. Identify project likely expand shareholder value. Finance projects generate return satisfies investor

2. Estimate future cash flow for project. May allow volatility in cashflow

3. Evaluate cash flows using decision rules. Recommend to accept/reject

4. If accepted, review outcome and adjustments to improve future

NPV

Net present value, favored/most powerful decision rule. Value of opportunity in dollars. NPV= FCF₁/(1+r) + FCF₂/(1+r)²+… FCF_N/(1+r)^N+FCF₀. FCF= free cash flow that project generate prior to paying investors for particular yr/time period. r=cost of capital/return investors want on project. Weighted avg across all investors

FCF₀=cash flow today is (-) b/c invested at start

Accept project if NPV>=0 - expected cash flows exceed initial investment

NPV portfolio

Shows NPV uses range values for discount rate, showing how sensitive to cost of capital.

Step 1: enter cash flows in finance calc

Step 2: select value for cost capital and calc project NPV

Step3: repeat step 2 until get enough NPV to form graph (profile). Increase cost of capital, decrease NPV. Larger return, project cashflow is worthless in present value terms. Large return=less extra wealth created for shareholders. Great risk/great volatility require larger returns. Risk project, lower NPV. Positive NPV, higher share price.

Issues/strengths of NPV

Issues: difficult to explain to professionals w/ limited biz training (NPV is change left over/surplus). NPV is sensitive to cost of capital and difficult assessing leads to misinformed decisions. Predicting costs and rates in advance is risky

Strengths: directly uses return required by investors. Direct measure of shareholder gain/loss

Independent (Types of projects and decision rules)

selecting project will not prevent firm from taking another project. Occurs when firms not capital or source constrained in making decision

NPV rule: take projects w/ NPV >=0

IRR rules: take all projects where r<= IRR

Mutually exclusive (Types of projects and decision rules)

Firm takes best project at expense of other projects. So, taking one project prevents firm from taking another

NPV rule: take project w/ highest NPV (if NPV>=0)

IRR rule: take project w/ largest IRR (where r>=IRR)

Contingent (Types of projects and decision rules)

Firm has to take several projects together or reject all projects

NPV rule: take all projects if combined NPV>=0

IRR rule: take all projects if combined IRR > r

Internal rate of return (IRR)

Represents rate of return earned on every dollar invested in project. Profit rate, % rate measure of success

NPV=0=FCF₁/(1+IRR) + FCF₂/(1+IRR)²+… FCF_N/(1+IRR)^N+FCF₀

IRR is where graph crosses x ais or NPV=0

IRR is hurdle rate as it is main rate firm can pay investors

If seeks less than IRR, project returns more than cost

Accept project r<=IRR or financing rate<=profit rate

Timing of cashflows (differing rates/size)

IRR and NPV use different discount rates in calculations. NPV uses cost of capital, IRR is profiting rate. W/ different rates, size and time affect suggest choice. IRR can’t measure size of cashflow only rate. Accept NPV b/c direct measure of gain. Size of cashflows cause rules to disagree. IRR does not see magnitude, so project with small investment could have large internal rate of return

Issues/strengths IRR

Strengths: easier to convey b/c percentages easier to convey success. Does not require cost of capital which is difficult

Issues: does not directly use shareholder or owner in calculations b/c does not use cost of capital. → Does not measure gain in wealth

Switching signs w/ cashflows: having alternating period of positive cashflows

Multiple internal rates of return

Project cashflows switch more than once. Every sign switch we have on internal rate of return, we lose economic interpretation when we have more values. Creates multiple IRRs making it difficult to interpret which to use, leading to confusion in decision making

Crossover point

indifference point as will be fine w/ either project at cost of capital. NPV_AB=FCF₁/(1+r) + FCF₂/(1+r)²+FCF₀ NPV_A=NPV_B

Payback decision rule

calc how long takes to recover initial investment in project. Units are time, so measure in years. Shorter payback is efficient project. Measure liquidity

Two ways of calculation:

1. Assumes project pays same cash flow every year. Payback= absolute value(initial investment)/annual cashflow

2. Uneven, keep running total of net cash position for project. Shows remaining cash flows to be repaid to recover initial investment. We create another row called net cash

How firm decides payback period

Compare to market/industry norms and assess risk. Base standards off financial health and policies

NPV and payback

NPV assess profitability and payback offers insights into liquidity and capital recovery

Problems with payback

1. No clear value making payback acceptable

2. Ignores time value money

3. Ignores cashflows beyond payback period

Discounted payback

Calc amount time to recover initial investment. First calc PV of project cashflow and time to recover. Considers time value of money. Find PV of each project then net cash

Profitability index

ranks projects on efficiency and is useful when project has resource constraint. Compares value/ cost representing profits

Constrained budget

Constrained by money

1. PI= NPV/initial costs

2. PI=PV benefits/PV of costs=NPV+initial costs/initial costs

Resource constrained- not enough fixed assets/human capital to complete all projects

PI=NPV/amount of resources used

Resource constrained

Not enough fixed assets/human capital to complete all project. PI=NPV/amnt of resources used

Reinvestment rate

NPV assumes own cost of capital, IRR assumes firm’s own return. The assumption for NPV is more realistic

Cashflows

Measured on incremental basis. Change from accepting project. Measures project CF for all investors in firm. Prior payments to investors. Exclude interest payments to debt holders and dividends to stockholders. Not include CF from increase debt or new equity. Operation value of project. Measure operating performance w/o influence of financing decisions→ project itself creates value

After taxes b/c measures true cash/income by firm

Ignore sunk costs- exp occurred prior to decision

Include side effects- impact on firm (+ or -)

Opportunity cost- cost of alternative item or opportunity

Depreciation

Non cash expense. expense used of fixed asset over useful life.

Cash flow from op:EBIT(1-T)+depr → b/c not actual CF is added

EBIT=Sales rev-exp-depr

Also reduces taxable income, leading to tax savings, does not provide real cash benefit.

Depreciable basis- $ amount that can be depreciated by firm over useful life

Salvage value- expected selling value at end of useful life

Greater depr translates larger CF because tax benefits.

Accelerated cash flow increase deprecation early in project, increase NPV

Capital budgeting

Process where biz determines if project worth pursuing. estimates cash inflows or outflows. Applies NPV and IRR rules to determine to accept or reject. It determines avg return required by investors in firm for use of capital.