Corporate Finance Lectures
Winnebagel Corp. currently sells 21,000 motor homes per year at $59,000 each, and 7,500 luxury motor coaches per year at $96,000 each. The company wants to introduce a new portable camper to fill out its product line; it hopes to sell 16,000 of these campers per year at $9,500 each. An independent consultant has determined that if Winnebagel introduces the new campers, it should boost the sales of its existing motor homes by 2,500 units per year, and reduce the sales of its motor coaches by 1,200 units per year. What is the amount to use as the annual sales figure when evaluating this project?
*ONLY INCLUDE THE STUFF FROM THE NEW PROJECT In evaluating annual sales for the project
Expected Returns: 2 Options
*Option 1*: take average (arithmetic) of past returns: E(r)=Sum of returns/number of returns *Option 2*: if the sum returns or observations are more or less likely than others, we have to do a weighting: (picture)
EFN: Percentage of Sales Approach
*Overall Goal*: look at financing needed for chosen/target growth rate - There are man possible assumptions for varying quality about each item - This approach builds from assumptions of Chapter 4.3 except for: Fixed Assets: we will determine FA needed by capacity and utilization Dividend Policy: Will be given by management (i.e state in the problem) - Many of these assumptions are imperfect: depreciation, taxes, fixed assets, etc
Terms to Know: Technical Analysis, Fundamental Analysis, Growth Stocks, Value stocks, exchange traded funds
*Technical Analysis*: short term trading analysis, trading based on stock patterns and trends *Fundamental Analysis*: long term analysis of the strengths and weaknesses of a company, trading based on the intrinsic value of a stock *Growth Stocks*: looking to superior growth and price appreciation for most of the return, generally higher multiple *Value Stocks*: looking to dividends for most of future return, generally lower multiple *Exchange Traded Funds*: a portfolio of stocks (generally) traded on exchanges like an individual stock
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 (we will almost never do these)
Total Return = Suppose a stock had an initial price of $50 per share, paid a dividend of $.80 per share during the year, and had an ending share price of $60. Compute the percentage total return.
((P1-P0)+D)/P0
Capital Gain Yield=
(P1-P0)/P0
Example: - Corporate Bond yielding 7% - Municipal Bond yielding 5.5% You are married and have a combined income of $155,000 Which bond should you buy?
(need to look at tax rate to figure this out first) - Federal Tax Rate = 22% Corporate Bond: (0.07)*(1-0.22)= 0.0546 --> 5.46% Return Municipal Bond: 0.055--> 5.5% Return (no tax on municipal) *Buy municipal!* - similar question to this on exam!
*4 Determinants of Growth*: Areas of Concern
*1. Profit Margin* - Operating Efficiency *2. Total Asset Turnover*- Asset use efficiency *3. Financial Leverage*- Choice of Optimal debt/equity ratio *4. Dividend Policy* - Choice of how much to pay to shareholders versus reinvesting in the firm
Payback Period Decision Rule (*NOT ON EXAM*)
*Accept if the payback period is less than some preset limit* - in his first job the test was 3 years
Arithmetic vs. Geometric Mean
*Arithmetic Average*: return earned in an average period over multiple periods *Geometric Average*: average compound return per period over multiple periods The geometric average will be less than the arithmetic average unless all the returns are equal
Cash Flows From Capital Assets
*Change in Net Fixes Assets between periods, plus *After Tax Salvage value of the assets
NPV - Decision Rule
*If the NPV is positive, accept the project* - positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners - Remember, we're talking expected (pro forma) cash flows. These are inherently uncertain/risky. Excellent capital budgeting can still lead to ex post negative NPV projects being done - To handle risk typically firms use 2 or 3 forecasts (base, upside, downside)
Scenario Analysis
*Modeling different possible/probable outcomes and looking at what happens to NPV and IRR under different cash flow scenarios* Look at: - Base Case: management forecast - Best case: high revenues, low costs (only change sales for exam unless stated otherwise) - Worst case: low revenues, high costs (only change sales for exam unless stated otherwise) - Looking at the range of possible outcomes Best case and worst case are not necessarily probable, but they can still be possible
Net Present Value
- *NPV is the difference between the market value of a project and its cost* - Tells us how much value is created (or destroyed) from undertaking an investment - First step is to estimate expected future cash flows - Second step is to estimate the *required return* for projects of this risk level - *The third step is to find the present value of the cash flows and subtract the initial investment* - If the investment is non-standard (i.e. no cash outflow at t=0), we simply find the present value of all the cash flows
Components of Bond Prices
- All Risk/Reward - 1. Characteristics of that issuer - Often its rating, comparison with other similar bonds - 2. Inflation premium - slope of the yield curve - 3. Interest rate premium - longer term bonds have more risk
2.1 The Balance Sheet
- An accountant's snapshot of the firm's accounting value at a specific point in time - The Balance Sheet Identity is: Assets = Liabilities + Stockholders' Equity
Growth and External Financing
- At low growth levels, internal financing (RE) may exceed that required investment in assets - As the growth rate increases, the internal financing will not be enough, and the firm will have to go to a bank or the capital markets for money - Examining the relationship between growth and external financing required is useful tool in long range planning
Bond Concepts
- Bond prices and market interest rates move in opposite directions - When coupon rate>YTM, then price>par value (premium bond) - When coupon rate<YTM, then price<par value (discount bond)
EFN Options
- Borrow more short term (Notes payable) - Borrow more long term (LT Debt) - Sell more common stock (CS) - Decrease dividend payout, which increases the Additions to RE - Our first "taste" of capital structure!
Incremental Cash Flows: What matters?/ relevant cash flows (*ON EXAM*)
- Cash flows matter -- not accounting earnings - Incremental cash flows matter. *The Future* - Opportunity costs matter (another project may have a higher NPV) - Side effects like synergy (increased demand of existing products), cannibalism (new products causing customers to demand less), and erosion (same thing as cannibalism) matter - Taxes matter: we want incremental after-tax cash flows - Sunk costs *dont* matter. They are the past
The "Rate" is driven by...
- Current opportunity cost of money in the market inflation - Compensation for the risk of the investment - Inflation
Sinking of Titanic Example: - Cost of titanic was $7.5 Million - Insured with Lloyd's of London for $5 Million - In an efficient market what would you expect to be the impact of the White Star Line's Stock?
- Decrease of $2.5M because it's how much was lost IMM (parent company) stockL - Day before: $15.6 Million value - Day after: drop of $2.6 million in value - Supports strong or semistrong form efficiency
Summary - Investment Rules: Net Present Value (NPV)
- Difference between market value and cost - take the project if the NPV is positive - Has no serious problems - Preferred decision criterion
Summary - Investment Rules: Internal Rate of Return (IRR)
- Discount rate that makes NPV=0 - Take the project if the IRR is greater than the required return -same decision as NPV with conventional cash flows - *IRR is unreliable with nonconventional cash flows or mutually exclusive projects*
Estimating Dividends: Simplifying Cases: Differential/2-Stage/Non Constant Growth
- Dividend Growth is not consistent initially, but settles down to constant growth eventually - The price is computed using a multi-stage model
Good Decision Criteria
- Does the decision rule adjust for the time value of money? - Does the decision rule adjust for risk? - Does the decision rule account for ALL *incremental* cash flows? - Does the decision rule provide information on whether we are creating value for the firm? - Does the decision rule tell us how much value we are creating?
Advantages of Payback Period (*PAYBACK NOT ON EXAM*)
- Easy to understand - Adjusts (poorly) for uncertainty of later cash flows - Biased toward liquidity
Financial Planning Model *Ingredients*
- Economic Assumptions: explicit assumptions about the coming economic environment (economic growth/ recession, interest rates, tax rates) - Sales Forecast: many cash flows depend directly on the level of sales (often estimated using sales growth rate) - Pro Forma Statements: setting up the plan using projected financial statements allows for consistency and ease of interpretation - Asset Requirements: the additional assets that will be required to meet sales projections - Funding Requirements: the amount of financing needed to pay for the required assets - Plug Variable: determined by management deciding what type of financing will be used to make the balance sheet balance
Sensitivity Analysis
- Evaluating the results of changing one variable while keeping the other variables constant - What happens to NPV and IRR when we change one variable at a time - The greater the volatility in NPV in relation to a specific variable, the larger the *forecasting risk* associated with that variable, and the more attention we want to pay to its estimation
Role of Financial Planning
- Examine interactions - help management see the interactions between decisions - Explore options - give management a systematic framework for exploring its opportunities - Avoid surprises - help management identify possible outcomes and plan accordingly - Ensure feasibility and internal consistency - help management determine if goals can be accomplished and if the various stated (and unstated) goals of the firm are consistent with one another
Long Term Planning: WHY SHOULD WE DO IT?
- Forces us to think about the Future - Forces us to think about Goals (List of things to accomplish) - Forces us to establish our Priorities
Payback Period (*NOT ON EXAM*)
- How long does it take to get the initial cost back in a nominal sense? Computation: - Estimate the cash flows - Subtract the future cash flows from the initial cost until the initial investment has been recovered
Disadvantages of Payback Period (*PAYBACK NOT ON EXAM*)
- 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
Multiple Cash Flows Using a Spreadsheet
- In Excel: =NPV(rate, CF1, CF2, CF3...)+CF0 - rate is the discount rate - CF1 is the cash flow in period (year) 1, 2 in year 2, etc - Last example: =NPV(12%,200,400,600,800)=$1,432.93
Review of Capital Budgeting: What is the number one objective?
- Increase Shareholder Value - We accept those projects that increase shareholder value (prioritize) - How do we make capital budgeting decisions? - Build a model estimating the cash flows - Determine the required return (cost of capital) - Apply the decision rule (NPV, IRR Payback, Cash on Cash)
Elements of Financial Planning
- Investment in new assets - determined by capital budgeting decisions - Degree of financial leverage . - determined by capital structure decisions - Liquidity requirements - determined by NWC decisions - Cash paid to shareholders - determined by dividend policy decisions - 1st three are our "3 questions in finance"
Cash Flow(s) from buying or selling capital assets (CapEx)
- It costs money to buy a business, build a factory, etc. - We can sell the assets at the end, but we need to consider taxes (ATSV)
Review of Capital Budgeting: What are the steps
- Lay out the assumptions - Build the cash flows: Operating cash flow, capital expenditure cash flow, net working capital cash flow - add them together
Summary - Investment Rules: Payback Period
- Length of time until initial investment is recovered - Take the Project if it pays back within some specified period - Doesn't account for Time value of money, and there is an arbitrary cutoff period
Financial Planning Process: Assumptions and Scenarios (*This is the Heart of It*)
- Make realistic assumptions about important variables - Run several scenarios where you vary the assumptions by reasonable amounts - Determine, at a minimum, worst case, best case, and base case scenarios
NPV vs. IRR
- NPV and IRR will generally give us the same decision - Exceptions: 1. Nonconventional Cash Flows - cash flow signs change more than once 2. Mutually Exclusive Projects - Initial Investments are substantially different (issue of scale), - timing of cash flows is substantially different
Conflicts between NPV and IRR
- NPV directly measures the *increase in value* to the firm. - Whenever there is a *conflict between NPV and another decision rule*, you should *always use NPV* - IRR is unreliable in the following situations: - Nonconventional cash flows - Mutually exclusive projects
Nonconventional Cash Flows with NPV, IRR, Payback
- NPV handles nonconventional cash flows perfectly - just do the same thing as always - payback generally doesnt make any sense - IRR gets complicated: IRR finds the rate which sets NPV=0 - Cash flows all positive or all negative = no solution - Cash flows change signs more than once = multiple solutions - Cash flows positive then negative: one solution...
Strong Form Efficiency - most extreme (*NOT ON EXAM*)
- Prices reflect all information, including public and private - If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed - Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns
Semi-strong Form Efficiency(*NOT ON EXAM*)
- Prices reflect all publicly available information including trading information, annual reports, press releases, etc. but do not capture all (inside) information - If the market is semi-strong form efficient, then investors cannot earn abnormal returns by trading on public information - Implies that fundamental analysis will not lead to abnormal returns - In reality, some stocks - larger well followed - have more efficiency than others
Example with Financial Constraints (*THIS IS ON EXAM!*)
- Project A has highest NPV for a single project - Project C has highest IRR for a single project - Projects B + D has the highest total NPV within the budget at $111.90 - *SO: you'd do all if possible, but B and D given the budget*
The Real World of Forecasting: Limits/Risks in our Projections
- Projections are wrong 100% of the time - We make the best projections we can with the best information available but we don't have a crystal ball - How much confidence do we have in our projections? - Tools we can use to help us analyze to make the best decisions: scenario analysis, sensitivity analysis, simulation analysis
Buying and Selling Long Term Assets
- Refers to fixed/ durable assets, not office supplies - Purchase: Normally designated year 0, Equal to cost of the thing purchased - Sale: normally at the end of last year of operation, NOT equal to sales (market) price (find after-tax salvage value ATSV) (*ATSV not on exam*)
EFN Options if Excess Financing
- Repay some short-term debt (decrease Notes Payable) - Repay some long term debt (decrease LT Debt) - Buy back stock (decrease Common Stock and Additional Paid in Capital) - Pay more in dividends (reduce Additions to RE) - Increase cash amount - Take all employees for a ski day
Systematic Risk
- Risk factors that affect a large number of assets - Also known as non-diversifiable risk or market risk - Includes such things as changes in GDP, inflation, interest rates, etc.
Unsystematic or Idiosyncratic Risk
- Risk factors that affect a limited number of assets - Also known as idiosyncratic/unique/asset-specific risk - Includes such things as labor strikes, part shortages, etc.
EFN Assumptions: Income Statement
- Sales & Costs grow at rate of sales growth - Depreciation: is ignored/missing, or you can think absorbed by cost above - Interest: *does not change* - Taxes: constant tax *rate* each year - Dividends: same *rate* as last year unless otherwise stated - Net income minus dividends= Addition to RE on balance sheet
Advantages of IRR
- Setting a required rate of return is intuitively appealing (takes into account the risk of the project) - It is a simple way to communicate the value of a project to someone who doesn't know all the estimation details - If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task
IRR and Nonconventional Cash Flows (*NONCONVENTIONAL CASH FLOWS NOT ON EXAM*)
- When the cash flows change sign more than once, there is more than one IRR (basically if there's a negative in the outstreams like Year 3 CF= -3000) - When you solve for IRR you are solving for the root of an equation, and when you cross the x-axis more than once, there will be more than one return that solves the equation - If you have more than one IRR, which one do you use to make your decision? You can't use IRR with unconventional Cash Flows
Changes in Net Working Capital (NWC)
- When we first start, we have to put cash in the register and inventory on the shelves - We generally get this $$ back at the end -- assume this in our class *always add back NWC
Developing the Model
- You could continue to push back the year in which you will sell the stock - You would find that the price of the stock is really just the *present value of all expected future dividends*
Sample Problem: •Your stock investments return 8%, 12%, and -4% in consecutive years. What are the arithmetic and geometric returns? •What is the sample standard deviation of the above returns? •What does the variance and standard deviation tell you about the probability of various return possibilities?
- gives same thing using var.s instead of var and same with using stdev.s and stdev
discounted rate
- helps find current value of future value
Example: Variance and Standard Deviation (*NOT ON EXAM*)
- here in excel we use =stdev and =var to get those.. maybe ask him what he wants but probs just =stdev and =var cuz he didnt even know those were a thing
Figure 12.4
- investing in small stocks in 1925 and sold in 1934 = you lost half your investment but not in long run - Hold onto your stock even if you're scared it's decreasing because it might increase in future - Treasury bills are risk free rate because the government always finds a way to pay them back in the US. (100% of the time youre going to get your money back)
PMT is used only for payments that...
- occur repeatedly at equal increments of time - Are of constant amounts
Non-Constant Growth Model: Example •Suppose a firm is expected to increase dividends by 20% by next year and by 15% for the year after that. •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.
- use NPV in excel to find last number using Div 1 and Div2+Appreciation - we can look at it as if we buy the stock today and receive $1.20 dividend in year 1, receive the $1.38 dividend in year 2 and then immediately sell it for $9.66
EFN Assumptions: Balance Sheet
-assume current assets - (all except PP&E) - vary directly with sales - Fixed assets will be determined by capacity: existing vs. needed - Accounts Payable and other current liabilities will vary directly with sales (except Notes Payable) - *so everything in NWC (assets and liabilities) grows with sales growth* - Notes payable and long term debt: do not change - Retained Earnings: changes by "addition to retained earnings" from the income statement (only number we actually needed from the IS)
Features of Common Stock
-voting rights -proxy voting -classes of stock Other Rights: -share proportionally in declared dividends -share proportionally in remaining assets during liquidation -preemptive right- first shot at new stock issue to maintain proportional ownership if desired
Risk Free Asset's Beta is ALWAYS
0!!!
EAC: Two general approaches (*NOT ON EXAM*)
1) Lay out cash flows, repeating project as needed until get matching lives: - Not my recommendation (may not work, can be tricky) - *wont teach or test this* 2) EAC (for each option): - Step 1: find NPV of a single iteration - Step 2: convert NPV to an annual amount (the EAC); use same rate, useful life as NPER, NPV becomes PV - Step 3: choose better option by comparing EACs... if costs choose "smaller" EAC, if benefit choose "larger"
2 Fundamental Assumptions/ Determinants in Financial Planning Process?
1. *Planning Horizon*: Divide decisions into short-run decisions (usually next 12 months) and long-run decisions (usually 2-5 years) 2. *Aggregation*: combine capital budgeting decisions into large projects - decide how much to aggregate (company, divisions, locations?)
Assume we will accept the project if it pays back within two years. Year 1: 165,000 - 63,120 = 101,880 still to recover Year 2: 101,880 - 70,800 = 31,080 still to recover Year 3: 31,080 - 91,080 = 60,000 more than we invested gets paid back by the end of year 3 (*PAYBACK NOT ON EXAM*)
2.34 Years
"Recent" Market Volatility
2008 was one of the worst years for stock market investors in history - the S&P 500 plunged 37% - The index lost 17% in October alone From March '09 to Feb '11, the S&P doubled in value Long-term treasury bonds gained over 40% in 2008 - They lost almost 26% in 2009 the markets (i.e. people) tend to forget the bad times somewhat quick
*Suppose your firm earns $12 million in taxable income* : What is the average tax rate? (*NOT ON EXAM*)
34.17% Average rate: 4,100,000 / 12,000,000 = .3417 or 34.17%
*Suppose your firm earns $12 million in taxable income* : What is the marginal tax rate? (*NOT ON EXAM*)
35% Marginal rate comes from the table, and it is 35%
Excel: how much of your first (or second, etc) payment is interest?
=IPMT
Computing IRR
=IRR in excel and highlight all cash flows including CF0 - Note Year 0 is now inside parentheses - Have cash flows in consecutive cells and highlight all at once - Must expand to two decimal places
Excel: what is payment?
=PMT
Excel: How much of your first (or second, etc) payment is principal?
=PPMT
Debt to Equity Ration -- Why does it matter?
?
Reading Stock Quotes
???
Bonds and Bond Valuation
A bond is a legally binding agreement between a borrower and a lender that specifies the: - Par (face) value (normally $1000) - Coupon rate - Coupon payment (we assume always semi-annual) - Maturity date The yield to maturity (YTM) is the required market interest rate on the bond. - Not set by the bond, but instead by the market - Changing constantly
Equivalent Annual Cost (EAC) (*NOT ON EXAM*)
A special case of capital budgeting when: - Options are of unequal lives - We will need to replace/repeat at the end of the life In this case a simple NPV is misleading: - Generally ignores the replacement aspect
Why bonds?
After we figure out what we "want to buy" (Capital budgeting) we have to figure out how to pay for it (Capital Structure) or how much more money is needed if it is our existing operation (EFN) For the funding that we can't generate internally (retained earnings), we can either get more money from the owners (stock), or we can borrow it (debt). the primary form of corporate borrowing/debt is bonds
Table 12.3: Average Annual Returns and Risk Premiums
Average Return - Risk Free Rate=Risk Premium
How do we find the total return over multiple periods?
Average Return or Geometric Return
Your firm currently has $100,000 in current assets and $120,000 in current liabilities. You estimate for next year both will grow by 10% over this year. What is the estimated cash flow associated with next year's change to next working capital?
Current year working capital = Current assets - Current liabilities = $100,000 - $120,000 = -$20,000 Therefore, current year working capital is $-20,000. Next year working capital = (Current assets*110%) - (Current liabilities *110%) = ($100,000 *110%) - ($120,000*110%) = $110,000 - $132,000 = -$22,000 Therefore, estimated cash flow associated with next year's change to next working is $2,000 (-$22,000-$20,000*-1).
Dividend Yield =
D/P0
One-Period Example •Suppose you are thinking of purchasing the stock of Moore Oil, Inc. •You expect it to pay a $2 dividend in one year, and you believe that you can sell the stock for $14 at that time. •If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
Compute the PV of the expected cash flows Price = (14 + 2) / (1.2) = $13.33 - in excel, find pv using 16 as FV
Stock Market
Dealers vs. Brokers New York Stock Exchange (NYSE) - Largest stock market in the world - License holders (1366) - Designated market makers (DMMs) - Floor brokers - Supplemental liquidity providers (SLPs) floor activity
Debt versus Equity
Debt is not ownership interest in the firm. Debt owners generally do not have voting power, shareholders do have voting power. Debt is considered a cost of doing business and accordingly interest payments are tax deductible (means it's taken out before taxes are calculated so it lowers tax espense). Dividends are paid after taxes and are not deductible. Unpaid debt is a liability of the firm. At liquidation debt is paid before equity. Debt is said to be senior in the capital structure
Capital Budgeting is...
Decision Making - What is the best use of our money and time
Depreciation Tax Shield
Depreciation * Tax Rate
Beta (β)
Describes the relationship between the movement of an individual asset and the movement of the market as a whole - Total risk of each individual security is no longer relevant, only the systematic component counts - β= Covariance of a risky asset with the market portfolio - β = Covariancei,m/Standard Dev of market^2 (the slope of a regression) - As a result, β of the market is 1 - β of a riskless asset is 0
Slide 30 Amortization Example Day 3
Consider a $10M, 5-year amortizing loan, with monthly payments and an APR of 7%: What is the payment (again)? =PMT(0.07/12, 60, 10000000, 0) = -$198.011.99 How much of your first payment is interest? = IPMT(0.07/12, 1, 60, 10000000, 0) = $58,333.33 How much of your first payment is principal? = PPMT(0.07/12, 2, 60, 10000000) = $139,678.65 What is the loan balance after the first month? $10,000,000 - $139,678.65 = $9,860,321.35 How much of your second payment is interest? = IPMT(0.07/12, 2, 60, 10000000, 0) = $57,518.54 And so on you can repeat...
Amortization (Excel)
Consider a $10M, 5-year amortizing loan, with monthly payments and an APR of 7%: 1.What is the payment (again)?•=PMT(0.07/12, 60, 10000000, 0) = -$198.011.99 2.How much of your first payment is interest? •= IPMT(0.07/12, 1, 60, 10000000, 0) = $58,333.33 3.How much of your first payment is principal? •= PPMT(0.07/12, 1, 60, 10000000) = $139,678.65 4.What is the loan balance after the first month?•$10,000,000 - $139,678.65 = $9,860,321.35 5.How much of your second payment is interest?•= IPMT(0.07/12, 2, 60, 10000000, 0) = $57,518.54 6.And so on you can repeat...
Nonconventional Cash Flows
Conventional Project Cash Flows: - Year 0: negative cash flow - Years 1,2, etc positive cash flows Nonconventional Cash Flows... almost all others: - Positive then negative - All negative or all positive - change signs more than once
Ex: Municipal Bond yielding 4%, Corporate Bond yielding 5%, 32% Tax Rate
Corporate Bond: 0.05*(1-0.32) = 3.4% Municipal Bond yields 4% *Buy municipal bond because it yields a higher return!*
Municipal vs. Corporate: Which bond do you pay taxes on?
Corporate Bonds - No taxes paid on municipal bonds
Constant Dividend Growth Model (DGM)
Dividends are expected to grow at a constant percent per period
Example: You bought a stock for $35, and you received dividends of $1.25. The stock is now selling for $40. What is dollar return? What is percentage return?
Dollar Return = 1.25+(40-35)= *$6.25* Percentage Return = 6.25/35= *17.86%* or: Dividend yield = 1.25/35=3.57% Capital Gains Yield = (40-35)/35=14.29% Total Percentage Return = 3.57+14.29= 17.86%
To fund its new jet Boeing issued bonds. The bonds have a 6 3/8% coupon and mature in 2026. The yield on this bond is currently 6%. How much are you willing to pay for this bond today? RATE NPER PMT PV FV
Don't know answer buy give it a try lol... I got $1023.55 when I tried
USE _____ FUNCTION TO FIND EAC
PMT!!!!!
Two-Period Example•Now, what if you decide to hold the stock for two years? •In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. •Now how much would you be willing to pay?
PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)^2 = 13.33 - In excel, find PV of dividend1 using 2 as FV - Find PV of div 2 using 16.80 as FV - Add them together (gives same answer)
Three-Period Example•Finally, what if you decide to hold the stock for three years? •In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. •Now how much would you be willing to pay?
PV = 2 / 1.2 + 2.10 / (1.2)^2 + (2.205 + 15.435) / (1.2)^3= 13.33
Perpetuity basic formula
PV= C / r
Current Assets and Current Liabilities
Payed off within the next year
Future Value Formula
FV=PV(1+r)^n
You are reviewing a new project and have estimated the following cash flows: Year 0: TCF = -165,000 Year 1: TCF = 63,120; NI = 13,620 Year 2: TCF = 70,800; NI = 3,300 Year 3: TCF = 91,080; NI = 29,100 •Your required return for assets of this risk level is 12%.
ITS A TRICK! The Net income has nothing to do with calculating NPV! Will be on exam NPV = 12627.41
Zero Growth Dividend Model
If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula: P0=D/R
Change in NWC
If the NWC INCREASED, the change is positive. You just subtract it from the Total cash flow equation at the end, so the actual increase/decrease stays the same, it only changed when you calculate TCF cuz you subtract NWC. - If it says what are the CASH FLOWS associated with the change(s) to NWC, that's when you do the opposite so if change is positive, make it negative cuz in the overall cash flows it is subtracted ... ... changes to CF associated with NWC is Change in NWC*-1 .. if just change in NWC dont multiply by -1
Cash Flow for Stockholders
If you buy a share of stock, you can receive cash in two ways: - Dividends: The company pays dividends out of after tax r - Appreciation: You sell your shares, hopefully at a price higher than you paid If I hope to profit from a gain on the sale, ask yourself what the next person is willing to pay? - It should be the PV (at that point) of the subsequent dividends plus PV subsequent sale... - Keep repeating this iteration, and the fair value today simplifies to only being the PV of the (potentially infinite) stream of dividends
Dollar Return: Example: You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your dollar return?
Income = 30 + 30 = 60 Capital Gain = 975-950=25 Total Dollar Return = 60+25 = *$85*
What actually matters? (*ON EXAM*)
Incremental Cash Flows - Remember: Incremental cash flows arise as a consequence of selecting a project
To Find Last Cash Flow, after adding back depreciation, what should you add?
Initial investment in NWC + ATSV
What is the goal of the firm?
Make money for stockholders/ maximize shareholders value
Changes in Net Working Capital
Many projects require an increase in NWC (inventory, receivables, and other current assets) when initiated; this is a cash outlay at the beginning of the project Dont forget: when possible, reduce NWC at the end of a project -- this is a cash inflow at the end of the project - Take cash out of business, collect receivables, sell off inventory - If in doubt -- ASK!! will I get the WC back at the end?
Tax rates discussed in the book are just federal taxes
Many states and cities have income taxes as well, and those taxes should figure into any analysis that we conduct
We are concerned with the taxes that we will pay if a decision is made. Consequently, the ________ tax rate is what we should use in our analysis
Marginal!
Marginal vs. Average Tax Rates (*NOT ON EXAM*)
Marginal: % tax paid on the next dollar earned Average: total tax bill / taxable income
The Most important Number in Finance
Market Risk Premium!! - Excerpts from JP Morgan
Market Return-Risk Free Rate=
Market Risk Premium!!! (if it gives u market risk premium need to use that as the E(Rm)-Rf variable) - Example in last notecard
From Last Question: What is the expected change to share price at the time we announce this project? (assume there are 10,000 shares outstanding)
Market value would go up by $1.26 (12627.41/10000)
From Last Question: What would be the expected effect of announcing this project at t=0 to firm value?
Market value would increase by $12627.41
IRR and Mutually Exclusive Projects (*MUTUALLY EXCLUSIVE PROJECTS ARE ON EXAM!*)
Mutually Exclusive Projects -If you choose one, you cannot choose the other - Ex you can choose to attend grad school at either Harvard or Standford, but not both Intuitively, you would use the following decision rules: - NPV - choose the project with the higher NPV - IRR - choose the project with the higher IRR - We'll see that IRR in this case might be misleading - NPV still works
Decision Criteria Test - Payback (*NOT ON EXAM*) •Does the payback rule account for the time value of money? •Does the payback rule account for the risk of the cash flows? •Does the payback rule provide an indication about the increase in value? •Does the decision rule tell us how much value we are creating? •Should we consider the payback rule for our primary decision rule?
No, No, No, No, and No!
Annuity Example: •After carefully going over your budget, you have determined you can afford to pay $632 per month toward a new car. •You call up your local bank and find out that the going rate is 12% per year, with monthly payments and no money down on a four year loan. •How much can you borrow?•To determine how much you can borrow, we need to calculate the present value of $632 per month for 48 months at 1 percent per month.
•You borrow money TODAY so you need to compute the present value .48 N; 1 I/Y; -632 PMT; PV = 23,999.54 ($24,000): •Excel: =PV(0.01,48,-632,0) will give you 23,999.54
*Generally the higher the fixed cost component, the ____ the project is BECAUSE... *
RISKIER!! because you have less control over it, so even if you don't have the demand to pay for it, you still have to pay those costs
Bond Characteristics, Risk & Return (*SECURED Vs. UNSECURED NOT ON EXAM*) and (*SENIOR vs. JUNIOR NOT ON EXAM*) and (*CALLABLE VS. NONCALLABLE NOT ON EXAM*)
Security - more security = less risk = lower return, i.e. lower yield to maturity - 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 - more senior=less risk=lower return Callability-callable =more risk= higher return
What is agency, or the principle-agent problem? (*NOT ON EXAM*)
The shareholder and the agent representing you may have conflicting viewpoints
Example: Airlines, Oil Companies, and Risk
Think about oil prices: - higher gas prices are good for oil companies - higher gas prices are bad for airlines - hold a portfolio or both, and changes to gas prices are washed out - We would call that diversifiable (unsystematic) risk Now think about a recession: - A recession is bad for oil companies - A recession is bad for airlines - Hold a portfolio of both, and you still will get hurt by the recession - We would call that undiversifiable (systematic) risk
So what risk gets rewarded?
Think about professions: - if you work in an inherently risky profession, you are likely to get extra compensation for it (ex Deadliest Catch) - If you work in an inherently safe profession, but do your job in a way that introduces unnecessary risk, your boss probably won't pay you more - It is the same with investing: you will only get compensated for the unavoidable risk Systematic Risk: - The portion we can't avoid, and therefore for which we expect to be compensated - *Measured in units of Beta:* - B=0 implies no (systematic) risk... when no risk at all known as "risk free" - B=1 normalized to the risk of the market (fully diversified portfolio)
The dividend in year 5 is considerably higher than the sum of the original dividend plus five increases of 40$ on the original $1.10 dividend
This is due to *compounding*
Annual Percentage Rate (APR) (*NOT ON EXAM*)
This is the (annual) rate that is generally required to be quoted by law - Truth in Lending Laws - Ironic, because APR is misleading! - Does not take into account compounding By definition, APR= period rate times the number of periods per year Consequently, to get the period rate we rearrange the APR equationL - Period rate = APR/number of periods per year You should NEVER divide the effective rate by the number of periods per year - it will NOT give you the period rate
What is (ought to be) the goal of the firm? (*ON EXAM*)
To Maximize Profit and Make Money/ maximize the value of shares
Risk, Return, and Financial Markets
We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets (a wealth of historical data) Lesson from capital market history: - There is a reward for bearing risk - The greater the potential reward, the greater the risk - This is called the risk-return tradeoff In simplified terms, we will speak of: - Reward as expected return - Risk as standard deviation/variance, or in terms of Beta - Does adding this stock to the portfolio make it more or less risky?
Time Value of Money (TVM) -- Why do we care?
We care because money today is worth more than money tomorrow: - Because of inflation - Because of opportunity cost - Because of risk we won't get the money tomorrow To aggregate cash flows into one equivalent sum, we need to adjust for all of the above
The three bullets above, taken together, form the...
framework upon which we will build this semester
Fixed vs. Variable Costs
helpful framework to evaluate the risk of a project All costs that vary in relation to sales are variable - Materials, power, people Costs that stay the same regardless of the sales volume are foxed - Rent, insurance, security, technology Total costs = variable costs plus fixed costs
How much the firm spends on long term assets and short term assets =
how much the firm earns - operating cash flow
Perpetuity
infinite series of equal payments
Assets exactly equal
liabilities + equity
Assets are listed in the order of
liquidity - the amount of time it would take to convert them to cash in an operating business
financial decisions are incremental; applicable tax rate is the ________ rate
marginal
We should use the...
marginal rate with an expected additional 35,000 in taxes
Cash and A/R are _____ liquid than property plant and equipment
more!
Suppose a stock had an initial price of $60 per share, paid a dividend of $.60 per share during the year, and had an ending share price of $72. What was the dividend yield and the capital gains yield?
ooo forgot to write this down shiiit look in hw
semi-strong form efficiency continued(*NOT ON EXAM*)
people repeatedly try to trade on "inside" (nonpublic) information - Ex martha steward - suggests this info might not always be already in asset prices - trading on this info is illegal! - whole division of SEC trying to catch these people some people believe insider trading pays, but only sufficient to compensate for the risk involves - risk reward tradeoff
EAR Formula
remember that the APR is the quoted rate, and m is the number of compounding periods per year - APR/m is the period rate
How do we calculate the market risk premium?
return-risk free rate
The operations section of the income statement reports the firm's...
revenues and expenses from principal operatoins
Present Value examples in Day 3 TVM Apr and EAR slides, starting at slide 7 (*EAR, APR, Period Rates not on exam*)
review these before exam!
Remember that shareholders' equity consists of...
several components. - total equity includes all of these components not just the "common stock" item. - in particular, retained earnings belong to shareholders
The balance sheet does not list...
some very valuable assets, such as the people who work for the firm
What are the two types of risk called
systematic and unsystematic risk
The left-hand side of the balance sheet lists...
the assets of the firm. - Current assets are listed first because they are the most liquid. - Fixed assets can include both tangible and intangible assets, and they are listed at the bottom because they generally are not very liquid. These are a direct result of management's investment decisions - Investment decisions are not limited to investments in financial assets
The right hand side of the balance sheet lists...
the liabilities and equity (or ownership) components of the firm. - Since the balance sheet has to balance, total equity = total assets- total liabilities. - The portion of equity that can most easily fluctuate to create this balance is retained earnings. - The right hand side of the balance sheet is a direct result of management's financing decisions
Liabilities are listed in the order in which...
they come due
To calculate APR?
use =RATE*Compounding Periods Per Year
In NPV calculation in Excel, be sure to...
use cash flow year 1-whatever and input rate, then subtract the initial investment
Salvage value (or ATSV if after tax)
what youll sell it for at the end
Example: Operating at Less than Full Capacity
•Suppose that the company is currently operating at 80% capacity. Full Capacity sales = 5000 / 0.80 = 6,250 Estimated sales = $5,500, so we would still only be operating at 88%-- (for our lesson we do not ever shrink fixed assets) Therefore, no additional fixed assets would be required (still $4,000). Pro forma Total Assets are then = 6,050 + 4,000 = 10,050 Total Liabilities and Owners' Equity = 10,250 EFN = 10,050 - 10,250 = - 200 = 200 Excess financing
Another Example of Operating at Less than Full Capacity: 95%
•Suppose that the company is currently operating at 95% capacity. Full Capacity sales = 5000 / 0.95 = 5,263 Estimated sales = $5,500, so we would still only be operating at 104.5% 100% is the max by assumption Therefore, we need to add 4.5% in fixed assets (4.5% of 4,000 = 180 new) Pro forma Total Assets are then = 6,050 + 4,180 = 10,230 Total Liabilities and Owners' Equity = 10,250 EFN = 10,230 - 10,250 = - 20 = 20 Excess financing
Quick Quiz/ know these
•What is the purpose of long-range planning?•What are the major decision areas involved in developing a plan?•What is the percentage of sales approach? •How do you adjust the model when operating at less than full capacity? •What is the internal growth rate? •What is the sustainable growth rate? •What are the major determinants of growth?
NWC =
current assets - current liabilities
NWC =
current assets - current liabilities - an increase in NWC is an investment of the firm
Workshop!
do it
Practice problem at the end of slides F3010 Cash Flows
do it!
The income statement measures...
financial performance over a specified period of time
The non-operating section of the income statement includes all...
financing costs, such as interest expense
*Suppose your firm earns $12 million in taxable income* : What is the firm's tax liability? (see pic) (*NOT ON EXAM*)
$4,100,000 Tax liability: .15(50,000) + .25(75,000 - 50,000) + .34(100,000 - 75,000) + .39(335,000 - 100,000) + .34(10,000,000 - 335,000) + .35(12,000,000-10,000,000)= $4,100,000
Systematic versus Unsystematic Risk: Classify the following events as mostly systematic or mostly unsystematic. Is the distinction clear in every case?
- Short term interest rates increase unexpectedly (systematic I think) - The interest rate a company pays on its short term debt borrowing is increased by its bank (unsystematic) - Oil prices unexpectedly decline (unsystematic) - An oil tanker ruptures, creating a large oil spill (unsystematic I think) - A manufacturer loses a multi-million dollar product liability suit (unsystematic) - A supreme court decision substantially broadens producer liability for injuries suffered by product users (systematic or unsystematic?) - The government announces that inflation unexpectedly jumped by 2 percent last month (systematic) - Big Widget's quarterly earnings report, just issued, generally fell in line with analysts' expectations (unsystematic) - The government reports that economic growth last year was at 3%, which generally agreed with most economists' forecasts (systematic) - The directors of Big Widget die in a plane crash (unsystematic) - Congress approves changes to the tax code that will increase the top marginal corporate tax rate. The legislation has been debated for the pervious six months (unsystematic I think cuz it only affects top marginal corporations)
c. At what discount rate would the company be indifferent between these two projects? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
- Take the difference between the cash flows and compute irr of difference
Tax Reform: Went from Marginal tax rate to Flat Corporate Tac of 21%... What is the impact of this?
- Taxes impact income; important to financial decisions - Taxes come from various sources: Federal, state, excise - Taxes are always changing - taxes can be a very important component of the decision making process, but what we learn about tax specifics now could change tonorrow - Consequently, it is important to keep up with the changing tax laws and to utilize specialists in the tax area when making decisions where taxes are involved
Yahoo Finance Ford Motor Symbol F
- Tells you Ford has gone down (trading at lower end of years returns) - B=0.8 means less risky than general market - 0.6/8.73=6.08% (yield from income alone) - 1 year target of $9.33 means it will only go up $0.40 so won't make you a ton of money but less risky
Risk Premium
- The "extra" return earned for taking on risk - Treasury bills are considered to be risk-free - The risk premium is the return over and above the risk-free rate
•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?
- The NPV is positive at a required return of 15%, so you should Accept! - If you use the financial calculator, you would get an IRR on 10.11% which would tell you to Reject - If you use Excel, you will get #NUM! or ERROR! - You need to recognize that there are non-conventional cash flows and look at the NPV profile
Arithmetic vs. Geometric Mean: Which is better?
- The arithmetic average is overly optimistic for long horizons - The geometric average is overly pessimistic for short horizons - So, the answer depends on the planning period under consideration: - Short/near term: use the arithmetic - Long term: use the geometric
The value of a firm/ investment/ asset should be seen as...
- The discounted present value of the cash flows - Cash flows because we care about cash - Discounted because "time is money" - cash later worth less than cash today
Estimating Dividends: Simplifying Cases: Constant dividend Growth
- The firm will increase the dividend by a constant *percent* every period - The price is computed using the growing perpetuity model
Estimating Dividends: Simplifying Cases: Zero Growth
- The firm will pay a constant dividend forever - This is like a preferred stock - The price is computed using the perpetuity formula
The Internal Growth Rate
- The internal growth rate tells us how much the firm can grow assets using retained earnings as the only source of financing./ *growth that can happen with no new external financing* - No external Financing required - Addition to RE then is the only source of new funds -the internal growth rate assumes that the dividend payout ratio is constant - Use most recent, not pro forma, info for ROA and Internal Growth Rate ROA=NI/Total Assets b=retention ratio= (1-dividend payout ratio) Internal Growth Rate=*(ROAxb)/(1-ROAxb)*
Effective Annual Rate (EAR) (*NOT ON EXAM*)
- This is the actual rate paid (or received) after accounting for compounding that occurs during the year - If you want to compare two alternative investments with different compounding periods, you need to compute the EAR and use that for comparison
Internal Rate of Return (IRR)
- This is the most important alternative to NPV - It is often used in practice and is intuitively appealing - It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere - a simple way to communicate the value of a project to someone who doesnt know all the estimation details - if IRR is high enough, you may not need to estimate a required return, which is often a difficult task - *In the real world this is the dominant means of capital budgeting*
Variance and Standard Deviation (*NOT ON EXAM*)
- Variance and standard deviation measure the volatility of asset returns - The greater the volatility, the greater the uncertainty - Historical Variance = sum of squared deviations from the mean/(number of observations-1) *=STDEV.S In Excel (not STDEV.P)* - in class he just did =stdev tho lol Standard Deviation==square root of variance Probabilistic variance=Sum of Probability(return=average return)^2 or =var.s in excel or =var as he did in class
Estimating Dividends: Simplifying Cases: Multiples
- We assume similar stocks are priced at similar ratios to a key measure (i.e. sales, earnings, whatever) - The price is that key measure times the common multiple
Capital Budgeting in Practice
- We should consider several investment criteria when making decisions - NPV and IRR are the most commonly used primary investment criteria - Payback is a commonly used secondary investment criteria - Most PE firms also use and talk about cash on cash return: This is the multiple of cash flows in the investment period, against the initial investment (does not take into account a discount rate) - not testable/ how many times the initial investment gets returned over the life of the investment
IRR Definition and Decision Rule
-Definition: IRR is the return that makes the NPV = 0 -Decision Rule: *Accept the project if the IRR is greater than the required return*
Sloan Transmissions, Inc., has the following estimates for its new gear assembly project: price = $2,800 per unit; variable costs = $560 per unit; fixed costs = $3.0 million; quantity = 86,000 units. Suppose the company believes all of its estimates are accurate only to within ±10 percent. What values should the company use for the four variables given here when it performs its best-case scenario analysis? What about the worst-case scenario?
-Unit price for best case scenario will be high and unit price for worst case scenario will be low - Fixed costs and variable costs will be lower with best case scenario and higher with worst case scenario - Unit sales will be higher for best case scenario and lower for worst case scenario - Adjust accordingly
If I must increase NWC...
I put cash into the business (-)
3 Types of Cash Flows
1. Cash Flow from Operations (OCF) 2. Cash Flow from purchase or sale of long-lives assets (CapEx) 3. Cash required or generated by changed in net working capital (NWC)
Examples of reconciling items "non cash expenses"
1. Depreciation (most common example) - You never write a check made out to "depreciation" - Affects both OCF, and sale of fixed assets (ATSV) 2. Receivables/ Payables (net working capital in general) - Accounting recognizes revenues and expenses at time of transfer of goods/ services - Need to ask if cash was exchanged at the same time - OCFS look like (i.e. assume) all cash, so NWC is done to correct and/or offset
Important Questions
1. How does our plan affect the timing and risk of our cash flows? 2. Does the plan point out inconsistencies in our goals? 3. If we follow this plan, will we maximize owners wealth?
Standard Deviation or Total Risk is divided into two broad groups:
1. Systematic Risk 2. Unsystematic or Idiosyncratic Risk
3 Central Questions in Finance
1. What are we going to buy (capital budgeting) 2. How do we pay for it? (Capital Structure) 3. How do we keep the lights on? (NWC)
What are the three central questions in finance? (*ON EXAM*)
1. What are we going to buy? (Capital Budgeting) 2. How are we going to pay for it? (Capital Structure) 3. How do we keep the lights on? (Liquidity/ NWC)
Which of the following should be treated as an incremental cash flow when computing the NPV of an investment? A. reduction in the sales of a company's other products caused by the investment. B. Expenditure on plant and equipment that has not yet been made and will be made only if the project is accepted. C. Cost of research and development undertaken in connection with the product during the past three years. D. Annual depreciation expense from the investment. E. Dividend payments by the firm. F. Resale value of plant and equipment at the end of the project's life. G. Salary and medical costs for production personnel who will be employed only if the project is accepted.
A, B, D*Tax only, F, and G - D matters because it counts in taxes but you add it back - E doesnt matter because it's not NPV
Apply MARCS depreciation rate to which book value? Beginning of year book value of original book value?
ALWAYS APPLY MARCS DEPREC TO ORIGINAL BOOK VALUE!
Risk and Reward
Academia and Wall Street agree on the premise that bearing risk has its rewards Question becomes how do you measure and identify risk to reap higher returns? Key explanations: - CAPM: Single Factor Model - APT and Fama-French-Carhart Multi-Factor Models
The Capital Asset Pricing Model (CAPM)
Academic Theory (William Sharpe, John Lintner, & Fischer Black) Investors receive no premium for risks that can easily be eliminated - Since asset-specific risk (unsystematic risk) can be eliminated by holding a well diversified portfolio, return should be only based upon market risk (systematic risk) - Market risk of an asset is measured by Beta (β)
From Last Question: Do we accept of reject the project?
Accept it
Cash Flows do not equal
Accounting Income! - We care about cash!!! This is the driver of Capital Budgeting
Definitions of Market Efficiency (*Not on exam!*)
An efficient market constantly finds the correct "price": *the best estimate of the discounted present value of its cash flows based on the best available information* But what information should we expect to already be incorporated (priced) into that calculation? There are three general models of information that might already be incorporated: - All past trading information (price and quantity): weak form efficiency - All public information: semi-strong form efficiency - All information: strong form efficiency These - and some level in between - are still actively disputed - Most academics, and academic studies, support a semi-strong view *What are Models - approximations of the world to explain behavior*
Stock Valuation Using Multiples
Another common valuation approach is to multiply a benchmark PE ratio by earnings per share (EPS) to come up with a stock price The benchmark PE ratio is often an industry average or based on a company's own historical values The price-sales ratio, price to EBITDA (or just about anything for that matter) can also be used
Example: Computing Averages: What is the arithmetic and geometric average for the following returns? Year 1: 5% Year 2: -3% Year 3: 12%
Arithmetic Average: (5+(-3)+12)/3= *4.67%* Geometric Average = [(1+.05)*(1-.03)*(1+.12)]^(1/3)-1= *4.49%* *or =average and =geomean(1+returns)-1*
The most recent financial statements for Crosby, Inc., follow. Sales for 2018 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, fixed assets, and accounts payable increase spontaneously with sales...If the firm is operating at full capacity and no new debt or equity is issued, what external financing is needed to support the 20 percent growth rate in sales? (Do not round intermediate calculations.)
Basically, just create a projected Balance Sheet and income Statement, using percentage of sales for everything that says it will grow spontaneously with sales, and leaving everything else the same or calculating it how you normally would. Then, the difference between Assets and Total liabilities and SE is the EFN
Making a Decision (not tested)
Beware of "Paralysis of Analysis": at some point you must make a decision Some general tips: - if the majority of your scenarios have a positive NPV, then you can accept the project - if your NPV analysis is robust to a wide range of estimates of a variable, you should be able to focus on another variable - if a particular variable/scenario leads to a negative NPV with a small change in the estimates, this is where to focus on getting it right -Good analysis can help weigh the risks, and even allow hedging of unnecessary risk - Good projects can still end badly: brief board, boss, investors on what to expect under diff scenarios ahead of time
Review: When rates go up...
Bond prices go down!
After Tax Salvage Value (ATSV) (*NOT ON EXAM*)
Book Value = Purchase Price - Accumulated Depreciation The net cash flow from the sale of the asset is: ATSV = Sales price - Tax on Salvage
Market price is not the same as...
Book value
Market Risk Premium
CAPM is built on the market risk premium - Aka the equity risk premium Key driver of return expectations Reasons it might be lower today than in the past - Lower taxes today - Buybacks today - Economic stability today - Lower transaction costs today The "most important number"
_______ is KING
CASH - in finance, the most important item that can be extracted from financial statements i the actual cash flow of the firm - Cash flow received from the firm's assets must equal the cash flows to the firm's creditors and stockholders - in other words, the cash generated by assets enables the firm to pay its debts and provide a return to shareholders - Accounting cash flow and financial cash flow are not necessarily equal -
CF (A)=
CF (B) + CF (S)
Multiple Cash Flows: You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year and $800 at the end of the fourth year. You can earn 12 percent on very similar investments. What is the most you should pay for this one? or How much is the investment worth?
Calculator: Year 1 CF: N = 1; I/Y = 12; FV = 200; CPT PV = -178.57 Year 2 CF: N = 2; I/Y = 12; FV = 400; CPT PV = -318.88 Year 3 CF: N = 3; I/Y = 12; FV = 600; CPT PV = -427.07 Year 4 CF: N = 4; I/Y = 12; FV = 800; CPT PV = - 508.41 Total PV = 178.57 + 318.88 + 427.07 + 508.41 = 1,432.93 Remember the sign convention. The negative numbers imply that we would have to pay $1432.92 today to receive the cash flows in the future - we can only add cash flows together within (and not across) periods. - We can add them here because they have all been converted to their year 0 equivalents
What does CAPM stand for?
Capital Asset Pricing Model
NWC: Current Assets
Cash and other assets that are expected to be converted to cash within the year - Cash - Marketable securities - Accounts receivable - Inventory
Different Classes of Stock
Class A, B, C, D Typically different voting rights Example Ford: - Class A: common share on the market over 1 billion - elect 60% of directors - Class B- over 70 million shares - elect 40% of directors - all owned by the Ford family Alphabet (Google) - Class A: 1 vote per share - Class B: Ten votes per share Sergey Brin and Larry Page together own 83% of these shares and have 51% voting power - Class C: No votes per share
For example, imagine you have 40% of your money in Tesla stock and 60% in Facebook. Assume the expected return on Tesla is 16% and on Facebook is 12%
E(R)=0.4*16%+0.6*12%= *13.6%*
Free Cash Flow =
EBIDAT - Cap Ex - Change in WC
Common Misconceptions about EMH
Efficient markets do not mean that you can't make money They do mean that, on average, you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns Market efficiency will not protect you from wrong choices if you do not diversify - you still don't want to "put all your eggs in one basket"
Cap Ex =
Ending Net Fixed Assets - Beginning Net Fixed Assets + depreciation
Change in WC =
Ending Net Working Capital - Beginning Net Working Capital
NWC Convo with Dad
Evaluating weather the company has the cash flows to pay off their liabilities in the short run - also evaluates if you have too much cash in your business
Simulation Analysis (not on quiz)
Expanded Sensitivity Analysis Often done as Monte Carlo Simulation: - assign probability distributions to unknowns (sales, prices, costs, etc) - run thousands of iterations - Find NPV of each as one data point The output is a probability distribution for NPV with an estimate of the probability of obtaining a positive NPV The simulation only works as well as the information that is entered: - Some of the worst real world outcomes resulted from models that failed to assign sufficient likelihood to particular scenarios
The Importance of Financial Markets
Financial Markets allow companies, governments, and individuals to increase their utility (economics term for being better off) - Savers have the ability to invest in financial assets so that they can defer consumption and earn a return to compensate them for doing so - Borrowers have better access to the capital that is available so that they can invest in productive assets - The importance of "making these markets" cannot be emphasized enough Financial markets also provide us with information about the returns that are required for various levels of risk - *this information tells us the "rate" to use to discount our cash flows -- what is the required rate of return for the risk taken*
Lecture Tip: the annuity factor approach is a short-cut approach in the process of calculating the present value of multiple cash flows and it is only applicable to a finite series of level cash flows
Financial calculators have reduces the need for annuity factors, but it may still be useful from a conceptual standpoint to show that the PVIFA is just the sum of the PVIFs across the same time period
Bond Valuation in Excel
Five pieces of information are relevant: - Rate, Nper, Pmt, PV, FV - Key is putting them in correctly
If higher IRR but lower NPV...
GO WITH HIGHER NPV - Accept project A because higher NPV
Issues with CAPM
How do you derive β? - Regression against the market - What proxy for the market? - S&P 500, Wilshire 5000? - All risky assets? Stocks, bonds, real-estate, collectibles, human capital Using what time interval? - Value line uses last 260 weekly observations - Merrill Lynch uses 60 monthly observations - Different time frames give different answers
At the end of the project...
I can pull all NWC out (+)
What EMH Does and Does NOT Say ((*Efficiency NOT ON EXAM*)
Investors can throw darts to select stocks - This is almost, but not quite, true. An investor must still decide how risky a portfolio he wants based on risk aversion, expected return, and diversification Prices are random and unpredictable - Prices reflect information. The price CHANGE is unpredictable, as it is driven by *new* information, which by definition, arrives randomly. - Therefore, financial managers cannot "time" stock and bond sales. What does this mean for you? - in the long run all back to the risk/reward relationship - the long run rewards investors who take some risk - it is hard over time to beat the market
Why is NPV the tool we use for all the three questions and goals?
It shows financial gain and loss
Cash IS
KING - because cash is most liquid
Diversifying Your Portfolio
Key Things to Understand: - Portfolio return=weighted average of returns - Portfolio variance does not equal weighted average of variances - Portfolio Beta= weighted average of Beta's (*PORTFOLIO BETA AND PORTFOLIO AVG RETURN NOT ON EXAM*) Given the above, let's: - Examine how portfolio weights affect returns and variance - Examine introduction of risk-free asset - Understand relation between risk and return
_______ is Key
Liquidity
What is the main way we approach questions in finance ?
Look at the discounted present value of incremental cash flows (NPV)
Comprehensive Problem: Go to Yahoo Finance and look up Ford Motor company (ticker symbol F). Get to the Analysis tab and look up the 5-year growth estimate. Assume this a good estimate of dividend growth and that this will be the constant growth of the dividend. Use Ford's beta, a risk-free rate of 2%, and a market risk premium of 10% to calculate the required return. Estimate the value of Ford per share, and compare this to the quoted price.Then assume that a basket of car company stocks trades at a multiple of 10 times forward year EPS. Estimate Fords stock price per share using this method. What would you conclude about Ford's value based on your analysis?
Look on Excel Sheet for Numbers and how he got this... go over it didn't get it in class and too tired to do it rn
__________ is the accountant's "bottom line"
Net income
Do sunk costs matter?
NO!!! ON exam! It's a trick! - only relevant costs are looking forward
Evaluating NPV Estimates
NPV estimates are just that - estimates A positive NPV is a good start *Forecasting Risk*: How sensitive is our NPV to changes in the cash flow estimates; more sensitive =greater forecasting risk *Sources of Value*: Why does this project create value? - Some example: market (i.e. monopoly) power, economies of scale, product differentiation, cost advantages, distribution access
Definition of NWC
NWC = current assets - current liabilities If NWC increases, you need to put cash into the business If NWC decreases, you can recognize cash coming out - The amount in or out is the cash flow from change to NWC
OFC =
Net Income + Depreciation + Interest
NASDAQ
Not a physical exchange - 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 and dealers - Level 3: view and update quotes, dealers only Large portion of technology stocks
Cash Flows from Operations
OCF = EBIT - Taxes + Depreciation (we ignore interest, that is a capital structure decision - which we will study later) or OCF = Net Income + Depreciation + Interest - These are the cash flows that actually run the business
NWC: Current Liabilities
Obligations that are expected to require cash payment within the year - accounts payable - Accrued wages - Taxes owed
financially constrained firms
Our base/ normal assumption: - Firm can do all NPV>0 projects - Think Elon Musk At times this may not hold in reality - Limits to capital spending budget (internal or external) - Limits to managers time and focus What to do? - choose mix of projects maximizing firm value subject to budget *(i.e. choose highest NPV summed across projects)*
•Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% (annually/APR) with quarterly compounding. What is the price?
P0=0.5/(0.1/4)=$20 or 2/0.1=$20
Weak Form Efficiency(*NOT ON EXAM*)
Prices reflect all past market information such as price and volume The current price of a stock reflects the stocks own past prices Implies that technical analysis will not lead to abnormal (above market) returns, only fundamental analysis will Debate over what the empirical evidence indicates. What form of efficiency do you think the markets display? - Despite some form of market efficiency, there is a large group of people trying to beat the market: technical traders/fund managers and others - Worry 1: it generally doesn't work - some have been able to do it for a while - Worry 2: the biggest profits seem to be for writing books on how to do it, rather than actually doing it - Worry 3: if you really knew how to do it, would you sell a book giving away your secret?
Bond Valuation
Primary Principle: - value (price) of financial securities=PV of expected future cash flows Bond value is, therefore, determined by - the present value of the coupon payments plus the present value of the par value Interest rates (i.e. the discount rate) are inversely related to present value (i.e. the bond's price) Meaning bond prices and interest rates move in opposite directions
The 6 P's
Prior Proper Planning Prevents Poor Performance - Avoid Surprises - Develop contingency plans
XYZ has the following financial information for 2012: Sales = $2M, Net Inc. = $0.4M, Div. = $0.1M CA = $0.4M, F.A. = $3.6M CL = $0.2M, LTD = $1M, CS = $2M, RE = $0.8M What is the sustainable growth rate? If 2013 sales are projected to be $2.4M, what is the amount of external financing needed, assuming XYZ is operating at full capacity, and profit margin and payout ratio remain constant?
ROE = net income / shareholders' equity = $.4M / ($2M + $.8M) = .1429 Payout ratio = dividends/net income = .1M/.4M = .25 Plowback ratio (b) 1 - payout ratio = 1 - .25 = .75 Sustainable growth rate = ROE X b / 1 - ROE X b = .1429 X .75 / (1 - (.1429 X .75)) = .12 Profit margin = net income/sales = .4M/2M = .2 Projected net income = profit margin X projected sales = .2 X $2.4M = $.48M Projected addition to retained earnings = projected net income X (1 - payout ratio) = $.48M X (1-.25) = $.48M X .75 = $.36M % change in sales = ($2.4M - $2M)/$2M = .2 2012 total assets = $.4M + $3.6M = $4M Projected total assets = $4M X 1.2 = $4.8M Projected C.L. = $.2M X 1.2 = $.24M Projected R.E. = 2012 R.E. + projected addition to R.E. = $.8M + $.36M = $1.16M Projected liabilities and owners' equity = projected C.L. + LTD + C.S. + projected R.E. = $.24M + $1M + $2M + $1.16M = $4.4M External Financing Needed = projected assets - projected liabs. and OE = $4.8M - $4.4M = $.4M
NWC is ______ at the _____ of the project
Recovered at the end
The accounting definition of income is
Revenue - Expenses = Income
Future Value examples also in slides
Review these before exam!
CAPM Equation
Risk Free Rate of Return *Plus* Market Risk Premium E(Ri)=Rf+βi[E(Rm)-Rf]
Rating Agencies
S&P, Moodys, Fitch Rate the capacity to pay and the likelihood of default
OCF =
Sales - Expenses = EBDIT EBDIT- Depreciation = EBIT EBIT-Taxes+Depreciation = OCF *on our equation sheet
ATSV
Sales Price - Tax on Gain/Loss
Fixed Asset Practice Problems: At utilization 70%, 100% growth
Utilization=70%*(1+1)=140% Grow fixed assets by 40%
Figure 12.11
Standard dev tells you the variation from the mean
Key Takeaways for External Financing Needed (EFN) Problems
Start with the Pro Forma Income Statement - Revenue and costs typically grow by growth rate - Depreciation (for us) will be constant or ignored - Interest does NOT change - Taxes at same RATE - Dividends per stated policy - Remainder after dividend payout is addition to RE Then go to Balance Sheet: - Current assets and current liabilities change with growth - Fixed assets only increase (never decrease) to meet new sales - Long-term debt, and contributed capital do NOT change - RE changes by addition to RE above Fixed Assets: - If at capacity, increase by percent growth - If growth leads to less than 100% does not change - If growth takes from <100% to >100% changed by % over 100 - So at 80% grow by 50% = 120% of capacity, grow by 20% - at 75% grow by 66.67%=125% of capacity, grow by 25%
Fixed Asset Practice Problems: At utilization 80%, 50% growth
Utilization=80%*(1+0.5)=120% Grow Fixed Assets by 20%
When you figure out changes in NWC...
Subtract increase from original cash, accounts receivable, inventory, accounts payable, etc... Original-Increase/decrease - unless it's a liability, then do the opposite - basically just put the opposite of what's actually happening So, if it increases, it'll be negative and vice versa
Beta is
Systematic Risk
For which type of risk should investors expect to be rewarded?
Systematic risk
EFN= (*EFN IS ON EXAM but just know how to change net fixed assets and calculate EFN with projected numbers*)
TA-(L+OE) TA: Total assets L: total liabilities OE: owners equity - Where all of these are from the *projected* balance sheet - Need to come up with this much additional debt or equity to make balance sheet balance TA>T (L&OE)=need financing TA<T(L&OE)=projecting a surplus, no financing needed
The Sustainable Growth Rate
Tells us how much the firm can grow by using internally generated funds and issuing debt to maintain a constant/desired debt/equity ratio. *how much firm can grow without having to issue any new external equity, but issuing debt to maintain a constant debt/equity ratio* No Equity Financing Required - So addition to RE is again the new equity, and we also get some new debt (up to maintaining same ratio) Assumptions: - The sustainable growth rate also assumes that the dividend payout ratio is constant - No new external equity is issued, but debt increases with growth ROE=NI/Total Equity b=retention ratio= (1-dividend payout ratio) Sustainable Growth Rate=(ROExb)/(1-ROExb)
Comparing two stocks: Coca Cola: Beta of 0.74 Tesla: Beta of 1.19
Tesla has a higher risk and a higher potential return - Coke = less risk and more mature
Parker & Stone, Inc., is looking at setting up a new manufacturing plant in South Park to produce garden tools. The company bought some land six years ago for $5.5 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent these facilities from a competitor instead. If the land were sold today, the company would net $5.8 million. The company wants to build its new manufacturing plant on this land; the plant will cost $13 million to build, and the site requires $820,000 worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in fixed assets when evaluating this project?
The $5.5 million acquisition cost of the land six years ago is a sunk cost. The $5.8 million after tax value of the land is an opportunity costs if the land is used rather than sold. The $13 million After tax cash outlay and the $820, 000 grading expenses are the initial fixed asset investments needed to get the project going. Therefore the proper year zero cash flow to us3 in evaluating this project is $5,800,000 + 13, 000, 000 + $820, 000 =$19, 620, 000 = $19.62 million.
Things to Remember
You ALWAYS need to make sure that the interest rate and the time period match - If you are looking at annual periods, you need an annual rate - If you are looking at monthly periods, you need a monthly rate If you have an APR based on monthly compounding, you have to use monthly periods for lump sums, or adjust the interest rate appropriately if you have payments other than monthly In excel, always make sure 3 things match in regards to time/frequency: rate, nper, and pmt
Expected Return of a Portfolio of Assets
The expected return of a portfolio of assets is the weighted average of the returns:
The Risk-Return Tradeoff
The general rule: - The more volatile (or risky) a return is, the greater the expected return demanded will be - Is all risk equal? in other words, should we expect all risk(s) to produce higher returns? Real World Example: what would we expect about risk given the relative wages for the following jobs? - Job A: "Greenhorn deckhands could expect to earn between $3,000 and $10,000 per season" (I believe a season is around 1 month) - Job B: You earn the Federal minimum wage: $7.25/hour
Annuities and Excel
You can use the PMT entry in the PV formula for each regularly occurring payment - Sign conversions are critical!
Percentage Returns
The sum of the current income received plus the change in value of the asset, divided by the initial investment - It is generally more intuitive to think in terms of percentage, rather than dollar returns *Dividend Yield = Dividend/Beginning Price* *Capital Gains Yield = (Ending Price-Beginnning Price)/Beginning Price* *Total Percentage Return = (dividend+ending price-beginning price)/beginning price)* or Dividend Yield+Capital Gains Yield or just *Dollar Return/Beginning Price*
Dollar Returns
The sum of the current income received plus the change in value of the asset, in dollars *Total Dollar Return = income from investment + capital gain (or loss) due to change in price*
Stocks and Dividends
The value of any asset/company/investment is... the discounted present value of its expected cash flows - For a stock, those cash flows come in the form of dividends Dividends are not a liability of the firm until a dividend has been declared by the Board - Consequently, a firm cannot go bankrupt for not declaring dividends - We call the owners/shareholders the "residual claimants" - Debt gets paid first, the owners get whatever is left over Dividends and Taxes - Dividend payments are not considered a business expense; therefore, they are not tax deductible - The taxation of dividends received by individuals depends on the holding period, 20% is short term (less than 1 year) and 15% if longer than one year - Dividends received by corporations have a 50% exclusion from taxable income
What Makes Markets Efficient?
There are many investors out there doing research - as new information comes to market, this information is analyzed and trades are made based on this information - Therefore, prices should reflect all available public information If investors stop researching stocks, then the market will/would not be efficient - Creates a strange paradox: we advise all of you in investments to quit trying to pick stocks, but if everyone heeded the advice markets would no longer be efficient!
Measuring Risk
There is no universally agree-upon definition of risk The usual measures of risk are *variance* and *standard deviation* - Variance and standard deviation measure the dispersion of actual returns around the security's mean return - The standard deviation (the square root of the variance) is the standard statistical measure of the spread of a sample, and it is the measure used in most cases - Its interpretation is facilitated by a discussion of the *normal distribution - the bell curve*
What is a Return and How do we calculate it?
Total Return = Appreciation plus coupon or dividends
Standard Deviation is
Total Risk
Total 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 Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk Thought experiment: can the same asset provide a different return to different investors? - What if I hold the asset as part of a diversified portfolio, and you put all your money into this one investment?
Which does standard Dev measure? What about Beta?
Total Risk; Systematic Risk
Government Bonds
Treasury Securities - Federal government debt - T-bills: pure discount bonds with original maturity less than one year -T-notes: coupon debt with original maturity between one and ten years - T-bonds: coupon debt with original maturity greater than ten years - All pay federal but not state taxes Municipal Securities: - Debt of state and local governments - Varying degrees of default risk, rated similar to corporate debt - Interest received is *tax-exempt* at the federal and often the state level
What investment gives us the risk free rate?
Treasury stocks?
Features of Preferred Stock
Typically have a preference Dividend - Stated dividend that must be paid before dividends can be paid to common stockholders - Most preferred dividends are cumulative -- any missed preferred dividends have to be paid before common dividends can be paid For Private Companies, institutional investors (venture capital and private equity) often use Convertible Preferred Stock as the vehicle - Fixed minimum accruing dividend (not paid in cash) - today 6-8% - At liquidation (sale of IPO) either Preferred return (investment amount plus accrued dividends) or convert to common at negotiated price - Sometimes liquidation preference of more than 1x - Often a mandatory redemption period (typically 5 years)
Amortization of Loans
Unlike the workshop example last time, many loans (mortgages, cars, some business loans) require payments of both interest and principal - Types of Loans: Interest only (payback principal at end), Straight line amortization (each principal every year), sloped amortization (dont need to worry about for this class) But a principal payment - Reduces amount of loan - Which reduces interest owed per period So for a fixed payment - the interest paid goes down - the principal paid (per payment) goes up This is called the amortization of the loan: - Balance sheet effect: debt decreases - Income statement effect: interest decreases, but less interest tax deduction - plus usual effects (payment reduces cash on hand on B/S)
Fixed Asset Practice Problems: At utilization 100%, 30% growth
Utilization = 100%*(1+0.3)=130% Grow Fixed Assets by 30%
Fixed Asset Practice Problems: At utilization 60%, 50% growth
Utilization=60%*(1+0.5)=90% Do not change fixed assets
Opportunity Cost
What it is worth now
Sunk Costs
What you already paid
Present Value Formula
Where Ct is the cash flow at date T, r is the appropriate interest rate, and T is then the number of periods between "now" and the payment
Municipal Securities
Why Buy Them? - Tax advantaged How do we compare the after tax yield of corporate versus government (municipal) bonds?? Multiply the YTM by one minus the tax rate and compare
For example, consider a project with forecast sales of $1M, $1.5M, $2.0M, $2.0M, where it is assumed inventory must be 10% of sales. What are the cash flows associated with changes to NWC (assume zero inventory to start)?
Y1 = 10% of change to sales * (-1) = -$100,000 Y2 = 10% of change to sales * ( -1) = -$50,000 Y3 = 10% of change to sales * ( -1) = -$50,000 Y4 = 10% of change to sales * ( -1) = $0 If business ends, you can liquidate NWC Y4 then = 10% of previous sales = +$200,000
Decision Criteria Test - IRR •Does the IRR rule account for the time value of money? •Does the IRR rule account for the risk of the cash flows •Does the IRR rule provide an indication about the increase in value? •Does the decision rule tell us how much value we are creating? •Should we consider the IRR rule for our primary decision criteria?
Yes, Yes, Yes, No, and Maybe
Decision Criteria Test for NPV Does the NPV rule account for the time value of money? • Does the NPV rule account for the risk of the cash flows? • Does the NPV rule provide an indication about the increase in value? • Does the decision rule tell us how much value we are creating? • Should we consider the NPV rule for our primary decision rule?
Yes, Yes, Yes, Yes, and YES!
Efficient Market Hypothesis (*Efficiency not on exam)
Your book says stock/bond prices are in equilibrium or are "fairly" priced - should be true of all frequently traded assets, financial or otherwise If this is true, then you should not be able to earn "abnormal" or "excess" returns - Keep in mind this means on average, or in expectation - Actual returns will almost always differ from expected, sometimes dramatically Efficient markets *DO NOT* imply that investors cannot earn a positive return in the stock market - think about CAPM - On average, we expect a return "in proportion to" a stock or investment's riskiness( but what type of risk?) - But these are just averages... any given year or years can differ by quite a bit
*always remember*: the expected return is an average across _________
a (possibly) wide range of actual possibilities!!!
What is a bond?
a debt investment in which an investor loans money to an entity (corporate or governmental) that borrows the funds for a defined period of time at a fixed interest rate. Bonds are used by companies, municipalities, states, and U.S. foreign governments to finance a variety of projects and activities Bonds are commonly referred to as fixed-income securities...
What's associated with Net Working Capital?
cash Accounts receivable Inventory Accounts payable
Your firm currently has: $5,000 in cash, $10,000 in accounts receivable, $7,500 in inventory, and $100,000 in PP&E. You also have $12,500 in accounts payable and $75,000 in long-term debt. You are considering undertaking a new project. If you do the project, among other changes you predict your cash will rise to $7,500 and inventory to $10,000, while accounts receivable would drop in this scenario to $8,000 and PP&E to $90,000. Accounts payable would increase to $15,000. Assuming you accept the project, what are the cash flows associated with the change(s) to net working capital?
cash -2500 Accounts receivable 2000 Inventory -2500 Accounts payable 2500 Total Change -500
Market value is different than
accounting or book value
when calculating bond prices(PV) in excel.. PMT and FV need to be
both negative or both positive. Need to be same sign
