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**Unformatted text preview: **TBS 907 SPRING 2005 MODULE 1 (Contd) Present Value and The Opportunity Cost of Capital Topics Covered Present Value Net Present Value NPV Rule Opportunity Cost of Capital Managers and the Interests of Shareholders Present Value
Present Value
Value today of a future cash flow. Discount Rate Interest rate used to compute present values of future cash flows. Discount Factor Present value of a $1 future payment. Present Value Present Value = PV PV = discount factor C1 Present Value
Discount Factor = DF = PV of $1 DF = 1 (1+ r ) t Discount Factors can be used to compute the present value of any cash flow. Valuing an Office Building
Step 1: Forecast cash flows Cost of building = C0 = 350 Sale price in Year 1 = C1 = 400 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 7%, then Cost of capital = r = 7% Valuing an Office Building
Step 3: Discount future cash flows PV = C1 (1+ r ) = 400 (1+ .07 ) = 374 Step 4: Go ahead if PV of payoff exceeds investment NPV = - 350 + 374 = 24 Net Present Value
NPV = PV - required investment C1 NPV = C0 + 1+ r Risk and Present Value Higher risk projects require a higher rate of return Higher required rates of return cause lower PVs PV of C1 = $400 at 7% 400 PV = = 374 1 + .07 Risk and Present Value
PV of C1 = $400 at 12% 400 PV = = 357 1 + .12 PV of C1 = $400 at 7% 400 PV = = 374 1 + .07 Net Present Value Rule Accept investments that have positive net present value Net Present Value Rule Accept investments that have positive Example Suppose we can invest $50 today and receive $60 in one year. Should we accept the project given a 10% expected return? net present value 60 NPV = -50 + = $4.55 1.10 Opportunity Cost of Capital
Example You may invest $100,000 today. Depending on the state of the economy, you may get one of three possible cash payoffs: Economy Payoff Slump Normal Boom $80,000 110,000 140,000 80,000 + 110,000 + 140,000 Expected payoff = C1 = = $110,000 3 Opportunity Cost of Capital
Example continued The stock is trading for $95.65. Next year's price, given a normal economy, is forecast at $110 Opportunity Cost of Capital
Example continued The stocks expected payoff leads to an expected return. expected profit 110 - 95.65 Expected return = = = .15 or 15% investment 95.65 Opportunity Cost of Capital
Example continued Discounting the expected payoff at the expected return leads to the PV of the project 110,000 PV = = $95,650 1.15 The Value of Common Stocks Stocks & Stock Market
Common Stock Ownership shares in a publicly held corporation. Secondary Market market in which already issued securities are traded by investors. Dividend Periodic cash distribution from the firm to the shareholders. P/E Ratio Price per share divided by earnings per share. Stocks & Stock Market
Book Value Net worth of the firm according to the balance sheet. Liquidation Value Net proceeds that would be realized by selling the firm's assets and paying off its creditors. Market Value Balance Sheet Financial statement that uses market value of assets and liabilities. Valuing Common Stocks
Expected Return The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the market capitalization rate. Div1 + P1 - P0 Expected Return = r = P0 Valuing Common Stocks
Example: If Fledgling Electronics is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00? 5 + 110 - 100 Expected Return = = .15 100 Valuing Common Stocks
The formula can be broken into two parts. Dividend Yield + Capital Appreciation Div1 P - P0 Expected Return = r = + 1 P0 P0 Valuing Common Stocks
Capitalization Rate can be estimated using the perpetuity formula, given minor algebraic manipulation. Div1 Capitalization Rate = P0 = r-g Div1 =r= +g P0 Valuing Common Stocks
Return Measurements Div1 Dividend Yield = P0 Return on Equity = ROE EPS ROE = Book Equity Per Share Valuing Common Stocks
Dividend Discount Model Computation of today's stock price which states that share value equals the present value of all expected future dividends. Valuing Common Stocks
Dividend Discount Model Computation of today's stock price which states that share value equals the present value of all expected future dividends. Div1 Div2 Div H + PH P0 = + +...+ 1 2 H (1 + r ) (1 + r ) (1 + r )
H Time horizon for your investment. Valuing Common Stocks
Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? Valuing Common Stocks
Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return? 3.00 3.24 350 + 94.48 . PV = + + 1 2 3 (1+.12) (1+.12) (1+.12) PV = $75.00 Valuing Common Stocks
If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. Valuing Common Stocks
If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY. Div1 EPS1 Perpetuity = P0 = or r r
Assumes all earnings are paid to shareholders. Valuing Common Stocks
Constant Growth DDM A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model). Valuing Common Stocks
Example continued If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends? $3.00 $100 = .12 - g g =.09 Answer The market is assuming the dividend will grow at 9% per year, indefinitely. Valuing Common Stocks If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher. Payout Ratio Fraction of earnings paid out as dividends Plowback Ratio Fraction of earnings retained by the firm. Valuing Common Stocks
Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = return on equity X plowback ratio FCF and PV Free Cash Flows (FCF) should be the theoretical basis for all PV calculations. FCF is a more accurate measurement of PV than either Div or EPS. The market price does not always reflect the PV of FCF. When valuing a business for purchase, always use FCF. FCF and PV Valuing a Business The value of a business is usually computed as the discounted value of FCF out to a valuation horizon (H). The valuation horizon is sometimes called the terminal value and is calculated like PVGO. FCF1 FCF2 FCFH PVH PV = + + ... + + 1 2 H (1 + r ) (1 + r ) (1 + r ) (1 + r ) H FCF and PV Valuing a Business FCF1 FCF2 FCFH PVH PV = + + ... + + 1 2 H (1 + r ) (1 + r ) (1 + r ) (1 + r ) H
PV (free cash flows) PV (horizon value) FCF and PV
Example
Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6% Year
1 2 3 4 5 6 10.00 12.00 14.40 17.28 20.74 23.43 1.20 2.00 - .80 1.44 2.40 20 1.73 2.88 20 2.07 3.46 20 2.49 2.69 - .20 20 2.81 3.04 - .23 13 7 8 9 10 26.47 28.05 29.73 31.51 3.18 1.59 1.59 13 3.36 1.68 1.68 6 3.57 1.78 1.79 6 3.78 1.89 1.89 6 Asset Value Earnings Investment Free Cash Flow - .96 - 1.15 - 1.39 .EPS growth (%) 20 FCF and PV
Example continued
Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6% . 1 1.59 PV(horizon value) = = 22.4 6 (1.1) .10 - .06 .80 .96 1.15 1.39 .20 .23 PV(FCF) = - - - - - 2 3 4 5 6 1.1 (1.1) (1.1) (1.1) (1.1) (1.1) = -3.6 FCF and PV
Example continued
Given the cash flows for Concatenator Manufacturing Division, calculate the PV of near term cash flows, PV (horizon value), and the total value of the firm. r=10% and g= 6% . PV(business) = PV(FCF) + PV(horizon value) = -3.6 + 22.4 = $18.8 TBS 907 SPRING 2005 MODULE 1 (Contd) Why Net Present Value Leads to Better Investment Decisions than Other Criteria Topics Covered NPV and its Competitors The Payback Period The Book Rate of Return Internal Rate of Return Capital Rationing NPV and Cash Transfers Every possible method for evaluating Cash Every possible method for evaluating projects impacts the flow of cash about the company as follows. Investment opportunity (real asset) Invest Firm Shareholder Investment opportunities (financial assets) Shareholders invest for themselves Alternative: pay dividend to shareholders Payback The payback period of a project is the number of years it takes before the cumulative forecasted cash flow equals the initial outlay. The payback rule says only accept projects that "payback" in the desired time frame. This method is very flawed, primarily because it ignores later year cash flows and the the present value of future cash flows. Payback
Example Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.
Project A B C C0 C1 C2 C3 Payback Period NPV@ 10% - 2000 500 500 5000 - 2000 500 1800 0 - 2000 1800 500 0 Payback
Example Examine the three projects and note the mistake we would make if we insisted on only taking projects with a payback period of 2 years or less.
Project A B C C0 - 2000 - 2000 C1 500 500 Period 500 5000 3 1800 0 2 500 0 2 C2 C3 Payback NPV@ 10% + 2,624 - 58 + 50 - 2000 1800 Book Rate of Return
Book Rate of Return Average income divided by average book value over project life. Also called accounting rate of return. book income Book rate of return = book assets
Managers rarely use this measurement to make decisions. The components reflect tax and accounting figures, not market values or cash flows. Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? 2,000 4,000 NPV = -4,000 + + =0 1 2 (1 + IRR ) (1 + IRR ) Internal Rate of Return
Example You can purchase a turbo powered machine tool gadget for $4,000. The investment will generate $2,000 and $4,000 in cash flows for two years, respectively. What is the IRR on this investment? 2,000 4,000 NPV = -4,000 + + =0 1 2 (1 + IRR ) (1 + IRR ) IRR = 28.08% Internal Rate of Return
2500 2000 1500 NPV (,000s) 1000 500 0
10 0 IRR=28% -500 -1000 -1500 -2000 20 30 60 10 40 50 70 80 Discount rate (%) 90 Internal Rate of Return
Pitfall 1 Lending or Borrowing? With some cash flows (as noted below) the NPV of the project increases s the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. Internal Rate of Return
Pitfall 1 Lending or Borrowing? With some cash flows (as noted below) the NPV of the project increases s the discount rate increases. This is contrary to the normal relationship between NPV and discount rates. NPV Discount Rate Internal Rate of Return
Pitfall 2 Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates. The following cash flow generates NPV=0 at both (50%) and 15.2%. C0 - 1,00 Internal Rate of Return
Pitfall 2 Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates. The following cash flow generates NPV=0 at both (50%) and 15.2%. NPV 1000 500 0 -500 -1000 IRR=-50% IRR=15.2% Discount Rate Internal Rate of Return
Pitfall 3 Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem. Project Internal Rate of Return
Pitfall 3 Mutually Exclusive Projects Internal Rate of Return
Pitfall 4 Term Structure Assumption We assume that discount rates are stable during the term of the project. This assumption implies that all funds are reinvested at the IRR. This is a false assumption. Internal Rate of Return Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. Note the previous example. Internal Rate of Return
HP-10B -350,000 16,000 16,000 466,000 CFj CFj CFj CFj {IRR/YR} EL-733A -350,000 16,000 16,000 466,000 IRR CFi CFfi CFi CFi Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. Note the previous example. BAII Plus CF 2nd 16,000 16,000 {CLR Work} ENTER ENTER IRR CPT -350,000 ENTER 466,000 ENTER All produce IRR=12.96 Profitability Index When resources are limited, the profitability index (PI) provides a tool for selecting among various project combinations and alternatives A set of limited resources and projects can yield various combinations. The highest weighted average PI can indicate which projects to select. Profitability Index
NPV Profitability Index = Investment
Example We only have $300,000 to invest. Which do we select? Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 What To Discount
Only Cash Flow is Relevant What To Discount
Points to "Watch Out For" Do not confuse average with incremental payoffs Include all incidental effects Do not forget working capital requirements Forget sunk costs Include opportunity costs Beware of allocated overhead costs INFLATION RULE Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows. Use real interest rates to discount real cash flows. You will get the same results, whether you use nominal or real figures Inflation Inflation
Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for 3 additional years (4 years total). If discount rates are 10% what is the present value cost of the lease?
1+nominal interest rate 1 + real interest rate = 1+inflation rate Inflation
Year 1 2 3 4 Example nominal figures Cash Flow PV @ 10% 8000 8000 1.10 = 7272.73 8240 8000x1.03 = 8240 2 = 6809.92 1.10 8487 .20 8000x1.032 = 8240 = 6376.56 3 1.10 8000x1.033 = 8487.20 8741.82 = 5970.78 1.104 $26,429.99 Inflation
Year 1 2 3 4 Example real figures Cash Flow
8000 1.03 8240 1.032 8487.20 1.033 8741.82 1.034 PV@6.7961%
7766.99 1.068 7766.99 1.0682 7766.99 1.0683 7766.99 1.0684 = 7766.99 = 7766.99 = 7766.99 = 7766.99 = 7272.73 = 6809.92 = 6376.56 = 5970.78 = $26,429.99 Equivalent Annual Cost
Equivalent Annual Cost The cost per period with the same present value as the cost of buying and operating a machine.
present value of costs Equivalent annual cost = annuity factor Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method.
Year 1 15 10 Machine A B 2 5 6 3 5 6 4 5 PV@6% 28.37 21.00 EAC 10.61 11.45 Timing Even projects with positive NPV may be more valuable if deferred. The actual NPV is then the current value of some future value of the deferred project. Net future value as of date t Current NPV = (1 + r )t Timing
Example You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV? Harvest Year
0 1 Net FV ($1000s) 50 64.4 % change in value 28.8 2 77.5 20.3 3 4 5 89.4 100 109.4 15.4 11.9 9.4 Timing
Example continued
You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV? 64.4 NPV if harvested in year 1 = = 58.5 1.10 Timing
Example continued
You may harvest a set of trees at anytime over the next 5 years. Given the FV of delaying the harvest, which harvest date maximizes current NPV? 64.4 NPV if harvested in year 1 = = 58.5 1.10
0 1 Harvest Year 2 3 64.0 67.2 4 5 NPV ($1000s) 50 58.5 68.3 67.9 Fluctuating Load Factors
Two Old Machines 750 units Annual output per machine Operating cost per machine 2 750 = $1,500 PV operating cost per pachine 1,500/.10 = $15,000 PV operating cost of two machines 2 15,000 = $30,000 Fluctuating Load Factors
Annual output per machine Capital cost pe machine Two New Machines 750 units $6,000 Operating cost per machine 1 750 = $750 PV operating cost per pachine 6,000 + 750/.10 = $13,500 PV operating cost of two machines 2 13,500 = $27,000 Fluctuating Load Factors
One Old Machine Annual output per machine Capital cost pe machine Operating cost per machine 500 units 0 2 500 = $1,000 One New Machine 1,000 units $6,000 1 1,000 = $1,000 PV operating cost per pachine 1,000/.10 = $10,000 6,000 + 1,000 / .10 = $16,000 PV operating cost of two machines ................................$26,000 ...

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