Dr. H. H. Friedman
Review for Final--Corporation Finance

(1A)  A computer that costs $10,000 has the following cash inflows: Year 1=$2,400, Year 2 = $5,000, Year 3 = $4,000, and Year 4 = $3,000. The firm's cost of capital is 10%. (a) What is the payback period? [2.65 years] (b) What is the discounted payback period?[3.33 years](c) Solve for the NPV and the Profitability Index  [$1,368 and 1.137] (d) Calculate the IRR [16%] 
(1B)  A printer that costs $10,000 has the following cash inflows: Year 1=$5,000, Year 2 = $3,000, Year 3 = $10,000, and Year 4 = $2,000. The firm's cost of capital is 12%. (a) What is the payback period? [2.2 years] (b) What is the discounted payback period?[2.44 years]
(1C)  A printing press costs $100,000 and has the following cash inflows:  Year 1 = $30,000, Year 2 = $40,000, and Year 3 = $60,000. The firm's cost of capital is 12%.   (a) What is the NPV and Profitability Index? [$1,383 and 1.0138]
(1D)  A lathe costs $50,000 and has the following cash inflows:  Year 1 = $10,000, Year 2 = $20,000, and Year 3 = $25,000. The firm's cost of capital is 15%.   (a) What is the NPV and Profitability Index? [-$9,744 and 0.805.  Note that when NPV is negative, the P.I. is less than one]

(2A) A lathe that costs $200,000 has the following cash inflows: Year 1=$120,000, Year 2 = $50,000, Year 3 = $74,500. The firm's cost of capital is 10%. (a) What is the payback period? [2.40 years] (b) What is the discounted payback period?[2.89 years](c) Solve for the NPV and the Profitability Index  [$6,386 and 1.032] (d) Calculate the IRR [12%]
(2B)  A machine that costs $5,000 has the following cash inflows: Year 1=$3,000, Year 2 = $2,000, Year 3 = $6,000. The firm's cost of capital is 14%. (a) What is the payback period? [2 years] (b) What is the discounted payback period?[2.2 years](c) Solve for the NPV and the Profitability Index  [$3,220 and 1.644]
(2C)  A college needs a new heating plant.  A heating plant designed by the AB Company costs $100,000,000 to construct and $4,000,000 per year in annual maintenance; a plant designed by the XY Company costs $60,000,000 to construct and $9,000,000 per year in annual maintenance. Both plants have an expected life of 17 years.   Which heating plant would you recommend?  [Below a 10% interest rate,  AB;   greater than 10%, XY]

(3A) A machine that costs $50,000 has the following cash inflows: Year 1=$28,100, Year 2 = $30,000, Year 3 = $10,000. The firm's cost of capital is 15%. (a) What is the payback period? [1.73 years] (b) What is the discounted payback period?[2.43 years](c) Solve for the NPV and the Profitability Index  [$3,694 and 1.074] (d) Calculate the IRR [20%]
(3B)  A machine that costs $10,000 has the following cash inflows: Year 1=$4,000, Year 2 = $5,000, Year 3 = $14,000. The firm's cost of capital is 20%. (a) What is the payback period? [2.07 years] (b) What is the discounted payback period?[2.39 years](c) Solve for the NPV and the Profitability Index  [$4,907 and 1.49] (d) Calculate the NTV [$8,480]
(3C) A computer that costs $100,000 has the following cash inflows: Year 1=$30,000, Year 2 = $50,000, Year 3 = $70,000. The firm's cost of capital is 14%. (a) Calculate the NTV [$17,838] (b) Calculate the IRR [about 20%]
(3D) A copying machine that costs $50,000 has the following cash inflows: Year 1=$10,000, Year 2 = $15,000, Year 3 = $35,000. The firm's cost of capital is 16%. (a) Calculate the NTV [-$12,189]

(4) A press that costs $30,000 has the following cash inflows: Year 1=$10,000, Year 2 = $15,000, Year 3 = $7,350. The firm's cost of capital is 15%. (a) What is the payback period? [2.68 years] (b) What is the discounted payback period?[never] (c) Solve for the NPV and the Profitability Index
[-$5,130 and 0.83] (d) Calculate the IRR [4%]

(5) The cost of Project X is $40,000
Year 1 inflows:  -$5,000     .10 probability;   $10,000   .40 probability;    $20,000    .50 probability
Year 2 inflows   -$10,000    .20 probability;   $20,000   .30 probability;    $40,000    .50 probability
Year 3 inflows   -$20,000    .20 probability;   $40,000   .25 probability;    $20,000    .55 probability

(a) If a firm uses the following approach to risk:   no risk = 10%; low risk = 12%; medium risk = 15%; and high risk = 20% and this project is classified as medium risk, should this project be undertaken?  [ yes, NPV =$1,064]  (b)  Using the above data, if the firm uses a certainty equivalent approach and the certainty equivalent coefficients (alpha) are all .8, should the company go ahead with this project?  [no, NPV = -$4096]

(6) The cost of Project X is $100,000
Year 1 inflows:  -$120,000     .20 probability;   $140,000   .40 probability;    $200,000    .40 probability
Year 2 inflows   -$200,000    .20 probability;    $100,000   .30 probability;    $150,000    .50 probability
(a) If a firm uses the following approach to risk:   no risk = 12%; low risk = 14%; medium risk = 16%; and high risk = 20% and this project is classified as medium risk, should this project be undertaken?  [ yes, NPV =$44,863]  (b)  Using the above data, if the firm uses a certainty equivalent approach and the certainty equivalent coefficients (alpha) are all .8, should the company go ahead with this project?  [yes, NPV = $21,458]

(7) A college is considering the purchase of one of two heating systems:  System X will cost $19 million and $1.5 million per year in maintenance and System Y will cost $5 million and $3.5 million in maintenance.  Both systems have an expected life of 30 years.  Which system should the college purchase?   [14% is the crossover rate.  Below 14% choose System X and above 14% choose System Y]

(8)  IBM just sold an 8.5% coupon bond with 30 years to maturity and interest paid annually.  Net proceeds to IBM were $859 and the corporate tax rate is 30%.  Solve for the cost of debt.  [7%]

(9)  AOL just sold a 12% coupon bond with 20 years to maturity and interest paid annually.  Net proceeds to AOL were $812 and the corporate tax rate is 1/3.  Solve for the cost of debt.  [10%]

(10)  AOL just sold preferred stock paying $9 per year.  The stock sold for $109 and underwriters received  $9 per share. The tax rate is 30%.  Solve for the cost of preferred stock. [9%]

(11)  EBAY just sold preferred stock paying $8 per year.  The stock sold for $57 and underwriters received $7 per share.   The tax rate is 40%.  Solve for the cost of preferred stock.  [16%]

(12)  Norton just sold a new issue common stock. The dividend next year is expected to be $9 and to grow at  3% per year.   The stock sold for $99 but the firm received $90 after flotation costs.  Solve for the cost of equity and the cost of retained earnings.  [13% and 12.09%]

(13)  Ricoh just sold a new issue of common stock. The dividend next year is expected to be $6 and to grow at  2% per year.   The stock sold for $40 but the firm received $36 after flotation costs.  Solve for the cost of equity and the cost of retained earnings.  [18.67% and 17%]

(14) What is the weighted cost of capital for the LWF Corporation? It consists of 50% debt, 25% preferred,  20% common, and 5% retained earnings. The cost of debt =10%, cost of preferred=12%, cost of common=18%, and the cost of retained earnings is 16%. [12.4%]

(15) What is the weighted cost of capital for the SURF Corporation? It consists of 60% debt, 5% preferred,  10% common, and 25% retained earnings. The cost of debt =12%, cost of preferred=16%, cost of common=19%, and the cost of retained earnings is 14%. [13.4%]

(16) What is the cost of not taking a cash discount if the terms are 1.5/10 net 90: [6.94%]

(17) What is the cost of not taking a cash discount if the terms are 3/10 net 70: [18.81%]

(18)  [You may not be responsible for calculation of the standard deviation.  Check with me in class.] What is the expected return and standard deviation of a portfolio that is invested 50% in Stock A and 50% in Stock B? [7.5% and 2.60%]

.75

.25

(19)  [You may not be responsible for calculation of the standard deviation.  Check with me in class.] What is the expected return and standard deviation of a portfolio that is invested 50% in Stock A and 50% in Stock B? [13% and 6%]

.90

.10

(20)  [You may not be responsible for calculation of the standard deviation.  Check with me in class.] What is the expected return and standard deviation of a portfolio that is invested 50% in Stock A and 50% in Stock B? [16.6% and 3.67%]

.70

.30

(21) Using CAPM, what return should be required for TAT stock. Its beta is 1.30, the risk-free rate (T-bills) is 5% and the rate of return on the market portfolio (S&P 500) is 22%? [27.1%]

(22) Using CAPM, what return should be required for XBAY stock. Its beta is 2.50, the risk-free rate (T-bills) is 4% and the rate of return on the market portfolio (S&P 500) is 20%? [44% ]

(23)  The beta for T-bills is: ____ .    The beta for the stock market as a whole, or an average stock, is:   ____.  [0, 1]

(24)  The portion of total risk caused by factors that affect the prices of all securities, e.g., political or economic changes, is known as  ____ risk  [systematic risk]

(25)  The portion of total risk that is unique to a firm or industry and can be eliminated by diversification is known as ___ risk   [unsystematic or unique risk]

(26)  Calculate the breakeven sales level and the Degree of Operating Leverage (DOL) if current Sales = $910,000; Total Variable Cost = $210,000; and Fixed Cost = $500,000.   [$650,000; 3.5]

(27)  Calculate the breakeven sales level and the Degree of Operating Leverage (DOL) if current Sales = $5,600,000; Total Variable Cost = $3,360,000; and Fixed Cost = $2,000,000.   [$5,000,000; 9.33]

(28) Leverage Examples:  Calculate the breakeven level of sales (S*), DOL, DFL, and DCL.

(29) {This topic may not be covered unless time permits it.} The ABC firm expects sales for the following year to be $1,000,000 (Quantity = 125,000) if they purchase a new plant.  They are not sure how to raise the money for the new  plant.  One possibility is to sell an additional $100,000 worth of debt at 8% interest (the firm will then have a total debt   of $200,000t at 8%).  Another possibility is to sell another 100,000 shares of common stock  What would be the effects on earnings per share (E.P.S.) of the two strategies.

[Answer:  If debt is employed, E.P.S. will be $1.25.  With equity, E.P.S. will be .65]

The Net  Income Approach -- Under the Net Income approach to valuation, the cost of debt and the cost of equity are unaffected by the capital structure.  Thus, the weighted average cost of capital (WACC) or overall cost of capital declines and the total value of the firm rises with the increased use of leverage (i.e., as the debt/capital ratio increases).  In other words, the more debt, the better.

The Net Operating Income Approach (Net Operating Income = EBIT) -- associated with the work of Modigliani-Miller.  This theory posits that as a firm becomes more leveraged (i.e., as the debt/capital ratio increases), the cost of equity rises and the WACC remains constant.  Thus, the total value of the firm remains constant as leverage is changed.    A major assumption of this theory is no taxes. 

However,  corporations in the United States do pay taxes. Furthermore, the  US Government  treats dividends on common and preferred stock differently from interest payments on a bond -- interest payments on bonds are tax-deductible to a corporation whereas preferred and common stock dividends are not.   In this case, both theories agree that the WACC goes down as financial leverage goes up. 

Most firms today claim that they have a target debt/capital ratio.  It is advisable to have some debt since leveraging can increase a firm's earnings per share, but it is not wise to have too much debt.  If a specific firm's debt/capital ratio is much higher than similar firms within the industry, this could have an adverse effect on its bond ratings.  Bonds may be rated as being very risky it the rating services believe that a firm has too much debt.