___You plan on sending your three children to college and your first child will begin school in exactly 10 years at which point you have to pay $45,000. Tuition will then grow at the rate of 3%. If your second child will start exactly two years after the first, and the third starts two years after the second how much will you have to put into your account monthly if your account pays 12% compounded annually? Assume that your first deposit is made today and your last deposit is made one month before you must pay your first tuition payment.


Now we want to have 408,336.18 in your account by the end of year 10. Recall that we are making monthly payments so we need to get a monthly EPR. The APR of a rate compounded annually is the same as the EAR.






___You are saving for the college education of your two children. One child will enter college in 5 years, while the other child will enter college in 7 years. College costs are currently $10,000 per year and are expected to grow at a rate of 5 percent per year. All college costs are paid at the beginning of the year. You assume that each child will be in college for four years. You currently have $50,000 in your educational fund. Your plan is to contribute a fixed amount to the fund over each of the next 5 years. Your first contribution will come at the end of this year, and your final contribution will come at the date at which you make the first tuition payment for your oldest child. You expect to invest your contributions into various investments which are expected to earn 8 percent per year. How much should you contribute each year in order to meet the expected cost of your children’s education?


Find PV of college costs in Year 5:


Find FV of educational fund in 5 years:

Now, find net amount needed in Year 5:


Finally, find PMT needed to accumulate $21,775.10 in Year 5:


___A firm is considering investing in a project. The cost the project is $100,000. The project will pay out $20,000 in year 1; $70,000 in year 2; $40,000 in year 3; $50,000 in year 4; and $30,000 in year 5. The project is scale enhancing.




–The firm issues only zero coupon bonds. It has 5 year zero coupon bonds outstanding, and these are the only type of bonds that it will issue in the future. Floatation costs on the bonds are 9%. The firm’s tax rate is 34%.



–The firm paid out $1,500,000 in dividends last year out of $5,000,000 of net income available to common stockholders. The book value of total owner’s equity is $25,000,000. Floatation costs on the firms common stock is 12%. The firm will have enough from retained earnings that it need not issue new shares.



  Shares outstanding Market Value Book Value Price Weight
Bonds 10,000 6,410,500 5,000,000 641.05 18.91%
Preferred Stock($100 par) 100,000 12,500,000 10,000,000 125 36.86%
Common Stock 250,000 15,000,000 15,000,000 60 44.23%
33,910,500 1







2)  NP=

3)   D=M×DR=100×0.1=10          NP= (1-F) =125(1-0.07) =116.25       ===8.6%


4)   =Total Dividends at T=0/Shares Outstanding = 1,500,000/250,000 = 6


ROE= ==     →    r===0.7     →      g=ROE × r=  × 0.7= 0.233




5) WACC=


6) PV=


7) NPV=

8) so Accept


9) New MVE=

10) New Price=




___The project is pays an indefinite stream of cash flows of $1,000,000 per year. The cost of the project is $15,000,000.  D=3  E=5  FC%=0.14  SO=200,000  Common Equity=Book value


–The firm’s common stock is currently selling for $56, last year the firm paid a dividend of $3 per share. The book value of shareholder’s equity is $5,000,000. The firm’s earning per share was $5. The firm’s floatation cost for common equity is 14%. The firm has 200,000 shares of common shares outstanding. The firm will not have to issue new common equity.


–The firm pays out 12% dividends on its preferred stock. Floatation costs are $3 per share. The price of the firm’s preferred stock is $30 per share.     DR=0.12   FC=3


–The firm’s 10 year zero coupon bonds are currently selling for $678 and the firm has a 35% marginal tax rate and a 25% average tax rate. T=0.35


  Book Value Market Value Price Weight
Bonds 3,000,000 3,500,000 678 21.88%
Preffered Stock($25 par) 2,500,000 2,500,000 30 15.62%
Common Stock 2,500,000 10,000,000 56 62.5%
16,000,000 1


2) NP=


3) D=


4) ROE=

5) WACC=


6) PV=


7) NPV=

8) so Reject


9) New MVE=


10) New Price=




___There are three securities that you can either buy or sell. Security A pays out $250 every month indefinitely with the first payment made two months from today. Security B pays out $250 every month indefinitely with the first payment starting 62 periods from today. Security C pays out 250 starting two months from now with the last payment made in month 61. If security A and B are fairly priced and security C sells for $3500, what should you do and why? Assume that you can earn 12% compounded annually on similar investments.


–First, we must get the effective periodic rate (EPR). Recall an APR that is annually compounded is exactly equal to its EAR.


EPR =  =  = 0.00949                           If security is fairly priced then Market Value = Present Value


A: First cash flow is at time 2, therefore we can either use the Regular Perpetuity Present Value formula (will give price at time 1) or the Perpetuity Due Present Value formula (will give price at time 2). In this case we will use the regular perpetuity formula.


(A)= =  = 26,346.87


However we need the present value at time 0 not at time 1. So we utilize the following:


(A)= ==26,099.22 = 


B: First cash flow is received at time 62, so we will price as of time 61.


(B)= =  = 26,346.87


However we need the present value at time 0 not at time 61. So we utilize the following


(B)= ==14,809.40 = 


C: (C) =PMT× = 250× = 11,396.95


(C)= ==11,289.82 >        so C is underpriced      Buy C    Sell A   Buy B




___A 4 year bond has a coupon rate of 12% and its yield to maturity is 13%. What is the price of the bond? What is the Macaulay duration of the bond? What is the modified duration of the bond? If the yield-to maturity changes to 15% what is the estimated new price of the bond? Is this a good estimate?




Period Coupon Payment Discount Factor Present Value Weight Weight*Period
1 60 60 0.93897 56.33803 0.05811 0.05811
2 60 60 0.88166 52.89956 0.05456 0.10912
3 60 60 0.82785 49.67095 0.05123 0.15369
4 60 60 0.77732 46.63939 0.04810 0.19242
5 60 60 0.72988 43.79285 0.04517 0.22584
6 60 60 0.68533 41.12005 0.04241 0.25447
7 60 60 0.64351 38.61037 0.03982 0.27876
8 60 1060 0.60423 640.48506 0.66060 5.28477
969.56 1 6.56






___Below is the distribution of returns for two stocks. In a world in which you can only hold one security which is the better investment and why?


Now assume that you can hold any combination of securities. Furthermore, the beta for Stock A is .8, the Beta for stock B is .4, expected inflation is 1.1%, and the real rate of return is 1.1%. The market risk premium is 4%.


State of the Economy Probability Stock A Returns Stock B Returns P*A A^2 P*A^2 P*B B^2 P*B^2
Recession 30%(0.3) -10% 1% -3 100 30 0.3 1 0.3
Moderate 20%(0.2) 5% 2% 1 25 5 0.4 4 0.8
Boom 50%(0.5) 18% 5% 9 324 162 2.5 25 12.5
    3.2 13.6


  A B
7% 3.20%
  12.17% 1.83%












___A Company just declared earnings of $1,000,000. Its earnings will grow 40% in year 1, 35% in year 2, 55% in year 3, 20% in year 4, and 5% thereafter. If the company has a payout ratio of 40% and a required rate of return of 14% what is the value of the stock today? (12 Points) What is the value of the stock at the end of year 10? Assume that there are 250,000 shares outstanding.


You can only do this over the constant growth period





___Balance Sheet


2006         200


Cash                                                         104            160                                                   Income Statement 2007


Accounts Receivable                             455            688                                                   Net Sales                              1509


Inventory                                                 553           555                                                   Cost of Goods Sold              750


Total Current Assets                             1112         1403                                                  Depreciation                         65


Net Plant Property and Equipment   1644         1709                                                  Interest Paid                         70


Total Assets                                            2756         3112                                                  Taxable Income                  624


Accounts Payable                                   232          266                                                    Taxes                                      212


Notes Payable                                         196          123                                                    Net Income                           412


Total Current Liabilities                         428          389


Long Term Debt                                     408          454


Common Stock and Paid in Surplus    600          640


Retained earnings                                1320         1629


Total Liabilities and Owners Equity   2756         3112






1) Current Ratio =


2) Quick Ratio =


3) Average Collection Period =


4) Inventory Turnover =


5) Efficiency Ratios:






___Calculate the following ratios from the financial statements below: 1) current ratio; 2) acid-test ratio; 3) debt ratio; 4) times interest earned ratio; 5) average collection period; 6)inventory turnover; 7) gross profit margin; 8)operating income return on investment; 9) fixed asset turnover; and 10) return on equity.


Income Statement                   2007                                    Balance Sheet                                       2007


Sales                                     5390                                                            Cash                                                           2694


Cost of Goods Sold    1961                                                            Accounts Receivable                                                3928


Other Expenses            343                                                               Inventory                                                                         6370


Depreciation                  723                                                               Current Assets                                      12992


Interest                              386                                                               Net Fixed Assets                                  22614


Earnings before Taxes                      1977                                                            Total Assets                                             35606


Taxes                                    672.18                                                       Current Assets                                      12992


Net Income                     1304.82                                                    Notes Payable                                       478


Current Liabilities                              3161


Long Term Debt                                  10290


Owner’s Equity                                     22155


Total Liabilities & Owner’s Equity 35606






–Gross profit=


–Operating income (EBIT) =


–Earnings before tax (EBT) =


–Earnings after tax (EAT) =


–Net income=






–When discount rate (required rate of return) falls,


When discount rate (required rate of return) rises, .


–If the coupon rate = required rate of return,


If the coupon rate> required rate,


If the coupon rate< required rate,



§   Investing in more than one security to reduce risk.


§   If two stocks are perfectly positively correlated, diversification has no effect on risk.


§   If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified.




§   Market risk (systematic risk) is non-diversifiable. This type of risk cannot be diversified away.


§   Company-unique risk (unsystematic risk) is diversifiable. This type of risk can be reduced through diversification




§   Beta is a measure of the “sensitivity” of an individual stock’s returns to changes in the market.


§   A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market.


§   A firm with a beta > 1 is more volatile than the market. (ex: technology firms)


§   A firm with a beta < 1 is less volatile than the market. (ex: utilities)


§   A stock with Beta = 0 has no systematic risk




1. Your company is considering an investment in a project which would require an initial outlay of $300,000 and produce expected cash flows in Years 1 through 5 of $87,385 per year. You have determined that the current after-tax cost of the firm’s capital (required rate of return) for each source of financing is as follows:


Cost of debt 8%     Cost of preferred stock 12%      Cost of common stock 16%


Long-term debt currently makes up 20% of the capital structure, preferred stock 10%, and common stock 70%. What is the net present value of this project?


a. $463     b. -$.22     c. $1,241     d. $1,568


2. As the size of a financing issue increases, the _____ decreases.


a. weighted cost of capital    b. flotation cost of the issue     c. effective tax rate       d. both a and b


3. Sonderson Corporation is undertaking a capital budgeting analysis. The firm’s beta is 1.5. The rate on six-month T-bills is 5%, and the return on the S&P 500 index is 12%. What is the appropriate cost for retained earnings in determining the firm’s cost of capital?


a.    13.1%         b. 15.5%       c. 17.7%       d. 19.9%


4. Sputter Motors has sales of $3,450,000, total assets of $1,240,000, cost of goods sold of $2,550,000, and an inventory turnover of 6.38. What is the amount of Sputter’s inventory?


a. $421,054      b. $638,112      c. $543,000       d. $399,687


5. GAAP, Inc. has total assets of $2,575,000, sales of $5,950,000, total liabilities of $1,855,062, and a net profit margin of 2.9%. What is GAAP’s return on equity?


A.    8.62% b. 23.97% c. 16.41% d. 4.48%


6. Given the following information for PepsiCo, determine the company’s weighted average cost of capital. Value Cost of Capital


Restaurant Division $5 Billion 13%      Snack Foods Division $7 Billion 12%      Beverages Division $13 Billion 8%


a. 10.12%      b. 11.00%      c. 12.10%       d. 13.00%


7. An example of liquidity ratio is the:      a. quick ratio.       b. debt ratio.          c. times-interest-earned.         d. return on assets.


8. The cost of capital for a firm which uses 45% debt at an after-tax cost of 10% and 55% common stock at a 15% cost is:


a. 12.25%.        b. 12.50%.         c. 12.75%.        d. 13.00%.


9. Which of the following is the best indicator of management’s effectiveness at managing the firm’s balance sheet?


a. Debt ratio            b. Total asset turnover        c. Times-interest-earned        d. Operating profit margin


10. Heavy Load, Inc. has sales of $3,450,000, total assets of $1,240,000, and total liabilities of $275,000, which consist strictly of notes payable. The firm’s operating profit margin is 16.1%, and it pays a 10% rate of interest on its notes payable. How much is the firm’s times-interest earned?


a. 15.6        b. 45.3       c. 20.2       d. 3.0


1) Which of the following statements is true?             a. Current assets consist of cash, accounts receivable, inventory, and net plant, property, and equipment.


b. The quick ratio is a more restrictive measure of a firm’s liquidity than the current ratio.


c. For the average firm, inventory is considered to be more “liquid” than accounts receivable


d. A successful firm’s current liabilities should always be greater than its current assets.


5) The question “Did the common stockholders receive an adequate return on their investment?” is answered through the use of:


a. liquidity ratios.        b. profitability ratios.        c. coverage ratios.         d. leverage ratios.


6) Cost of capital is:       a. the coupon rate of debt.          b. a hurdle rate set by the board of directors.     c. the rate of return that must be earned on additional investment if firm value is to remain unchanged.            d. the average cost of the firm’s assets.



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