PRACTICE MIDTERMS

MIDTERM EXAM: FALL 1985

1. You are a prudent individual who wants to plan for your retirement. You are now 25 and plan to work for the next 40 years. You will retire at 65. Your actuarial tables tell you that you will live to be 85 (i.e. 20 years after retirement). You estimate that your expenses each year after your retirement till your death will be \$20000 (Assume that your expenses are at the end of each year). How much do you have to set apart at the end of each year for the next 40 years to be able to afford this? (Assume that you can invest the money at 10%) [ 5 points]

2. You have been observing the progressive gentrification of San Francisco with interest. You realize that the time is ripe for you to start and run an aerobic exercise center. You find an abandoned warehouse in Fisherman's Wharf which will meet your needs and rents for \$48000/ year. You estimate that it will initially cost \$50000 to renovate the place and buy Nautilius equipment for the center. (There will be no salvage and the entire initial cost is depreciable) You have done a market survey which leads you to believe that you will get 500 members each paying \$500/year. You have also found 5 instructors you can hire for \$24000/year apiece. Your tax rate if you start making profits will be 40% and you choose to use straight line depreciation on your initial investment. If your discount rate is 15% and you expect to retire to the Bahamas in ten years, answer the following questions:

(a) Is this a good investment? ( 5 points)

(b) How sensitive is your conclusion to your assumptions about the number of members you expect to have? (i.e. How much margin for error do you have on this estimate?) ( 2 points)

3a. Your superior is a cantankerous and very stubborn man who believes that the simplest approaches are the best. Your firm has just bought a van, with a five-year lifetime, for \$10000. You superior wants you to use straight line depreciation. You claim that using double declining balance depreciation will save you money. If your discount rate is 10% and your tax rate is 40%, show him how much you will save in present value dollars. ( 3 points)

3b. Brooks Brothers is thinking of investing in a new line of punk rocker clothes for the new executive. You have been hired to evaluate the project. You find that, if the project is accepted, you could use an abandoned warehouse already owned by Brooks with a book value of \$500000. Your superior had been planning to rent this warehouse out to another firm for \$100000/ year. If your tax rate is 40%, your discount rate is 15%, you use straight line depreciation and your project lifetime is 10 years, what is the opportunity cost of this investment? ( 4 points)

4. You have just been given the following information on Dodger Corp and the S&P 500.
 Year Dodger Corp S&P 500 Prices Levels 1979 40 150 1980 36 150 1981 34.2 145.5 1982 20.52* 160.05 1983 22.57 163.25 1984 22.34 159.99

* Stock split 2:1

a. What is your beta estimate for this firm? ( 3 points)

b. What portion of total variance is systematic and what portion is unsystematic?

c. What is the required rate of return on Dodger Corp? (Rf=7%, E(Rm)-Rf=8%) ( 1 point)

CORPORATE FINANCE: MIDTERM EXAM

Spring 1988

1. You have collected returns on AD Corporation and the NYSE index for five years:
 Year AD Corp NYSE 1981 10% 5% 1982 5% 15% 1983 -5% 8% 1984 20% 12% 1985 -5% -5%

a. Estimate the intercept (alpha) and slope (beta) of the regression. (2 pts)

Use enclosed worksheet to show work.

b. If you bought stock in AD Corp. today how much would you expect to make as a return over the next year? [The six-month T.Bill rate is 6%] (1)

c. Looking back over the last five years, how would you evaluate AD's performance relative to the market? ( 1 point)

d. Assume now that you are an undiversified investor and that you have all of your money invested in Ad Corporation. What would be a good measure of the risk that you are taking on? How much of this risk would you be able to eliminate if you diversify? (2 points)

e. AD is a diversified company and is planning to sell off one of its divisions. The division under consideration has assets which comprise half of the book value of AD Corporation, and 20% of the market value. Its beta is twice the average beta for AD Corp (before divestment). What will the beta of AD Corporation be after divesting this division? ( 2 points)

2. You are graduating in June and would like to start your own business making wine coolers. You collect the following information on the initial costs:

Cost of Plant & Equipment = \$ 500000

Licensing & Legal Costs = \$ 50000

You can claim an investment tax credit of 10% on plant & equipment. You also have been left a tidy inheritance that will cover the initial cost, and is currently invested in a CD earning 10%.

You estimate that you can sell one million bottles a year at \$1/bottle. You estimate your costs as follows:

Variable costs/bottle = 50 cents

Fixed Costs/ year = \$ 200000

Adding up state, local and federal taxes, you note that you will be in the 50% tax bracket. To be conservative, you assume that you will terminate the business in five years and that you will get nothing from the plant and equipment as salvage. (You also use straight line depreciation.) As a final consideration, you note that starting this business will mean that you will not be able to take the investment banking job you have been offered (which offered \$ 75000/year for the next five years.). Should you take on the project? ( 5 points)

3. You have just completed the analysis of a capital budgeting proposal and have concluded that the NPV=-5000. (You used a 12% discount rate) Before you decide that the project is not worthwhile, you note that you assumed that all the \$400000 in financing needed for the project comes from equity, and that you could easily borrow \$200000 to finance the project. If the borrowing is an 8% five-year term loan, would it make any difference to your conclusion? ( 3 points)

4. TRUE or FALSE

1. Initial public offerings are usually underpriced by investment bankers

TRUE FALSE

2. When choosing between two projects, you always choose the one which has the higher NPV.

TRUE FALSE

TRUE FALSE

3. The IRR >discount rate if the NPV>0

TRUE FALSE

MIDTERM EXAM: SPRING 1989

1. You are an expert at working with PCs and are considering setting up a software development business. To set up the enterprise, you anticipate that you will need to acquire computer hardware costing \$ 100000 (The lifetime of this hardware is five years for depreciation purposes, and straight line depreciation will be used). In addition, you will have to rent an office for \$50000/ year. You estimate that you will need to hire five software specialists at \$ 50000/ year to work on the software, and that your marketing and selling costs will be \$ 100000/ year. You expect to price the software you produce at \$100/unit and to sell 6000 units a year. The actual cost of materials used to produce each unit is \$ 20. Your tax rate will be 40% and the appropriate opportunity cost is 12%.

a. Should you accept the project? ( 4 points)

b. How sensitive is your decision to the number of units that you sell? ( 1 points)

2. You are an analyst for a sporting goods corporation that is considering a new project which will take advantage of excess capacity in a existing plant. The plant has a capacity to produce 50000 tennis racquets, but only 25000 are being produced currently though sales of the rackets are increasing 10% a year. You want to use some of the remaining capacity to manufacture 20000 squash rackets each year for the next ten years (which will use up 40% of the total capacity), and this market is assumed to be stable (no growth). An average tennis racquet sells for \$100 and costs \$40 to make. The tax rate for the corporation is 40% and the discount rate is 10%. Is there an opportunity cost involved? If so, how much is it? ( 4 points)

3. You have estimated the returns on XYZ corporation and on the overall market for five years:
 Year Rxyz Rm 1982 20% 15% 1983 -10% -5% 1984 30% 25% 1985 10% 15% 1986 0% -10%

a. Estimate the beta for this stock. ( 2 points)

b. Estimate the alpha for this stock. ( 1 point)

c. What does the alpha tell you about the stock's performance over the five years? ( 1 point)

d. What is the expected return on XYZ corporation if you use the CAPM? (The riskfree rate is 9%) ( 1 point)

e. If XYZ corporation has a current debt/equity ratio of 50%, what would its beta be if it increased its debt/equity ratio to 200% ? (The tax rate is 40%) ( 2 points)

4. You have been called in to evaluate whether a pension fund is adequately funded to meet its obligations. The cashflow obligations of the fund are defined below:

\$ 1 million a year : 1990-94 ( Years 1-5)

\$ 2 million a year : 1995-99 ( Years 6-10)

\$ 5 million a year : 2000-09 ( Years 11-20)

How much would the fund need to have right now to meet these obligations, if the interest rate on its deposits is 10% ? ( 4 points)

CORPORATE FINANCE: MIDTERM EXAM

Spring 1990

1. You have been hired to run the pension fund for a small company with five employees. You estimate, based upon their ages and retirement schedules, that your liabilities under the plan will be as follows:
 Years Expected cash payments 6-10 \$ 100,000 11-20 \$ 250,000 21-25 \$ 100,000

You currently have \$ 500,000 in investments in the plan. You want to fully fund all your above-listed liabilities by the end of year 5. How much would you have to set aside each year for the next five years to ensure this, if your opportunity cost is 8%? ( 5 points)

2. You are examining the viability of a capital investment that your firm is interested in. The project will require an initial investment of \$500,000 and the projected revenues are \$400,000 a year for five years. The projected cost-of-goods-sold is 40% of revenues and the tax rate is 40%. The initial investment is primarily in plant and equipment and can be depreciated straight-line over five years. (The salvage value is zero.) The project makes use of other resources that your firm already owns:

(a) Two employees of the firm, each with a salary of \$40,000 a year, who are currently employed by another division will be transferred to this project. The other division has no alternative use for them, but they are covered by a union contract which will prevent them from being fired for three years (during which they would be paid their current salary.)

(b) The project will use excess capacity in the current packaging plant. While this excess capacity has no alternative use now, it is estimated that the firm will have to invest \$ 250,000 in a new packaging plant in year 4 as a consequence of this project using up excess capacity (instead of year 8 as originally planned).

(c) The project will use a van currently owned by the firm. While the van is not currently used, it can be rented out for \$ 3000 a year for five years. The book value of the van is \$10,000 and it is being depreciated straight line (with five years remaining for depreciation).

The discount rate to be used for this project is 10%.

(1) What (if any) is the opportunity cost associated with using the two employees from another division (described in (a))? (1 point)

(2) What, if any, is the opportunity cost associated with the use of excess capacity of the packaging plant? (1 point)

(3) What, if any, is the opportunity cost associated with the use of the van ? (1 point)

(4) What is the after-tax operating cashflow each year on this project? ( 1 point)

(5) What is the net present value of this project? (1 point)

3. You own a rental building in the city and are interested in replacing the heating system for the building. You are faced with the following alternatives:

a. A solar heating system, which will cost \$ 12,000 to install, \$ 500 a year to run, and will last forever. (Assume that your building will too.)

b. A gas-heating system, which will cost \$ 5,000 to install, \$ 1000 a year to run, and will last 20 years.

c. An oil-heating system, which will cost \$ 3,500 to install, \$ 1200 a year to run, and will last 15 years.

If your opportunity cost is 10%, which of these three options is best for you? ( 5 points)

4a. You run a regression of monthly returns of XYZ corporation on the S&P 500 index and come up with the following output (All data was entered in percent):

Intercept of the regression = 0.0015

X-coefficient of the regression = 1.50

Standard error of X-coefficient = 0.25

R squared = 0.40

There are one million shares outstanding, and the current market price is \$ 30. The firm has \$ 30 million in debt outstanding. (The firm has a tax rate of 40%)

a. What would an investor in XYZ's stock require as a return, if the current 6-month T.Bill rate is 6%? ( 1 point)

b. What proportion of this firm's risk is diversifiable? ( 1 point)

c. Assume now that XYZ has three divisions, of equal size (in market value terms). It plans to divest itself of one of the divisions (with a beta of 1.0) for \$ 20 million in cash and acquire another firm (which has a beta of 2.0) for \$ 50 million (It will borrow \$ 30 million to complete this acquisition). What will the beta of XYZ be after this acquisition? ( 3 points)

CORPORATE FINANCE: MIDTERM EXAM

Fall 1990

1. You are the negotiator for the New York Mets and are trying to negotiate a contract with Darryl Strawberry. His agent has let you know that Mr. Strawberry is seeking a five year contract paying him \$ 4 million a year for five years. You make a counter-offer of \$ 3 million a year for the first five years and offer to continue to pay him \$ 1 million a year for the next five (so that the total nominal value of the contract is \$20 million).
 Years Mr. Strawberryís demand Your offer 1-5 \$4,000,000 \$ 3,000,000 6-10 ------ \$1,000,000

[The appropriate discount rate is 10%]

(a) How much would Mr. Strawberry lose in present value dollars if he accepted your offer?(2 points)

(b) How much more would you have to pay over the last five years (over and above the \$1 million that you have offered him) so as to allow him not to lose in present value terms? ( 2 points)

2. You are considering a capital budgeting proposal to make 'glow-in-the-dark' pacifiers for anxious first-time parents. You estimate that the equipment to make the pacifiers would cost you \$50,000 (which you can depreciate straight line over the lifetime of the project, which is ten years) and that you can sell 15,000 units a year at \$2 a unit. The cost of making each pacifier would be \$0.80 and the tax rate that you would face would be 40%. You also estimate that you will need to maintain an inventory at 25% of revenues for the period of the project and that you can salvage 80% of this working capital at the termination of the project. Finally, you will be setting up the equipment in your garage, which means you have to pay \$2000 a year to have your car garaged at a nearby private facility (Assume that you can deduct this cost for tax purposes). To estimate the discount rate for this project, you find that there are comparable firms being traded on the financial markets with the following betas:
 Company Debt-Equity ratio Tax rate Beta Nuk-Nuk 0.50 0.40 1.3 Gerber 1.00 0.50 1.5

You expect to finance this project entirely with equity and the current T.Bill rate is 8.5%.

(a) What is the appropriate discount rate to use for this project? (2 points)

(b) What is the after-tax operating cashflow each year for the lifetime of the project? (2 points)

(c) What is the NPV of this project? (2 point)

3. You are a financial analyst for a company that is considering a new project. If the project is accepted, it will use 40% of a storage facility that the company already owns but currently does not use fully. The project is expected to last ten years and the discount rate is 10%. You research the possibilities and find that the entire storage facility can be sold for \$100,000 and a smaller facility acquired for \$ 40,000. The book value of the existing facility is \$60,000 and both the existing and the new facilities (if it is acquired) would be depreciated straight line over ten years. The ordinary tax rate is 40% and the capital gains rate is 25%. What is the opportunity cost, if any, of using the storage capacity? ( 4 points)

4. You run a regression of stock returns on XYZ Corp. against market returns and come up with the following regression:

Rxyz = 0.0015 + 1.5 Rmkt

The company has, in market value terms, \$500 million of debt and \$500 million of equity. The company currently has two divisions. Division A, which has a market value of \$ 600 million, produces vacuum cleaners and you find five listed companies on the exchange which make only vacuum cleaners which have an average beta of 1.31 and an average debt equity ratio of 20%. Division B produces widgets and you cannot find any comparable companies (textbook examples notwithstanding).(Assume that all companies face a tax rate of 50%.)

(a) What is the beta for division B? ( 3 points)

(b) If the company divests itself of Division B and increases its debt-equity ratio to 2, what would the company's beta be? (3 points)

CORPORATE FINANCE: MIDTERM EXAM

Spring 1991

1.You have been hired by a company to manage its pension fund obligations. You estimate that the firm will have an obligation to pay out a lump sum of \$10 million in 10 years. The interest rate that you can make on your investments currently is 8%.

a. How much would you need to set aside an annuity each year for the next ten years to get to \$10 million ? ( 1 point)

b. Assume that you set aside the annuity in (a) each year for the next five years and that the interest rate then drops from 8% to 6% after year 5. How much more (or less) would you need to set aside each year over the remaining five years to have \$10 million at the end of year 10? (3 points)

2. You have been hired as a capital budgeting analyst by a sporting goods firm. It manufactures athletic shoes and has captured 10% of the overall shoe market (The total market is worth \$100 million a year). The fixed costs associated with manufacturing these shoes is \$2 million a year and variable costs are 40% of revenues. The company's tax rate is 40%.

The firm believes that it can increase its market share to 20% by investing \$10 million in a new distribution system (which can be depreciated over the system's life of 10 years to a salvage value of zero) and spending \$1 million a year in additional advertising. The company proposes to continue to maintain working capital at 10% of Annual Revenues. The discount rate to be used for this project is 8%.

a. What is the initial investment for this project? (1 point)

b. What is the annual operating cashflow from this project? (2 points)

c. What is the NPV of this project? (1 point)

d. How much would the firm's market share have to go up for you to be indifferent to taking or rejecting this project? ( 2 points)

3. Your company is considering producing a new product. You have a production facility that is currently used to only 50% of capacity and you plan to some of the excess capacity for the new product. The production facility cost \$50 million five years ago when it was built and is being depreciated straight line over 25 years. (In real dollars, assume that this cost will stay constant over time.)
 Product Line Capacity Used Growth Rate Revenues Fixed Costs Variable Costs Old Product 50% 5% p.a. 100 Mil 25 Mil 50 Mil/Yr New Product 30% 10% p.a. 80 Mil 20 Mil 44 Mil/Yr

The new product has a life of 10 years, the tax rate is 40% and the appropriate discount rate (real) is 10%.

a. If you take on this project, when would you run out of capacity? (1 point)

b. When you run out of capacity, what would you lose if you chose to cut back production (in present value after-tax dollars)? (You have to decide which product you are going to cut back production on) (2 points)

c. What would the opportunity cost (to be assigned to this new product) be if you chose to build a new facility when you run out of capacity instead of cutting back on production? (1 point)

4. You run a regression of XYZ stock's returns against the market returns over a five-year time period (using monthly data) and come up with the following output:

Intercept = .20%

Slope = 1.20

Your stock had an annualized standard deviation of returns of 40% whereas the market standard deviation was only 20%. The riskfree rate, on average, over the last five years has been 6% and it is currently at 7%. The annualized dividend per share currently is \$2.00 and the stock is currently selling for \$50 (There are 100,000 share outstanding)

a. Evaluate the performance of XYZ over the five-year time period of your analysis. Did it do better or worse than expected (using the CAPM)? If so, how much better or worse did it do than expected? (1 point)

b. What proportion of XYZ risk is diversifiable? (1 point)

c. What would you expect XYZ's stock price to be one year from today? (1 point)

d. XYZ currently has \$ 5 million in debt outstanding and the tax rate is 40%. XYZ is planning on selling one of its divisions for \$ 5 million (This division has an asset beta of 0.5). It will use the proceeds to pay \$3 million as dividends to its stockholders and the remaining \$2 million to repay debt. What will the beta be after the restructuring? (3 points)

CORPORATE FINANCE: MIDTERM EXAM

Fall 1992

1. You have been hired to run a pension fund for a major corporation. The firm currently has \$5 million in the fund, and expects to have cash inflows of \$2 million a year for the first five years followed by cash outflows of \$ 3 million a year for the next five years. Assume that interest rates are at 8%.

a. How much money will be left in the fund at the end of the tenth year? ( 4 points)

b. If you were required to pay a perpetuity after the tenth year (starting in year 11 and going through infinity) out of the balance left in the pension fund, how much could you afford to pay?

(1 point)

2. You are currently employed at a major investment bank and are making \$ 50,000/year (and expect to make that amount each year for the next five years). A friend comes to you with an idea for a project to make soundproof glass shields for cars to protect parents from whiny kids. You will have to quit your job, and the project will require an initial investment in equipment of \$350,000 (which can be depreciated straight line over five years to a salvage value of \$100,000). You expect to sell 10000 units at \$50/unit each year for the next five years. It will cost you \$20 per unit to manufacture and other fixed costs will amount to \$50,000/year. You own a house (which you are renting out right now for \$14,000/year), that you think you can use for this project. (You cannot depreciate this house if you rent it, but you can claim depreciation of \$10,000 a year if you take this project) In addition your tax rate is 40% and your discount rate is 10%.

a. What is the opportunity cost (if any) of using your house for this project? (1 point)

b. What is the opportunity cost (if any) of having to quit your job to take this project? (1 point)

c. What is the after-tax cashflow each year from this project? (1 point)

d. What is the NPV of this project? (1 point)

e. How many units would you have to sell to break even? (2 points)

3. You are trying to choose a new siding for your house. A salesman offers you two choices:

a. Wooden siding, which will last ten years, cost \$5000 to install and \$1000/year to maintain

b. Aluminium siding, which will last forever, cost \$15,000 to install and will have a lower maintentance cost per year

If your discount rate is 10%, how much your maintenance costs have to be for you to choose to go with aluminium siding? (4 points)

4. You have just done a regression of monthly stock returns (on XYZ corp.) on monthly market returns over the last five years and come up with the following regression:

RXYZ = 0.5% + 1.2 RM

The variance of the stock is 50% and the variance of the market is 20%. The current riskfree rate is 3% (It has come down 2% over the last year). The stock is currently selling for \$50, down \$4 over the last year, and has paid a dividend of \$2 during the last year and expects to pay a dividend of \$2.50 over the next year. The NYSE composite has gone down 5% over the last year, with a dividend yield of 3%.

a. What is the expected return on XYZ over the next year? (1 point)

b. What would you expect XYZ's price to be one year from today? ( 1point)

c. Evaluate the performance of XYZ over the last year. (2 points)

d. What proportion of the risk of XYZ Corporation is due to the market? ( 1 point)

CORPORATE FINANCE: MIDTERM EXAM

Fall 1993

1. Derrick Coleman, a forward for the New Jersey Nets, has been offered a seven-year, \$ 75 million contract, where he will be paid \$9 million a year for the next three years, and \$12 million a year for the following four years. The appropriate discount rate is 8%.

a. What is the present value of this contract? ( 2 points)

b. He is weighing an alternative offer from the Minnesota Timberwolves, where he will be paid \$8 million a year for the next seven years and an additional \$25 million at the end of the seventh year. What is the present value of this contract? (1 point)

c. What would the payment at the end of the seventh year need to be for Mr. Coleman to be indifferent between the two offers? (2 points)

2. You are analyzing a project that plans to invest \$20 million in a new theme park called "Bonehead Park" , based upon the infamous cartoon on MTV, Beavis and Butthead. The park will take two years to build and the expenditure will also be spread out across the two years.

Today: \$10 million

One year from now: \$5 million

Two years from now: \$5 million

Once the park is built, you expect to attract teenagers in record numbers, and have revenues of \$10 million a year for the next ten years (your assumed project life). The park will cost \$3 million a year to operate, and the depreciation will be \$1 million a year. You plan to build it on land that you already own, that you bought three years ago for \$1 million. If you do not take this project, you plan to lease the land out and make \$200,000 a year before taxes. At the end of the ten years, it is assumed that the park can be salvaged for book value. The tax rate is 40%, and the discount rate is 15%.

a. What is the initial investment (in present value terms)? (2 points)

b. What is the annual after-tax operating cashflow on this park? (1 point)

c. What is the NPV of the project? (1 point)

d. What would the NPV be, if, instead of stopping the project in the tenth year and salvaging, the project were assumed to continue for another ten years, with the same operating cashflows? (2 points)

3. You run your own business and spend \$2,000 a year on printing expenses, using an outside printing service. You estimate that it will cost you \$10,000 to buy your own printer, and \$500 a year to maintain this printer. If the printer life is ten years, and your discount rate is 10%, does it make sense to buy the printer? (Assume no inflation, and no taxes) (4 points)

4. You have just run a regression of weekly returns of EK Inc. against the S&P 500 over the last two years. You have misplaced some of the output and are trying to derive it from what you have.

a. You know the R squared of the regression is 0.48, and that your stock has a variance of 60%. The market variance is 20%. What is the beta of EK Inc.? (2 points)

b. You also remember that EK Inc. was not a very good investment during the period of the regression and that it did worse than expected (after adjusting for risk) by 0.01% a week for the two years of the regression. During this period, the average riskfree rate was 3.64%. What was the intercept on the regression? (2 points)

c. You are comparing EK Inc. to another firm called LMN Inc, which also has an R squared of 0.48. Will the two firms have the same beta? If not, why not? (1 point)

CORPORATE FINANCE: MIDTERM EXAM

Fall 1994

1. You are an investment advisor who has been approached by a client for help on his financial strategy. He has \$250,000 in savings in the bank. He is fifty five years old, and expects to work for ten more years, making \$100,000 a year. (He expects to make a return of 5% on his investments for the foreseeable future. You can ignore taxes)

a. Once he retires ten years from now, he would like to be able to withdraw \$80,000 a year for the following twenty five years (His actuary has told him he will live to be ninety years old.). How much would he need in the bank ten years from now to be able to do this? (1 point)

b. How much of his income would he need to save each year for the next ten years to be able to afford these planned withdrawals (\$80,000 a year) after year ten? (2 points)

c. Assume now that interest rates decline to 4% ten years from now. How much, if any, would he have to lower his annual withdrawal by, assuming that he still plans to withdraw cash each year for the following 25 years? (2 points)

2. You run a mail-order firm, selling upscale clothing. You are considering replacing your manual ordering system with a computerized system, to make your operations more efficient and to increase sales. (All the cash flows given below are in real terms.)

• The computerized system will cost \$10 million to instal, and \$500,000 to operate each year. It will replace a manual order system that costs \$1,500,000 to operate each year.
• The system is expected to last ten years, and have no salvage value at the end of the period.
• The computerized system is expected to increase annual revenues from \$5 million to \$8 million for the next ten years.
• The costs of goods sold is expected to remain at 50% of revenues.
• The tax rate is 40%.
• As a result of the computerized system, the firm will be able to cut its inventory from 50% of revenues to 25% of revenues immediately. There is no change expected in the other working capital components.

The real discount rate is 8%.

a. What is your expected cash flow at time=0? (1 point)

b. What is the expected incremental annual cash flow from computerizing the system? (3 points)

c. What is the net present value of this project? (1 point)

3. You have been asked to compare three alternative investments and make a recommendation.

• Project A has an initial investment of \$5 million, and after-tax cashflows of \$ 2.5 million a year for the next five years.
• Project B has no initial investment, has after-tax cash flows of \$ 1 million a year for the next ten years, and a salvage value of \$2 million (from working capital).
• Project C has an initial investment of \$10 million, another investment of \$5 million in ten years, and after-tax cashflows of \$ 2.5 million a year forever.

The discount rate is 10% for all three projects.

Which of the three projects would you pick? Why? (4 points)

4. You have run a regression of monthly returns on a stock against monthly returns on the S&P 500 index, and come up with the following output ñ

Rstock = 0.25% + 1.25 RMarket R2= 0.60

The current one-year treasury bill rate is 4.8%, the current ten-year bond rate is 7.25% and the current thirty-year bond rate is 8%. The firm has 10 million shares outstanding, selling for \$10 per share.

i. What is the expected return on this stock over the next year? (1 point)

ii. Would your expected return estimate change if the purpose was to get a discount rate to analyze a thirty-year capital budgeting project? (1 point)

iii. An analyst has estimated, correctly, that the stock did 4.2% better than expected, annually, during the period of the regression. Can you estimate the annualized riskfree rate that he used for his estimate? (2 points)

iv. The firm has a debt/equity ratio of 50%, and faces a tax rate of 40%. It is planning to issue \$50 million in new debt and acquire a new business for that amount, with the same risk level as the firm's existing business. What will the beta be after the acquisition? (2 points)

CORPORATE FINANCE

MID TERM EXAMINATION: Fall 1995

1. Mr. William Poirot has come to you for advice on his retirement planning. He is 45 years old, and has \$ 100,000 in his savings account. He also expects to receive an additional \$80,000, after taxes, in ten years, when he sells his house. He plans to work for 20 years more, and expects to save \$ 10,000 a year for the next 10 years, and \$ 15,000 a year for the following 10 years.

a. Assuming that he earns 5% on both his current and future savings, how much should he expect to have in savings, when he retires in 20 years? ( 2 points)

b. If Mr. Poirot plans to withdraw the money in equal annual installments over the 15 years following his retirement, how much can each withdrawal be? (Assume that the interest rate continues to be 5% after the twentieth year.) ( 1 point)

c. How would your answer to (a) change if interest rates are expected to rise to 6% after ten years? ( 2 points)

2. You watched a product demonstration for a wonder mop at a demonstration fair, and were so impressed that you paid \$ 50,000 for the rights to the product. You are now analysing whether you should start producing the wonder mops, and have collected the following information ñ

• The equipment needed to manufacture the mop will cost \$150,000, and it can be depreciated straight line over a 5-year life time to a salvage value of \$ 25,000.
• You will be using a building that you currently own, but rent out, as the facility to house the equipment. You will have to obviously evict the current tenants, who pay you \$ 15,000 a year in rent. This building is being depreciated straight line, and is yielding \$5,000 in depreciation each year.
• You expect to sell 5,000 mops a year at \$ 40 a mop. The raw materials and labor associated with producting each mop will be \$ 10.
• You expect to spend \$ 50,000 a year producing infomercials (30-minute TV spots to promote your product).
• You will need to produce and maintain an inventory, equal to three months of sales, to meet demand. (This will have to occur before you sell any units.)
• Your tax rate is 40% and you estimate your discount rate to be 12%.

a. Estimate the opportunity cost of the rental building that will be used for the facilities. (1 point)

b. Estimate the net present value of the project. ( 4 points)

3. You have been asked to analyse a capital budgeting project, where the initial investment is \$ 100,000, and the project is expected to generate \$ 30,000 in real pre-tax cash flow savings each year for the next 5 years. The inital investment is depreciable, straight line, over 5 years to a salvage value of zero. The tax rate is 30% and the nominal discount rate is 10%. If the net present value of this project is \$10,705, estimate the expected inflation rate. ( 4 points)

4a. You have just run a regression of monthly returns on MAD Inc against returns on the S&P 500, and arrived at the following result ñ

RMAD = ñ 0.05% + 1.20 RS&P

The regression has an R-squared of 22%. The current T.Bill rate is 5.5% and the current T.Bond rate is 6.5%. The riskfree rate during the period of the regression was 6%.. Answer the following questions relating to the regression ñ

a. Based upon the intercept, you can conclude that the stock did

A. 0.05% worse than expected on a monthly basis, during the regression.

B. 0.05% better than expected on a monthly basis during the period of the regression

C. 1.25% better than expected on a monthly basis during the period of the regression.

D. 1.25% worse than expected on a monthly basis during the period of the regression.

E. None of the above. (1 point)

b. You now realize that MAD Inc went through a major restructuring at the end of last month (which was the last month of your regression), and made the following changes ñ

• The firm sold off its magazine division, which had an unlevered beta of 0.6, for \$ 20 million.
• It borrowed an additional \$ 20 million, and bought back stock worth \$ 40 million.

After the sale of the division and the share repurchase, MAD Inc. had \$ 40 million in debt and \$ 120 million in equity outstanding.

If the firmís tax rate is 40%, re-estimate the beta, after these changes. (5 points)