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:

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


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%

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)


1. Initial public offerings are usually underpriced by investment bankers


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



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



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%.

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%

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)


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%.

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:

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%)


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%]

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%.

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%.)


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%.

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%.

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%.

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)


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%.

(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%.

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

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%.


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%.

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%.

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.


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 real discount rate is 8%.

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

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.



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.

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

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

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)