Case Study: Aladdin Games

Problem Statement: Ted Heinlen, Chairman and Chief Executive Officer of Aladdin Games, Inc., has convened his weekly staff meeting to hear more about a new board game that the company’s creative staff has developed. At their last meeting, the executives heard details of the game itself, called “Wall Street Invaders,” from its originators. The game excited their interest. Mr. Heinlen said then that, in his modest opinion, “‘Wall Street Invaders” has a perfect combination of office politics, insider trading, personal ambitions, back-stabbing, and greed. It has the kind of real-life nonviolence that should appeal to everyone. I just don’t see how it can pos- sibly miss.”

Everyone at the prior meeting agreed with the boss’ assessment. They now meet again, a week later, to begin analyzing the financial aspects of producing and marketing the game. Sam Yamoto, vice president of sales, asks Igor Vukonovich, his marketing specialist, to present the results of their marketing research. Igor presents the following: “The total annual market for board games of the type

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Capital Budgeting: Risk Analysis with Scenarios ❧ 443

of ‘Invaders’ varies somewhat from year to year about a mean value of 180,000 sets—that is for our competitors as well as for us. The statistical data on which this value is based also indicate that the actual demand can be treated as normally distributed about the mean value with a standard deviation of 18,000 sets/year. In other words, our forecasts have a standard deviation of plus-or-minus 10 percent.”

“Okay,” says Ted. “So what would be our share of the market with ‘Invaders’?” Igor continues, “The share of the total market that ‘Invaders’ might be expected to capture for us depends

very much on its price. The less we charge our distributors, the less they have to charge the retailers, so that the less the retailers in turn have to charge their customers, the more sets we can sell.”

“Sounds reasonable,” Ted interjects. “So what are the numbers?” Igor resumes, “Well, we’re not really sure yet what our wholesale price must be to recoup our costs. Our

marketing research indicates that we should sell ‘Invaders’ to our wholesalers for between $4.25 and $5.25 a set. Based on prices within this range, we expect that our share of the total market will vary with price as shown by Chart A.”

Chart A. Effect of Wholesale Price of “Wall Street Invaders” on Aladdin’s Share of the Total Market for This Type of Board Game

Wholesale฀Price,฀$/set

$5.25 Market฀Share

“Okay, that gives us some numbers for market share we can work with.” Ted says. “We’ll need to figure out what’s the best wholesale price to give us the maximum profit. But at least that’s one variable we have under our own control and don’t have to leave for fate to decide.”

Turning to Geraldine Murray, the company’s vice president for manufacturing, Ted then asks, “How does the cost picture look to you, Gerri?”

Ms. Murray reports, “Our production specialists have gone over the equipment needs and the processes we expect to use. We don’t have final figures yet, but at this point in time we’re guessing. Sorry, I mean we’re estimating that our variable costs for producing ‘Invaders’ would most likely be about $2.15 a set. However, they could go as low as $1.60 a set or as high as $2.35. We just can’t say exactly until we resolve some quality issues with Sam’s marketing people and have a better idea of volume.”

“And what about the fixed costs for production?” asks Mr. Heinlen. “Again, we don’t know for sure yet,” Ms. Murray responds. “But we can say with reasonable certainty that

fixed costs won’t be any less than $86,000 or more than $98,000. That should cover our initial, one-time investment in equipment for getting ‘Invaders’ into production and putting it into the hands of our wholesalers. In between those numbers? I’d say any number in between is equally likely.”

“Okay,” says Ted. “I think that gives us some figures to work with. Let’s come back next week with a financial analysis based on the numbers that Sam and Gerri have thrown out. Can we do that, Ralph?” Ted asks, turning to Ralph Zimmerman, his vice president for finance. “What sort of basis do you think would be right for doing a financial analysis?”

Ralph responds, “Well, I would say that our experience has been that board games of the type of ‘Invaders’ will be popular with the public and will sell well for a limited time—something, I would say, on the order of five years. I would say that we ought to use a five-year period for evaluating the dollar return we might make on whatever Gerri says it will cost and whatever Sam says we might get from our sales. We can depreciate the initial investment by straight-line depreciation to a salvage value of zero at the end of five years. I would say whatever special equipment we buy to produce ‘Invaders’ will be worthless by the end of five years.”

“What about taxes and our cost of capital?” Ted asks. Ralph responds, “Our incremental tax rate for whatever profits we might make on ‘Invaders’ will be 40

percent. And I would certainly add, in view of the other possibilities we have for investing our limited capital, that we ought to earn a return on whatever we spend on ‘Invaders’ of at least 13 percent or we shouldn’t invest

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444 ❧ Corporate Financial Analysis with Microsoft Excel ®

in it. I mean by that that our cost of capital to invest in ‘Invaders’ will be about 13 percent. I would say that we shouldn’t accept anything less than that. And, frankly, with all the other financial commitments we have on the table, I would say we shouldn’t run too high a risk for making anything less than 13 percent after taxes.”

“What about selling and other nonproduction costs?” Ted asks. Ralph notes, “These are currently running about 30 percent of our sales revenues. I don’t see any reason

they should be different for ‘Wall Street Invaders’.” “Okay, that says it for now,” says Ted. “Let’s wrap a report around this and see what comes out. See you all again—same time, next week—and we’ll decide then whether or not to go ahead with this one.”

Solution: Figures 14-6 and 14-7 show the spreadsheet solution for Aladdin’s most probable outcome. The data values are entered in Rows 2 to 15.

Figure฀14-6

Spreadsheet Solution for Most Probable Scenario and Optimum Wholesale Price

1 ALADDIN GAMES

2 Total annual market forecast, sets

Selling price/Market share information 3 Standard forecast error, sets

Market Share 4 Minimum facility investment

Price,

Price^2 Data Forecast 5 Maximum facility investment

6 Equipment life, years

7 Salvage value

8 Depreciation method

St. Line

9 Minimum variable cost, $/set

10 Most probable variable cost, $/set

Average = 11 Maximum variable cost, $/set

LINEST OUTPUT

13 Non-production costs, % of sales

0.169% #N/A

14 Cost of capital and reinvest rate

2 #N/A

15 Tax rate

0.00001 #N/A 16 Most probable scenario

17 0 1 2 3 4 5 18 Total annual market, sets

19 Wholesale price, sets

$4.66 $4.66 20 Market share, percent

15.81% 15.81% 15.81% 21 Sets sold

28,462 28,462 28,462 22 Sales receipts, $

24 Unit variable cost, $/set

25 Total variable cost, $

$61,193 $61,193 $61,193 26 Gross profit

$71,451 $71,451 $71,451 27 Nonproduction expenses, 30% of sales

$39,793 $39,793 $39,793 28 Before-tax cash flow

$31,657 $31,657 $31,657 29 Annual depreciation

$18,400 $18,400 $18,400 30 Taxable income

$5,303 $5,303 $5,303 32 After-tax cash flow

33 Net present value, NPV

$694 34 Internal rate of return, IRR

13.31% 35 Modified internal rate of return, MIRR

13.17% 36 Break-even point, years

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Capital Budgeting: Risk Analysis with Scenarios ❧ 445

Figure฀14-7

Output of LINEST Command and Forecast Values

LM 2 Selling price/Market share information 3 Price,

Market Share

Fcst

4 $/set Price^2

R O 0.15%

T 0.05% S

10 LINEST OUTPUT

Average = 0.00%

R O –0.10%

PRICE, $/SET

2 #N/A

#N/A

Most Probable Scenario: Under the most probable conditions, the total market is 180,000 sets each year (i.e., the mean value entered in Cell B2), and the unit variable cost of production is $2.15/set (i.e., the most probable value in Cell B10).

For the facility investment, there is no most probable value because the possible values vary on a uniform distribution between the minimum and maximum values of $86,000 and $98,000. Any value in that range is equally likely. Therefore, as a proxy for the most probable value, we use the average of $92,000, since it is equally likely that the value is more than or less than the mean of a uniform distribution.

We will proceed by the following steps to complete the most probable scenario.

Total Annual Market, sets: In Cell C18, enter =B2. In Cell D18, enter =C18 and copy to E18:G18. Wholesale Price, per set: In Cell C19, enter 4.5 and format it as currency with two decimal places to give

$4.50. This is a trial value. We will change it later to find the value that maximizes the net present value at the end of five years. In cell D19, enter =C19 and copy it to Cells E19:G19.

Market Share: The market share will depend on the wholesale price. Therefore, we must link the value in Cell C20 for market share to the value in Cell C19 for wholesale price. To satisfy this need, we will use the market research results to develop a regression equation that relates the values for market share in Cells F5:F9 to the wholesale prices in Cells D5:D9.

We must first select an appropriate regression equation to relate market share to wholesale price. You should be able to do this by using the procedure covered in Chapter 3 to select an appropriate regression equation to relate annual sales to the year. You should be able to show that a linear regression equation does not provide a valid model, and that a quadratic regression equation is the most suitable type for relating Aladdin’s market share to wholesale price.

Return now to the spreadsheet of Figure 14-6 where Excel’s LINEST command has been used to determine the parameters of the quadratic equation. Supply values for the squares of the wholesale price by entering =D5^2 in Cell E5 and copy the entry to Cells E5:E9. Next, drag the mouse to highlight Cells D11:F15 and type =LINEST(F5:F9,D5:E9,1,1). Enter the command by pressing the Control, Shift, and Enter keys. This gives the results shown in Cells D11:F15 of Figure 14-6. To demonstrate the model’s validity, you can calculate the errors and create the chart shown in Columns H to M of Figure 14-7. (Columns H to M are not shown in Figure 14-6.)

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446 ❧ ® Corporate Financial Analysis with Microsoft Excel

The important cells of Figure 14-6 for this problem are the coefficients of the quadratic equation in Cells D11:F11. They indicate that the equation relating market share to wholesale price is

Y =− . 1 86029 0 96571 + . X − . 0 11429 X 2

where Y is the market share and X is the wholesale price in $/set. We will now use our quadratic equation to link the market share in Cell C20 to the wholesale price in C19. To do this, enter =F11+E11*C19+D11*C19^2 in Cell C20, then enter =C20 in D20 and copy it to Cells E20:G20 to repeat the values calculated in Cell C20.

Sets Sold: The number of sets sold each year is the product of the total annual market times the company’s market share. In Cell C21, enter =C18*C20 and copy it to D21:G21. Sales Receipts: The sales receipts each year is the product of the number of set sold times the selling price. In Cell C22, enter =C21*C19 and copy it to D22:G22. Investment: Because any value between the minimum and maximum values in Cells B4 and B5 is equally likely, their average is used as a proxy for the most probable investment. (Note the term “proxy.” The average is used for a uniform distribution because the probabilities are equal that the future value will be greater or less than the average, and no value in the range is more probable than any other.) Therefore, in Cell B23 enter =AVERAGE(B4:B5).

Unit Variable Cost: The most probable unit variable cost is the value $2.15 in Cell B10. Therefore, in cell C24 enter =B10, then enter =C24 in D24 and copy to E24:G24. Total Variable Cost: The total variable cost is the product of the number of units sold times the unit variable cost. Enter =C21*C24 in Cell C25 and copy the entry to Cells D25:G25. (When we do scenario analysis later, we will want the change in Cell C25 to be reproduced in Cells D25:G25.)

Gross Profit: Gross profit is the difference between sales revenues and the cost of goods sold (COGS). Enter =C22-C25 in Cell C26 and copy the entry to Cells D26:G26. Nonproduction Expenses: Nonproduction costs are given as 30 percent of sales in Cell B13. Therefore, to calculate nonproduction expenses, enter =$B$13*C22 in Cell C27 and copy the entry to Cells D27:G27.

Before-Tax Cash Flow: For Year 0, the before-tax cash flow is the outflow for the investment. Therefore, enter =-B23 in Cell B28. For other years, the before-tax cash flow is calculated by subtracting the nonproductive expenses from the gross profit. Therefore, enter =C26-C27 in Cell C28 and copy the entry to Cells D28:G28.

Depreciation: The investment is depreciated by the straight-line method over a period of five years to zero salvage value. You can calculate annual depreciation by entering =$B$23/$B$6 in Cell C29 and copying it to Cells D29:G29. Or use Excel’s function for straight-line depreciation. The syntax for Excel’s function for straight-line depreciation is =SLN(cost,salvage value,life). To use the SLN function, enter =SLN($B$23,$B$7,$B$6) in Cell C29 and copy the entry to Cells D29:G29.

It is worth noting that Excel also provides function commands for calculating depreciation by declining balance and sum of the years methods. Or it might be appropriate to use MACRS.

Taxable Income: The taxable income is calculated as the income (i.e., sales revenues) minus deductible expenses (i.e., total variable cost, nonproductive expenses, and depreciation). To include depreciation in what has already been calculated, enter =C28-C29 in Cell C30 and copy the entry to Cells D30:G30.

Tax: Tax equals the taxable income multiplied by the tax rate, which is given as 40 percent in Cell B15. Enter =C30*$B$15 in Cell C31 and copy the entry to Cells D31:G31. After-Tax Cash Flow: The after-tax cash flow for Year 0 is the outflow for the investment. Enter =B28 or =-B23 in Cell B32. For Years 1 to 5, the after-tax cash flow equals the before-tax cash flow minus the tax. Enter =C28-C31 in Cell C32 and copy the entry to Cells D32:G32.

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Capital Budgeting: Risk Analysis with Scenarios ❧ 447

Net Present Value: Use Excel’s function command NPV to calculate the net present values of the investment at the ends of Years 1 to 5. The syntax for this command is NPV(rate,range of values).

Enter =NPV($B$14,$C$32:C32)+$B$32 in Cell C33 and copy the entry to Cells D33:G33. When this entry is executed in Cell C33, it discounts the after-tax cash flow in Cell C32 back to the present at the rate given in Cell B14 (13%) and adds the value in Cell B32. Note that the value in Cell B32 (i.e., the cash outflow for the investment) is not included in the range of values to be discounted to the present because it is already a present value.

When the entry in Cell C33 is copied to Cells D33:G33, the range of values discounted back to the present increases by one year for each column. The entry in Cell G33 will be = NPV($B$14, $C$32:G32)+$B$32 and evaluates the investment’s net present value at the end of the fifth year.

Internal Rate of Return: Use Excel’s function command IRR to calculate the internal rate of return at the ends of Years 1 to 5. The IRR function returns the internal rate of return for a series of periodic cash flows, at least one of which is negative (here, the initial investment) and one or more are positive (here, the year end cash inflows). The syntax for this command is IRR(range of values,guess). If the guess value is omitted, Excel provides the default value of 0.10 (i.e., 10%). Excel uses the guess value as the starting point from which to do a series of calculations that ends when the calculated value of IRR converges to a solution with an accuracy of 0.00001 percent. The number of iterations is limited to 20. The calculations may fail to converge if the guess value is too far away from the solution. In this case, Excel returns the error message #NUM!. If this happens, try again with a different guess value that is closer to the solution.

Enter =IRR($B$32:C32) in Cell C34 and copy the entry to Cells D34:G34. If the error message #NUM! occurs, edit the cell entry by changing the guess value. Recall that in the calculation of an investment’s IRR, future cash inflows are assumed to be reinvested for the life of the project at the same rate as the IRR. This assumption is not likely to be satisfied for projects with very high or very low IRRs. If future cash inflows are reinvested at some other rate, the actual average rate of return will be different from the calculated value of IRR. Because of this problem, the IRR for an investment can be misleading. (See the discussion in Chapter 2 for details.)

Modified Internal Rate of Return: Use Excel’s MIRR function to return the modified internal rate of return for a series of periodic cash flows. MIRR differs from IRR in that it considers both the cost of capital for the investment and the interest received on any reinvestment of cash generated by the investment. The syntax for Excel’s MIRR function is MIRR(range of values,finance rate (or cost of capital),reinvest rate). Unless there is reason to use another value, the reinvest rate is assumed to equal the finance rate (i.e., the cost of capital for the investment).

Enter =MIRR($B$32:C32,$B$14,$B$14) in Cell C35 and copy the entry to Cells D35:G35. Break-Even Point: By definition, the break-even point is the time for an investment’s net present value to equal zero. To develop an expression for calculating the break-even point in Cell C36, note that the net present value is initially less than zero (because the investment in Year 0 is a cash outflow) and increases each year thereafter because the after-tax cash flows are positive.

To detect when the break-even point has been reached, we need to recognize when the net present value first becomes positive. If, for example, the net present value is negative at the ends of Years 1 and 2 and positive at the end of Year 3, we know that the break-even point is somewhere between the ends of Years 2 and 3. We can use linear interpolation between the NPVs at the ends of Years 2 and

3 to determine how far beyond the second year the net present value is zero. The development of an expression for identifying the years to break even was given in Chapter 12.

The following entry in Cell B36 is used to determine the break-even point for Aladdin’s investment:

=IF(D33>=0,C17-C33/(D33-C33),IF(E33>=0,D17-D33/(E33-D33), IF(F33>=0,E17-E33/(F33-E33),IF(G33>=0,F17-F33/(G33-F33),”Failed’)))).

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448 ❧ Corporate Financial Analysis with Microsoft Excel ®

This expression checks across the row of NPV values until it reaches a positive NPV at a year n. It then backs up one year to year n-1 and adds a fraction of a year equal to the quotient: -NPV n–1 /(NPV n–1 -NPV n ). (Note that the value of NPV n–1 is negative, so that using the minus sign before the quotient makes it positive.) If the value of NPV in the last column is still negative, the investment fails to break even over the duration of the analysis period.

Optimizing the Wholesale Selling Price: Recall that the value of $4.50/set we entered in Cell B19 was a trial value. We now want to determine the optimum value—that is, we want to find the value for the wholesale price that will give the greatest net present value. We will use Excel’s Solver tool to do this.

The Solver tool is accessed by clicking the Solver button on the Tools menu on the standard toolbar. Figure 14-8 shows the dialog box for the Solver tool with the entries for finding the optimum wholesale price the wholesale price the company should select for maximizing the investment’s net present value at the end of the five-year analysis period. Cell G33, the net present value at the end of five years, is therefore the target cell. We want to maximize its value by changing Cell C19, the wholesale price.

Solver identifies the optimum wholesale price as $4.66/set, which is slightly more than the trial value of $4.50/set. Under the most probable conditions, with the wholesale price set at $4.66/set, the net present value of the investment at the end of five years is $694, its internal rate of return is 13.31 percent, its modified internal rate of return is 13.17 percent, and its break-even point is 4.95 years. Although the analysis shows that the project is profitable under the most probable conditions, there should be some concern that the future might

be less favorable and the project would fail. Figure฀14-8

Solver Parameters Dialog Box with Entries for Finding Optimum Wholesale Price

Case Study: Aladdin Games