New Facilities

New Facilities

New facilities such as factories for manufacturing goods, office buildings, equipment for serving custom- ers, and management information systems are major investments. They involve large expenditures of capital with major impacts on cash flows and profit.

Case Study: Albertus Enterprises, Inc. Albertus Enterprises, Inc. is a large manufacturing firm. It plans to invest $800,000 in buying and installing new

factory equipment that will increase its production capacity. The company expects that the new equipment will increase its net annual income, after subtracting operating costs and other expenses from its revenues, by $350,000.

Albertus expects to pay for and have the equipment installed and operating during the first quarter of the year. As a result, the equipment will qualify for a full year’s depreciation for each year of its use. The company expects that the equipment will remain in use for five years, at the end of which time the company expects to sell the equipment for one-tenth of its original value. The company will pay tax on its capital gain if the equip- ment is sold at more than its book value at the time of sale, and the company will receive a reduction in its corporate tax if the equipment is sold at less than its book value at the time of sale.

Under IRS rules, new factory equipment has a class life of seven years. For tax purposes, the annual depreciation must be computed according to the Modified Accelerated Cost Recovery System (MACRS). (IRS Publication 534: Depreciation) Use the appropriate schedule in Figure 11-2 in Chapter 11 for the percentages of the capital investment to be depreciated each year. Note that because the equipment will be acquired in the first quarter of the year, Albertus will use values in the first column for the mid-quarter convention in the table.

The company will use a discount rate (i.e., cost of capital or “hurdle rate”) of 12.5 percent to evaluate the investment. It expects that any reinvestment of future cash flows would be at the same rate. Albertus pays a combined federal-state-local tax rate of 40 percent, based on its taxable income.

1. What is the investment’s net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR) at the end of five years? 2. What is the discounted payback period (or break-even point) for the capital investment? 3. Prepare a chart that shows how the net present value (NPV) of the capital investment changes with time, from the time of the investment to the end of five years. Identify the break-even point on the chart.

(Continued)

Capital Budgeting: Applications ❧ 403

4. Prepare a second chart that shows how the IRR and MIRR change with time, from the time of the investment to the end of five years. Identify the break-even point on the chart. 5. If the CFO of Albertus wishes to break even by the end of 3.5 years, how much would the annual year- end benefits from the investment have to be? 6. Examine the sensitivity of the investment’s NPV, IRR, and MIRR at the end of five years and the payback period to the annual benefits from the equipment. Use annual benefits from $200,000 to $500,000 in increments of $50,000. Prepare charts that show how the NPV, MIRR, and payback period vary with the annual benefits. 7. Would you recommend that Albertus invest in the new equipment? Justify your recommendation.

Solution: 1 and 2: Figure 13-1 is a spreadsheet solution for parts 1 and 2. Figure฀13-1

Capital Budgeting Analysis for Albertus Enterprises, Inc.

1 ALBERTUS ENTERPRISES, INC.

2 Equipment cost, including installation

3 Salvage value, as percent of cost

4 Market value, end of Year 5

5 Discount and reinvest rates

6 Tax rate

7 Year 0 1 2 3 4 5

8 Depreciation and Book Value Schedule

9 Depreciation base

10 Annual depreciation, per MACRS

10.93% 8.75% 11 Annual depreciation, dollars

87,440 $ 70,000 12 Year-end book value

13 Year-End Cash Flow Analysis

14 Regular income

350,000 $ 350,000 16 Taxable regular income

15 Annual year-end benefit

262,560 $ 280,000 17 Tax on regular income

105,024 $ 112,000 18 ATCF for regular income

19 Sale of equipment

20 Income from sale of equipment $ 80,000 21 Capital gain(loss)

$ (68,640) 22 Capital gain tax (benefit)

$ (27,456) 23 ATCF from sale of equipment

24 After-Tax Cash Flow Analysis

244,976 $ 345,456 26 Net present value

25 After-tax cash flow (ACTF)

27 Internal rate of return (IRR)

28 Modified internal rate of return (MIRR)

29 Discounted break-even point, years

Key Cell Entries

B29: =IF(D26>=0,C7 –C26/(D26–C26),IF(E26>=0,D7–D26/(E26–D26),IF(F26>=0,E7–E26/(F26–E26), IF(G26>=0,F7–F26/(G26–F26),“Failed”))))

C11: =$B$9*C10, copy to D11:G11

G21: =B4–G12

C12: =B9–C11

G22: =G21*B6

D12: =C12 –D11, copy to E12:G12

G23: =G20 –G22

C16: =C15–C11, copy to D16:G16

C25: =C18+C23, copy to D25:G25

C17: =C16*$B$6, copy to D17:G17 C26: =NPV($B$5,$C$25:C25)+$B$25, copy to D26:G26 C18: =C15–C17, copy to D18:G18

C27: =IRR($B$25:C25,–0.5), copy to D27:G27 C28: =MIRR($B$25:C25,$B$5,$B$5), copy to D28:G28

404 ❧ Corporate Financial Analysis with Microsoft Excel ®

Data values are shown in italics in the upper left corner of Figure 13-1. The market value of the equipment at the end of five years is calculated by the entry =B2*B3 in Cell B4. Annual depreciation and book value are calculated in rows 9 to 12. Values for the annual percentage depreciation for MACRS are entered as data in Cell C10:G10. Annual depreciation is calculated by entering =C10*$B$9 in Cell C11 and copying to D11:G11. Year-end book values are calculated by entering =B9-C11 in Cell C12, entering =C12-D11 in Cell D12, and copying the last entry to E12:G12.

Year-end after-tax cash flows from the regular income are calculated in Rows 15 to 18. In this example, the annual year-end benefits are the same each year, and we will examine the sensitivity of the results to the value. Therefore, enter the data value 350,000 in Cell C15, enter =$C$15 in Cell D15, and copy the entry in D15 to E15:G15. When a new value is entered in C15, this will result in the same value in all cells in the Range C15:G15.

The taxable regular income is calculated by entering =C15-C11 in Cell C16 and copying to D16:G16. The tax on the regular income is calculated by entering =C16*$B$6 in Cell C17 and copying to D17:G17. The after-tax cash flow for the regular income is calculated by entering =C15-C17 in Cell C18 and copying to D18:G18.

The series of calculations for the after-tax cash flow from the sale of the equipment at the end of year 5 is in Rows 20 to 23. The income from the sale of the equipment is calculated by entering =B4 in Cell G20. The capital gain(loss), which equals the difference between the book value at the time of sale minus the sale price, is calculated by entering =G20-G12 or =B4-G12 in Cell G21. Note that this is a loss because the book value is greater than the sale price. This creates a tax benefit, which is calculated by entering =G21*B6 in Cell G22. The after-tax cash flow from the sale of the equipment is calculated by entering =G20-G22 in Cell G23.

The series of calculations for the payoffs of the investment is in Rows 25 to 29. The after-tax cash flows from the investment are calculated by entering =-B9 in Cell B25, =C18 in Cell C25, copying the entry in C25 to D25:F25, and entering =G18+G23 in Cell G25.

The net present value at year 0 is entered as =B25 in Cell B26. The net present values for years 1 to 5 are calculated by entering =NPV($B$5,$C$25:C25)+$B$25 in Cell C26 and copying to D26:G26.

The internal rate of return at year 0 is entered as =-1 in Cell B27 and formatted as a percent. The internal rates of return for years 1 to 5 are calculated by entering =IRR($B$25:C25,-0.5) in Cell C27 and copying to D27:G27. (Note that the value -0.5 is a guess value. The guess should be changed to a better guess whenever the IRR command fails to converge to a value and returns an error message.)

The modified internal rate of return at year 0 is entered as =-1 in Cell B28 and formatted as a percent. The modified internal rates of return for years 1 to 5 are calculated by entering =MIRR($B$25:C25,$B$5,$B5) in Cell C28 and copying to D28:G28.

The discounted break-even or payback period is calculated in Cell B29 by the entry =IF(D26>=0,C7-C26/(D26-C26),IF(E26>=0,D7-D26/(E26-D26),

IF(F26>=0,E7-E26/(F26-E26),IF(G26>=0,F7-F26/(G26-F26),”Failed”))))

The results show that the investment’s net present value at the end of five years is $204,426, its internal rate of return is 22.34 percent, its modified internal rate of return is 17.74 percent, and its discounted break-even or payback period is 3.92 years.

3 and 4. The upper chart of Figure 13-2 shows that the curve for the net present value crosses the line for NPV = 0 at 3.92 years. The lower chart of Figure 13-2 shows that the curves for the internal rate of return and the modified internal rate of return reach a value of 12.5 percent, which is the cost of capital and the reinvestment rate, at 3.92 years. (Recall that breaking even requires the rate of return to equal the discount rate of money, which is equivalent to requiring the NPV to equal zero.)

(Continued)

Capital Budgeting: Applications ❧ 405

5. Figure 13-3 shows the results for increasing the annual year-end benefits in order to break even by the end of 3.5 years. This result is obtained by using Excel’s Solver tool with the settings shown in Figure 13-4. The results show that it would be necessary to increase the annual benefits to $389,444 in order for the investment to break even by the end of 3.5 years.

Figure฀13-2

NPV, IRR, and MIRR Charts for Albertus Enterprises, Inc.

ALBERTUS ENTERPRISES, INC. (NPV, IRR, AND MIRR CHARTS)

Break-even point (NPV = 0) is 3.92 years. $– $(200,000)

ALUE V $(400,000)

$(600,000) NET PRESENT

YEAR

30% Break-even point (IRR = MIRR = 12.5%) is 3.92 years.

IRR or MIRR –50% –60% –70% –80% –90%

YEAR

(Continued)

406 ❧ Corporate Financial Analysis with Microsoft Excel ®

Figure฀13-3

Results for Breaking Even by the End of 3.5 Years

1 ALBERTUS ENTERPRISES, INC.

2 Equipment cost, including installation

3 Salvage value, as percent of cost

4 Market value, end of Year 5

5 Discount and reinvest rates

6 Tax rate

7 Year 0 1 2 3 4 5

8 Depreciation and Book Value Schedule

9 Depreciation base

10.93% 8.75% 11 Annual depreciation, dollars

10 Annual depreciation, per MACRS

87,440 $ 70,000 12 Year-end book value

13 Year-End Cash Flow Analysis

14 Regular income

15 Annual year-end benefit

16 Taxable regular income

302,004 $ 319,444 17 Tax on regular income

120,802 $ 127,778 18 ATCF for regular income

19 Sale of equipment

20 Income from sale of equipment

$ 80,000 21 Capital gain(loss)

New values for the annual year-end benefits

$ (68,640) 22 Capital gain tax (benefit)

for investment to break even after 3.5 years

$ (27,456) 23 ATCF from sale of equipment

24 After-Tax Cash Flow Analysis

268,643 $ 369,123 26 Net present value

25 After-tax cash flow (ACTF)

83,856 $ 288,693 27 Internal rate of return (IRR)

17.57% 26.21% 28 Modified internal rate of return (MIRR)

15.34% 19.65% 29 Discounted break-even point, years

Figure฀13-4

Solver Settings for Figure 13-3

6. Figure 13-5 shows the results of a sensitivity analysis for annual year-end benefits ranging from $200,000 to $500,000 in increments of $50,000. (The analysis is in Columns I to Q of the spreadsheet of Figure 13-1.)

(Continued)

Capital Budgeting: Applications ❧ 407

Figure฀13-5

Sensitivity of the NPV, MIRR, and Break-Even Point to Annual Year-End Benefits

1 ALBERTUS ENTERPRISES, INC. 2 Sensitivity Analysis

3 Annual year-end benefit

200,000 $ 250,000 $ 300,000 $ 350,000 $ 400,000 $ 450,000 $ 500,000 4 NPV at end of 5 years

97,609 $ 204,426 $ 311,243 $ 418,061 $ 524,878 5 IRR at end of 5 years

36.63% 6 MIRR at end of 5 years

24.44% 7 Break-even point, years

Minimum annual benefits

for breaking even by the end of year 5 is $255,000.

15 $200,000 16 17 $100,000 18 T END OF 5 19 $– 20 NPV A $(100,000) 21 22 $(200,000) 23 $200,000

24 ANNUAL YEAR-END BENEFIT

14% 37 38 12% 39 MIRR A 10% 40 8% 41 $200,000

43 ANNUAL YEAR-END BENEFIT

49 4.5 50 51 4.0 52 53 3.5 54 O BREAK EVEN T 55 3.0 56 57 YEARS

62 ANNUAL YEAR-END BENEFIT

(Continued)

408 ❧ Corporate Financial Analysis with Microsoft Excel ®

You can use a one-variable input table to create the table at the top of Figure 13-5. To do this, enter the labels in Cells I3:I7. Make the following entries in Cells J3:J7 to connect cells in the main program with the sensitivity analysis portion of the spreadsheet shown at the top of Figure 13-5:

Cell J3: =C15 (This transfers the annual year-end benefit in Cell C15 to J3. Be sure the entries in Cells D15:G15 will vary when the value in Cell C15 is changed. One way to do this is to enter =C15 in Cell D15 and copy the entry to E15:G15.)

Cell J4: =G26 Cell J5: =G27 Cell J6: =G28 Cell J7: =B29 As these entries are made in Cells J3:J7, the cells will show the current values in C15, G26, G27,

G28, and B29. To hide these values so they won’t be confusing with the rest of the table, use the ;;; custom format (i.e., three semicolons). Figure 13-5 also shows the width of column J decreased. (You can also avoid showing the values in Cells J3:J7 by hiding column J.)

Enter the series of annual benefits in Cells K3:Q3. One convenient way to do this is to enter 200,000 and 250,000 in Cells K3:L3, center and format them as currency, select Cells K3:L3 with the mouse, grab the dark “move” box at the lower right corner of Cell L3, and drag to M3:Q3.

Highlight the range J3:Q7 and click on Table on the Data menu to access the Table dialog box shown in Figure 13-6. Enter C15 as the Row input cell and click OK or press Enter. The result is the set of values in Cells K4:Q7 of Figure 13-5. Format these to complete the table.

Figure฀13-6

Entries in the Table Dialog Box for Sensitivity Analysis

Plot the results to create the charts shown below the table in Figure 13-5. Note that the curve for years to break even does not extend to annual benefits less than $300,000, which is the lowest value for which the investment breaks even within the five-year analysis period. (If you really want to project the curve to lower values, you will have to generate additional values to do so. Or, you can recognize from the chart for NPV vs. Annual Benefit that the curve of the bottom chart would project to five years at annual benefits of approximately $255,000.)

7. Albertus should invest in the new equipment because its net present value is greater than zero and its rate of return is greater than the discount rate (or cost of capital). The equipment’s payback period is

3.92 years. The investment will more than break even unless the annual year-end benefits drop below approximately $255,000 from the expected value of $350,000.

Capital Budgeting: Applications ❧ 409

Case Study: The Dreyfuss Insurance Company The Dreyfuss Insurance Company is considering the installation of a local area network (LAN) that will serve

15 employees at its Seattle headquarters. Initial (startup) costs are as follows:

$60,000 Hardware฀acquisition Computers,฀network฀routers,฀servers,฀and฀wiring ฀ ฀20,000

Software฀acquisition Programming,฀licenses,฀and฀antivirus฀protection ฀ ฀10,000

Delivery฀and฀installation

Four-day฀project

฀ ฀5,000 Training Week฀of฀on-site฀training฀and฀computer฀tutorials ฀ ฀15,000

Support฀and฀maintenance Initial฀payment฀for฀the฀first฀year฀of฀a฀four-year฀maintenance฀contract฀ Continuing year-end annual costs are as follows: $12,000

Support฀and฀maintenance Three฀annual฀payments฀for฀the฀four-year฀maintenance฀contract,฀ made฀at฀the฀ends฀of฀the฀first,฀second,฀and฀third฀years

Year-end annual benefits are as follows: $50,000

Direct฀labor

Elimination฀of฀one฀worker

฀ ฀20,000 Support฀labor Savings฀from฀reducing฀secretarial฀and฀clerical฀support ฀ ฀5,000

Materials

Reduced฀cost฀of฀paper฀and฀photocopies

Depreciation: MACRS, 5-years life, first-quarter convention. IRS regulations provide that software included in the purchase price of a computer system can be added to the basis of the computer system and depreciated. (The depreciable base of the company’s investment is the sum of the costs of hardware, software, delivery, installation, and training.)

The company expects the system’s useful life will be four years, at which point the market value of the hardware and software will be zero and will be discarded. The risk-adjusted cost of capital is 12 percent, and the reinvest rate is 13 percent. Tax rate is 40 percent for regular income and 30 percent for capital gain or loss.

In your answers to the following, format dollar values to the nearest whole dollar, format percentages for IRR and MIRR with two decimal places, and format the number of years to break even with two decimal places.

1. Calculate the values for NPV, IRR, and MIRR at the ends of years 1, 2, 3, and 4. 2. Calculate the number of years to break even. 3. The company’s CFO is concerned with the effects of changes in the risk-adjusted cost of capital on the

net present value of the investment at the end of four years and the years to break even. Prepare a one- variable input table that shows the effect of risk-adjusted costs of capital from 10 to 15 percent on the net present value at the end of four years and the years to break even.

4. Use your results from part 3 to prepare charts showing the effect of the risk-adjusted cost of capital on the net present value at the end of four years and the years to break even. Values on the X-axis of the charts should range from 10 to 15 percent with major increments of 1 percent and minor increments of

0.5 percent. Values on the Y-axis of the NPV chart should have major increments of $5,000 and minor increments of $2,500. Values on Y-axis of the Years to Break Even chart should have major increments of 0.10 year and minor increments of 0.05 year.

(Continued)

410 ❧ ® Corporate Financial Analysis with Microsoft Excel

Solution: Figures 13-7 and 13-8 show the solution for this case study. Note that the annual payments for the maintenance and support contract are operating costs. These are incremental cash outflows that are tax deduct- ible expenses. The initial “up-front” payment of $15,000 is part of the company’s incremental cash outflow at time zero, and the other three payments of $12,000 each are part of the company’s incremental cash outflow at the ends of years 1, 2, and 3.

Figure฀13-7

Spreadsheet Solution for Dreyfuss Insurance Company Case Study

1 DREYFUSS INSURANCE COMPANY

2 Initial costs

3 Hardware acquisition

4 Software acquisition

5 Delivery and installation

7 Total cost (depreciable base)

8 Support and maintenance

Initial “up-front” payment

9 Initial cash outflow

10 Depreciation of hardware and software

11 MACRS, 5-year life, 1st quarter 12 Salvage value at end of third year

13 Continuing costs of operation

14 Support and maintenance

Paid at ends of 1st, 2nd, and 3rd years.\

15 Year-end benefits

16 Eliminate one worker

17 Reduce secretarial and clerical support

18 Reduce cost of paper and photocopies

20 Financial rates

21 Risk-adjusted cost of capital

22 Reinvest rate

23 Tax rate on regular income

24 Tax rate for capital gains or losses

25 Analysis (3-year period) 26 Year

27 Investment

28 Year-end benefits

75,000 $ 75,000 29 Support and maintenance

30 Before-tax cash flow

15.60% 11.01% 32 Annual depreciation

31 MACRS depreciation rate

14,820 $ 10,460 33 Taxable regular income

48,180 $ 64,541 34 Tax on regular income

19,272 $ 25,816 35 Capital loss (equals BV of investment)

$ 11,771 36 Tax benefit of capital loss

37 After-tax cash flow

10,760 $ 44,261 39 Internal rate of return

38 Net present value

18.1% 31.08% 40 Modified internal rate of return

16.1% 22.83% 41 Year to break even (i.e., for NPV = 0)

(Continued)

Capital Budgeting: Applications ❧ 411

Figure฀13-8

Sensitivity Analysis for Dreyfuss Insurance Company Case Study

42 DREYFUSS INSURANCE COMPANY

Cost of

NPV at End

Years to

Capital

of Four

Break Even

62 T END OF FOUR $40,000 63 64 NPV A

68 RISK-ADJUSTED COST OF CAPITAL

79 T O BREAK EVEN 80

87 RISK-ADJUSTED COST OF CAPITAL

412 ❧ Corporate Financial Analysis with Microsoft Excel ®