Chap009 (1)

by Brad Jordan and Joe SmoliraVersion 7.0

Chapter 9In these spreadsheets, you will learn how to use the following Excel functions:

The following conventions are used in these spreadsheets:

1) Given data in blue2) Calculations in red

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.To install these, click on the Office button then "Excel Options," "Add-Ins" and select"Go." Check "Analysis ToolPak" and "Solver Add-In," then click "OK."

Ross, Westerfield, and Jordan's Spreadsheet MasterEssentials of Corporate Finance, 7th edition

Naming cells

SLN

VDB

Solver

Scenario Manager

One-way Data Table

In these spreadsheets, you will learn how to use the following Excel functions:

The following conventions are used in these spreadsheets:

NOTE: Some functions used in these spreadsheets may require that the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.

Chapter 9 - Section 3Pro Forma Financial Statements and Cash Flows

Cans sold per year: 50,000 Price per can: $ 4.00 Variable cost per can: $ 2.50 Required return: 20%Fixed costs per year: $ 12,000 Manufacturing equipment: $ 90,000 Project life (years): 3 Initial net working capital: $ 20,000 Tax rate: 34%

RWJ Excel Tip

With these numbers, we can prepare the pro forma income statement, which will be:

Sales $ 200,000 Variable costs 125,000 Fixed costs 12,000 Depreciation 30,000 EBIT $ 33,000 Taxes (34%) 11,220 Net income $ 21,780

RWJ Excel Tip

Because capital budgeting requires numerous repetitive cash flows, it is an ideal application for Excel. When doing a capital budgeting problem, as in most Excel uses, you should do few or no calculations on your own, but rather let Excel do the calculations for you. We will begin with the shark attractant project. We have the following projections for the project:

In a problem with a number of different variables, it can be advantageous to name the cells. Click on the input cell for the number of cans sold per year, and look to the left of the Formula bar in the name bar and you will see the name "Units." We entered the name in the name bar to name the input in this cell. Whenever we want to use the input from this cell later, we can type in the name of the variable instead of referencing the cell. For example, if you look at the sales calculation below, you will see that the formula we used in this cell is Units * Price_per_unit. When naming cells, you should keep the names short but understandable. In addition, Excel does not allow spaces in the variable name, so we used an underscore instead of the space in Price_per_unit.

To calculate the depreciation each year for straight-line depreciation, we can divide the initial cost by the life of the equipment, or we can use the built-in Excel function SLN as we have done here. The SLN inputs we used in this case looks like this:

Average Accounting ReturnTo calculate the AAR, we need the average investment in assets each year. The total investment each year will be:

Year0 1 2

Net working capital $ 20,000 $ 20,000 $ 20,000 Net fixed assets 90,000 60,000 30,000 Total investment $ 110,000 $ 80,000 $ 50,000

So, the average assets are:

Average assets: $ 65,000

Now, we can calculate the operating cash flow each year, which will be:

EBIT $ 33,000 + Depreciation 30,000 - Taxes 11,220 Operating cash flow $ 51,780

So, the total cash flow for each year of the project will be:

Year0 1 2

Operating cash flow $ 51,780 $ 51,780 Changes in NWC $ (20,000)Capital spending (90,000)Total project cash flow $ (110,000) $ 51,780 $ 51,780

Given these cash flows, we can now calculate the NPV, IRR, and AAR of the project, which are:

The inputs are Cost, which is the initial cost, Salvage, which is the salvage value, and Life, which is the life of the asset. In general, we usually find it easier just to divide the cost by the life of the equipment in the cell rather than use this particular function, but it is available if you prefer.

NPV $ 10,647.69 IRR 25.76%AAR 33.51%

Because capital budgeting requires numerous repetitive cash flows, it is an ideal application for Excel. When doing a capital budgeting problem, as in most Excel uses, you should do few or no calculations on your own, but rather let Excel do the calculations for you. We will begin with the shark attractant project. We have the following

In a problem with a number of different variables, it can be advantageous to name the cells. Click on the input cell for the number of cans sold per year, and look to the left of the Formula bar in the name bar and you will see the name "Units." We entered the name in the name bar to name the input in this cell. Whenever we want to use the input from this cell later, we can type in the name of the variable instead of referencing the cell. For example, if you look at the sales calculation below, you will see that the formula we used in this cell is Units * Price_per_unit. When naming cells, you should keep the names short but understandable. In addition, Excel does not allow spaces in the variable name, so we used an underscore instead of the space in Price_per_unit.

To calculate the depreciation each year for straight-line depreciation, we can divide the initial cost by the life of the equipment, or we can use the built-in Excel function

Average Accounting ReturnTo calculate the AAR, we need the average investment in assets each year. The total investment each year will be:

Year3

$ 20,000 - $ 20,000

Year3

$ 51,780 $ 20,000

$ 71,780

Given these cash flows, we can now calculate the NPV, IRR, and AAR of the project, which are:

The inputs are Cost, which is the initial cost, Salvage, which is the salvage value, and Life, which is the life of the asset. In general, we usually find it easier just to divide the cost by the life of the equipment in the cell rather than use this particular function, but it is available if you prefer.

Chapter 9 - Section4More about Project Cash Flow

In practice, many assets are depreciated on a MACRS schedule for tax purposes. The three-, five-, and seven-year MACRS schedules are:

Property ClassYear 3-year 5- year 7-year

1 33.33% 20.00% 14.29%2 44.45% 32.00% 24.49%3 14.81% 19.20% 17.49%4 7.41% 11.52% 12.49%5 11.52% 8.93%6 5.76% 8.92%7 8.93%8 4.46%

For example, suppose we have an asset that falls in the five-year MACRS classification and the initial cost is:

Initial cost: $ 12,000

The depreciation for each year will be:

Year Depreciation1 20.00% $ 2,400.00 2 32.00% 3,840.00 3 19.20% 2,304.00 4 11.52% 1,382.40 5 11.52% 1,382.40 6 5.76% 691.20

100.00% $ 12,000.00

To find the book value of the asset, we subtract depreciation each year from the beginning book value. The book value of this asset each year will be:

Year Depreciation1 $ 12,000 $ 2,400.00 $ 9,600.00 2 9,600.00 3,840.00 5,760.00 3 5,760.00 2,304.00 3,456.00 4 3,456.00 1,382.40 2,073.60

MACRS percentage

Beginningbook value

Endingbook value

5 2,073.60 1,382.40 691.20 6 691.20 691.20 -

Pretax salvage value: $ 3,000 Tax rate: 34%

The aftertax salvage value, and therefore net cash flow from selling the asset at the end of the project (Year 6 in this case) will be:

Pretax salvage value: $ 3,000.00 Taxes on sale: (1,020.00)Aftertax salvage value: $ 1,980.00

The Majestic Mulch and Compost Company (MMCC)

Year 1 2 3 4Units sales 3,000 5,000 6,000 6,500 Price $ 120 $ 120 $ 120 $ 110 NWC to start $ 20,000 NWC % of sales 15%Variable cost $ 60 Fixed costs $ 25,000 Equipment $ 800,000 MACRS 14.29% 24.49% 17.49% 12.49%

20%Tax rate 34%Required return 15%

We will calculate the operating cash flow first, which we can calculate as net income plus depreciation. So, the pro forma income statements eachyear will be:

Pro Forma Income StatementsYear 1 2 3 4Revenues $ 360,000.00 $ 600,000.00 $ 720,000.00 $ 715,000.00 Variable costs 180,000.00 300,000.00 360,000.00 390,000.00 Fixed costs 25,000.00 25,000.00 25,000.00 25,000.00 Depreciation 114,320.00 195,920.00 139,920.00 99,920.00

When the asset is sold, taxes will be paid if the asset is sold for more than book value, or a tax rebate will be given if the asset is sold for less than book value. An easy way to calculate the taxes on the sale of the asset is (Book value - Market value)(Tax rate). Suppose the pretax salvage value of the asset and the tax rate are:

The MMCC capital budgeting problem is a more in-depth analysis. As before, we want to put all inputs in a separate cell and have Excel handle all the calculations. While we are entering the data in rows for each variable, we could enter the data in columns as well. The input information for the MMCC line of power mulching tools is:

Pretax salvage value

EBIT $ 40,680.00 $ 79,080.00 $ 195,080.00 $ 200,080.00 Taxes (34%) 13,831.20 26,887.20 66,327.20 68,027.20 Net income $ 26,848.80 $ 52,192.80 $ 128,752.80 $ 132,052.80 + Depreciation 114,320.00 195,920.00 139,920.00 99,920.00 OCF $ 141,168.80 $ 248,112.80 $ 268,672.80 $ 231,972.80

RWJ Excel Tip

Year 0 1 2 3Initial NWC $ (20,000) $ 20,000.00 $ 54,000.00 $ 90,000.00 Ending NWC 54,000.00 90,000.00 108,000.00 NWC cash flow $ (20,000) $ (34,000.00) $ (36,000.00) $ (18,000.00)

To find the aftertax salvage value, we need to calculate the taxes. We get:


So, the total cash flows for each year of the project are:

Project Cash Flows Year 0 1 2 3OCF $ 141,168.80 $ 248,112.80 $ 268,672.80 Change in NWC $ (20,000) (34,000.00) (36,000.00) (18,000.00)Capital spending $ (800,000)Total cash flow $ (820,000) $ 107,168.80 $ 212,112.80 $ 250,672.80

Finally, the NPV and IRR of the project are:

NPV: $ 65,484.83 IRR: 17.24%

A Note on MACRS Depreciation

Notice that in the income statements, we were careful to use absolute references in the variable costs, fixed costs, depreciation, and tax cells. That way, once we entered all the equations to calculate the net income during the first year, we simple copied and pasted the year 1 net income column to the rest of the years.

Next, we will calculate the change in net working capital. One way to do this is to calculate the difference between the beginning and ending net working capital. We also need to remember that the net working capital at the end of the project will be zero. So, the net working capital requirements each year are:

Equipment Life (Years)Year 3 5 7

1 33.33% 20.00% 14.29%2 44.44% 32.00% 24.49%3 16.67% 19.20% 17.49%4 5.56% 12.60% 12.49%5 10.80% 9.54%6 5.40% 8.68%7 8.68%8 4.34%9

101112131415161718192021

RWJ Excel Tip

There are actually six MACRS schedules, three-, five-, seven-, 10-, 15-, and 20-year schedules. The MACRS schedule is calculated using the depreciation according to the double declining balance method, and switching to straight-line depreciation when it is more advantageous. The three-, five-, seven-, and 10-year schedules use a factor of 2 (200%) when calculating the double declining balance depreciation amount, while the 15- and 20-year schedules use a factor of 1.5 (150%). Excel has a function, VDB, which can be used to construct a MACRS table. Below, we have constructed a MACRS table with all six schedules.

To construct the MACRS table, we used the variable declining balance (VDB) function. Constructing the MACRS table is tricky because of the half-year convention. Below you will see what we entered for the second year of the three-year MACRS schedule.

Cost is the cost of the equipment. In this case, we entered one in order to get the answers as a percentage rather than a dollar amount. Salvage is the salvage value, which is zero. Life is the life of the asset. Since we have a table here, we entered the column as a floating input and locked the row. This allows us to copy and paste the formula further down the table was well as across. The Start_period is the starting period for which we want to calculate the depreciation. With the half-year convention, we used the year and subtracted 1/2. To calculate the End_period, we used the MIN function. This function will return the lesser of the next year minus one-half, or the life of the asset. In most years we could have taken the next year minus one-half, but this would not work for the last year. Notice that this MIN function will not work for the first year since there is no prior year. So, for the first year, we eliminated the MIN function. Finally, the Factor is not shown on the picture above since Excel scrolls through the inputs in this case. We used a factor of two for the three-, five-, seven-, and 10-year schedules and a factor of 1.5 for the 15- and 20-year schedules.

Finally, note that the MACRS schedule is slightly different from the table presented in the textbook for the 6th and 8th year of the seven-year MACRS schedule. The reason is that the IRS publishes a MACRS schedule, which is the schedule we used in the textbook. However, you are allowed to calculate the schedule on your own based on the rules outlined by the IRS. If you do so, you will get the table above, not the table in the textbook (or the table published by the IRS!). In the future, we will use the table in the textbook for our calculations.

In practice, many assets are depreciated on a MACRS schedule for tax purposes. The three-, five-, and seven-year MACRS schedules are:

For example, suppose we have an asset that falls in the five-year MACRS classification and the initial cost is:

To find the book value of the asset, we subtract depreciation each year from the beginning book value. The book value of this asset each year will be:

The aftertax salvage value, and therefore net cash flow from selling the asset at the end of the project (Year 6 in this case) will be:

5 6 7 8 6,000 5,000 4,000 3,000 $ 110 $ 110 $ 110 $ 110

8.93% 8.92% 8.93% 4.46%

We will calculate the operating cash flow first, which we can calculate as net income plus depreciation. So, the pro forma income statements each

Pro Forma Income Statements5 6 7 8

$ 660,000.00 $ 550,000.00 $ 440,000.00 $ 330,000.00 360,000.00 300,000.00 240,000.00 180,000.00 25,000.00 25,000.00 25,000.00 25,000.00 71,440.00 71,360.00 71,440.00 35,680.00

When the asset is sold, taxes will be paid if the asset is sold for more than book value, or a tax rebate will be given if the asset is sold for less than book value. An easy way to calculate the taxes on the sale of the asset is (Book value - Market value)(Tax rate). Suppose the pretax salvage value of the asset and the tax rate are:

The MMCC capital budgeting problem is a more in-depth analysis. As before, we want to put all inputs in a separate cell and have Excel handle all the calculations. While we are entering the data in rows for each variable, we could enter the data in columns as well. The input information for the MMCC line of power mulching tools is:

$ 203,560.00 $ 153,640.00 $ 103,560.00 $ 89,320.00 69,210.40 52,237.60 35,210.40 30,368.80 $ 134,349.60 $ 101,402.40 $ 68,349.60 $ 58,951.20 71,440.00 71,360.00 71,440.00 35,680.00 $ 205,789.60 $ 172,762.40 $ 139,789.60 $ 94,631.20

4 5 6 7 8 $ 108,000.00 $ 107,250.00 $ 99,000.00 $ 82,500.00 $ 66,000.00 107,250.00 99,000.00 82,500.00 66,000.00 - $ 750.00 $ 8,250.00 $ 16,500.00 $ 16,500.00 $ 66,000.00

Project Cash Flows 4 5 6 7 8

$ 231,972.80 $ 205,789.60 $ 172,762.40 $ 139,789.60 $ 94,631.20 750.00 8,250.00 16,500.00 16,500.00 66,000.00

105,600.00 $ 232,722.80 $ 214,039.60 $ 189,262.40 $ 156,289.60 $ 266,231.20

Notice that in the income statements, we were careful to use absolute references in the variable costs, fixed costs, depreciation, and tax cells. That way, once we entered all the equations to calculate the net income during the first year, we simple copied and pasted the year 1 net income column to the rest of the years.

Next, we will calculate the change in net working capital. One way to do this is to calculate the difference between the beginning and ending net working capital. We also need to remember that the net working capital at the end of the project will be zero. So, the net working capital requirements each year are:

Equipment Life (Years)10 15 20

10.00% 5.00% 3.75%18.00% 9.50% 7.22%14.40% 8.55% 6.68%11.52% 7.69% 6.18%

9.22% 6.93% 5.71%7.37% 6.23% 5.28%6.55% 5.90% 4.89%6.55% 5.90% 4.58%6.55% 5.90% 4.46%6.55% 5.90% 4.46%3.28% 5.90% 4.46%

5.90% 4.46%5.90% 4.46%5.90% 4.46%5.90% 4.46%2.95% 4.46%

4.46%4.46%4.46%4.46%2.23%

There are actually six MACRS schedules, three-, five-, seven-, 10-, 15-, and 20-year schedules. The MACRS schedule is calculated using the depreciation according to the double declining balance method, and switching to straight-line depreciation when it is more advantageous. The three-, five-, seven-, and 10-year schedules use a factor of 2 (200%) when calculating the double declining balance depreciation amount, while the 15- and 20-year schedules use a factor of 1.5 (150%). Excel has a function, VDB, which can be used to construct a MACRS table. Below, we have constructed a MACRS table with all six schedules.

To construct the MACRS table, we used the variable declining balance (VDB) function. Constructing the MACRS table is tricky because of the half-year convention. Below you will see what we entered for the second year of the three-year MACRS schedule.

Cost is the cost of the equipment. In this case, we entered one in order to get the answers as a percentage rather than a dollar amount. Salvage is the salvage value, which is zero. Life is the life of the asset. Since we have a table here, we entered the column as a floating input and locked the row. This allows us to copy and paste the formula further down the table was well as across. The Start_period is the starting period for which we want to calculate the depreciation. With the half-year convention, we used the year and subtracted 1/2. To calculate the End_period, we used the MIN function. This function will return the lesser of the next year minus one-half, or the life of the asset. In most years we could have taken the next year minus one-half, but this would not work for the last year. Notice that this MIN function will not work for the first year since there is no prior year. So, for the first year, we eliminated the MIN function. Finally, the Factor is not shown on the picture above since Excel scrolls through the inputs in this case. We used a factor of two for the three-, five-, seven-, and 10-year schedules and a factor of 1.5 for the 15- and 20-year schedules.

Finally, note that the MACRS schedule is slightly different from the table presented in the textbook for the 6th and 8th year of the seven-year MACRS schedule. The reason is that the IRS publishes a MACRS schedule, which is the schedule we used in the textbook. However, you are allowed to calculate the schedule on your own based on the rules outlined by the IRS. If you do so, you will get the table above, not the table in the textbook (or the table published by the IRS!). In the future, we will use the table in the

Chapter 9 - Section 6Scenario and Other What-If Analyses

Scenario Analysis

Base caseUnit sales: 6,000 Price per unit $ 80 Variable costs per unit: $ 60 Fixed costs per year: $ 50,000

Initial cost: $ 200,000 Project life (years): 5 Required return: 12%Tax rate: 34%

Base Case Income StatementSales $ 480,000 Variable costs 360,000 Fixed costs 50,000 Depreciation 40,000 EBIT $ 30,000 Taxes (34%) 10,200 Net income $ 19,800

OCF $ 59,800

NPV $ 15,566 IRR 15.10%

To calculate the best case and worst case, we will use Scenario Manager, which is described below.

Scenario analysis is used to determine the range of possible outcomes for a project. Typically, the base case, best case, and worst case values are calculated when doing scenario analysis. Because of the repetitive nature of the calculations, spreadsheets are an excellent tool for doing the analysis. Consider the values presented in the example in the textbook:

With these values, we need to calculate the base case, best case, and worst case NPVs and IRRs. First, we want to calculate the NPV and IRR with the base case projections, which are:

Notice, in this case we calculated the NPV and IRR using the PV function and RATE function rather than the NPV and IRR functions. When the cash flows are the same for each year, we find this calculation easier.

RWJ Excel Tip

Scenario Manager is a powerful tool that allows you to evaluate different scenarios and is useful in cases such as this. To use Scenario Manager, we first need to select the cells that we will be changing, in this case cells D9 through D12. Next, go to the Data tab, click What-If Analysis, Scenario Manager. This will bring up a box that looks like this:

When you click on Add, another box comes up that will allow you to enter the scenario name. After entering the name, hit Add and another box will come up that looks like this:

Notice two things about this box. First, the values are changed to the best case values. This is because the image was captured after we had changed the values. Second, instead of cell names, i.e. D9, the variable in the cell comes up because we named each input cell, as well as the NPV and IRR cells. After we entered the values for the best case, we simply clicked Add, then added the worst case scenario. When the values for both scenarios are entered, click OK. This brings us to another box with the scenario names which we have already added.

Sensitivity Analysis

Fixed costs NPV $ 25,000 $ 75,044 $ 30,000 $ 63,149 $ 35,000 $ 51,253 $ 40,000 $ 39,357 $ 45,000 $ 27,461 $ 50,000 $ 15,566 $ 55,000 $ 3,670

Now that all the scenarios are entered, we can click on Summary, which brings up the final box. This box allows us to save the results in a separate spreadsheet. We entered cells D32 (NPV) and D33 (IRR) as the final results we wanted Scenario Manager to calculate, then clicked OK. The results are shown on the next tab.

In contrast to scenario analysis, sensitivity analysis holds all variables except one constant. This allows us to see how changes in one variable affects the NPV of a project. In this case, we will perform sensitivity analysis using fixed costs, although all other variables could be similarly examined. Using Excel, sensitivity analysis is most easily completed using a one-way data table. Below, you will see a table with the NPV for different levels of fixed costs:

$ 60,000 $ (8,226) $ 65,000 $ (20,122) $ 70,000 $ (32,017) $ 75,000 $ (43,913)

Graphically, the relationship between fixed costs and NPV looks like this:

RWJ Excel Tip

As you can see, there is a negative relationship between fixed costs and project NPV. We would expect this: As costs increase, the value of the project should decrease.

To set up a one-way data table, we need to first enter the inputs we want to use in the calculations in a column (or row). Since we have used a column here, one cell to the right and one cell above where the input values begin, we need to make the cell equal to the final value we want the data table to calculate, or in this case, the NPV. Notice that in our data table, this cell is C109. However, to make the data table look better, we have hidden this row. To unhide this row, select both rows 108 and 110, right click, and then select "Unhide." This first step is to highlight the entire column with the numbers we want used in the calculation, as well as the final calculation cell at the top of the adjacent column. Next, select the "Data" tab, then "What-If Analysis," and "Data Table." Finally, enter the original cell that contains the variable we want to use to calculate the values in the data table, which is cell D12 for fixed costs.

$25,000

$30,000

$35,000

$40,000

$45,000

$50,000

$55,000

$60,000

$65,000

$70,000

$75,000

$(60,000)

$(40,000)

$(20,000)

$-

$20,000

$40,000

$60,000

$80,000

$100,000

Sensitivity Analysis for Fixed Costs

Fixed Costs

Net

Pre

sent

Val

ue

Price per Unit

Uni

ts S

old

$ 70 $ 75 $ 80 5,000 $ (150,975.04) $ (91,496.24) $ (32,017.43) 5,200 $ (146,216.74) $ (84,358.78) $ (22,500.82) 5,400 $ (141,458.43) $ (77,221.32) $ (12,984.21) 5,600 $ (136,700.13) $ (70,083.87) $ (3,467.60) 5,800 $ (131,941.83) $ (62,946.41) $ 6,049.01 6,000 $ (127,183.52) $ (55,808.95) $ 15,565.62 6,200 $ (122,425.22) $ (48,671.50) $ 25,082.23 6,400 $ (117,666.91) $ (41,534.04) $ 34,598.84 6,600 $ (112,908.61) $ (34,396.58) $ 44,115.44 6,800 $ (108,150.30) $ (27,259.12) $ 53,632.05 7,000 $ (103,392.00) $ (20,121.67) $ 63,148.66

Units sales NPV-30% 4,200 $ (70,083.87)-20% 4,800 $ (41,534.04)-10% 5,400 $ (12,984.21)0% 6,000 $ 15,565.62

10% 6,600 $ 44,115.44 20% 7,200 $ 72,665.27 30% 7,800 $ 101,215.10

We should note that when you create a data table, you can change the input cells in which you entered the new values to analyze, but you cannot change the size or layout of the data table.

Of course, in our sensitivity analysis, we could be interested in how the NPV changes when two input variables change. Price and quantity sold are two variables that would seem to be related since a higher cost would likely result in fewer units sold. In this case, we can use a two-way data table to compute the NPV for changes in both of these variables. (Two-way data tables were introduced in Chapter 5.) The sensitivity analysis for price and units sold looks like this:

As you can see, when the price drops below $80, the project has a negative NPV for all units sold examined, while the units sold is not as important to the NPV for the range we examined in this table.

In the end, we are ultimately concerned with how sensitive the NPV is to changes in the inputs to the project. One way we can examine this is to determine how sensitive the NPV is to the same percentage change in the inputs. Below, we have constructed one-way data tables for each of the inputs to our project that we believe will vary. Notice that we have the base case values as inputs in these tables. The reason is that if we reference the original cells (D9 to D12), the calculation of the ranges will create a loop.

% Change from Base Case

NPV-30% $ 42.00 $ 272,514.06 -20% $ 48.00 $ 186,864.58 -10% $ 54.00 $ 101,215.10 0% $ 60.00 $ 15,565.62

10% $ 66.00 $ (70,083.87)20% $ 72.00 $ (155,733.35)30% $ 78.00 $ (241,382.83)


Variable cost per unit

To compare changes in each of the variables, we will graph the NPV for each of the sensitivity tables. Since the columns we wish to graph are separated, to select the four NPV columns, hold down the CTRL and ALT keys, then use the cursor to select the four columns. The sensitivity of the NPV to percentage changes in the base case values looks like this:

As you can see, the line with the steepest slope is the price per unit, followed closely the variable cost per unit. Since the NPV is most sensitive to changes in these two variables, we should concentrate our efforts in determining whether or not our estimates for these two variables are accurate.

-30% -20% -10% 0% 10% 20% 30%

$(400,000.00)

$(300,000.00)

$(200,000.00)

$(100,000.00)

$-

$100,000.00

$200,000.00

$300,000.00

$400,000.00

Sensitivity of NPV to Changes in Inputs

Unit sales

Price per unit


Fixed costs

Percentage Change from Base Case Value

Net

Pre

sent

Val

ue

To calculate the best case and worst case, we will use Scenario Manager, which is described below.

Scenario analysis is used to determine the range of possible outcomes for a project. Typically, the base case, best case, and worst case values are calculated when doing scenario analysis. Because of the repetitive nature of the calculations, spreadsheets are an excellent tool for doing the analysis. Consider the values presented in the

With these values, we need to calculate the base case, best case, and worst case NPVs and IRRs. First, we want to calculate the NPV and IRR with the base case projections,

Notice, in this case we calculated the NPV and IRR using the PV function and RATE function rather than the NPV and IRR functions. When the cash flows are the same for

Scenario Manager is a powerful tool that allows you to evaluate different scenarios and is useful in cases such as this. To use Scenario Manager, we first need to select the cells that we will be changing, in this case cells D9 through D12. Next, go to the Data tab, click What-If Analysis, Scenario Manager. This will bring up a box that looks like

When you click on Add, another box comes up that will allow you to enter the scenario name. After entering the name, hit Add and another box will come up that looks like

Notice two things about this box. First, the values are changed to the best case values. This is because the image was captured after we had changed the values. Second, instead of cell names, i.e. D9, the variable in the cell comes up because we named each input cell, as well as the NPV and IRR cells. After we entered the values for the best case, we simply clicked Add, then added the worst case scenario. When the values for both scenarios are entered, click OK. This brings us to another box with the scenario

Now that all the scenarios are entered, we can click on Summary, which brings up the final box. This box allows us to save the results in a separate spreadsheet. We entered cells D32 (NPV) and D33 (IRR) as the final results we wanted Scenario Manager to calculate, then clicked OK. The results are shown on the next tab.

In contrast to scenario analysis, sensitivity analysis holds all variables except one constant. This allows us to see how changes in one variable affects the NPV of a project. In this case, we will perform sensitivity analysis using fixed costs, although all other variables could be similarly examined. Using Excel, sensitivity analysis is most easily completed using a one-way data table. Below, you will see a table with the NPV for different levels of fixed costs:

Graphically, the relationship between fixed costs and NPV looks like this:

As you can see, there is a negative relationship between fixed costs and project NPV. We would expect this: As costs increase, the value of the project

To set up a one-way data table, we need to first enter the inputs we want to use in the calculations in a column (or row). Since we have used a column here, one cell to the right and one cell above where the input values begin, we need to make the cell equal to the final value we want the data table to calculate, or in this case, the NPV. Notice that in our data table, this cell is C109. However, to make the data table look better, we have hidden this row. To unhide this row, select both rows 108 and 110, right click, and then select "Unhide." This first step is to highlight the entire column with the numbers we want used in the calculation, as well as the final calculation cell at the top of the adjacent column. Next, select the "Data" tab, then "What-If Analysis," and "Data Table." Finally, enter the original cell that contains the variable we want to use to

$25,000

$30,000

$35,000

$40,000

$45,000

$50,000

$55,000

$60,000

$65,000

$70,000

$75,000

$(60,000)

$(40,000)

$(20,000)

$-

$20,000

$40,000

$60,000

$80,000

$100,000

Sensitivity Analysis for Fixed Costs

Fixed Costs

Net

Pre

sent

Val

ue

Price per Unit $ 85 $ 90 $ 95 $ 100 $ 27,461.38 $ 86,940.19 $ 146,418.99 $ 205,897.80 $ 39,357.14 $ 101,215.10 $ 163,073.06 $ 224,931.02 $ 51,252.90 $ 115,490.01 $ 179,727.13 $ 243,964.24 $ 63,148.66 $ 129,764.93 $ 196,381.19 $ 262,997.46 $ 75,044.42 $ 144,039.84 $ 213,035.26 $ 282,030.67 $ 86,940.19 $ 158,314.75 $ 229,689.32 $ 301,063.89 $ 98,835.95 $ 172,589.67 $ 246,343.39 $ 320,097.11 $ 110,731.71 $ 186,864.58 $ 262,997.46 $ 339,130.33 $ 122,627.47 $ 201,139.50 $ 279,651.52 $ 358,163.55 $ 134,523.23 $ 215,414.41 $ 296,305.59 $ 377,196.77 $ 146,418.99 $ 229,689.32 $ 312,959.65 $ 396,229.98

Price per unit NPV-30% $ 56.00 $ (327,032.31)-20% $ 64.00 $ (212,833.00)-10% $ 72.00 $ (98,633.69)0% $ 80.00 $ 15,565.62

10% $ 88.00 $ 129,764.93 20% $ 96.00 $ 243,964.24 30% $ 104.00 $ 358,163.55

We should note that when you create a data table, you can change the input cells in which you entered the new values to analyze, but you cannot change the size or layout

Of course, in our sensitivity analysis, we could be interested in how the NPV changes when two input variables change. Price and quantity sold are two variables that would seem to be related since a higher cost would likely result in fewer units sold. In this case, we can use a two-way data table to compute the NPV for changes in both of these variables. (Two-way data tables were introduced in Chapter 5.) The sensitivity analysis for price and units sold looks

As you can see, when the price drops below $80, the project has a negative NPV for all units sold examined, while the units sold is not as important to the

In the end, we are ultimately concerned with how sensitive the NPV is to changes in the inputs to the project. One way we can examine this is to determine how sensitive the NPV is to the same percentage change in the inputs. Below, we have constructed one-way data tables for each of the inputs to our project that we believe will vary. Notice that we have the base case values as inputs in these tables. The reason is that if we reference the original


NPV-30% $ 35,000.00 $ 51,252.90 -20% $ 40,000.00 $ 39,357.14 -10% $ 45,000.00 $ 27,461.38 0% $ 50,000.00 $ 15,565.62

10% $ 55,000.00 $ 3,669.86 20% $ 60,000.00 $ (8,225.91)30% $ 65,000.00 $ (20,121.67)


Fixed costs per year

To compare changes in each of the variables, we will graph the NPV for each of the sensitivity tables. Since the columns we wish to graph are separated, to select the four NPV columns, hold down the CTRL and ALT keys, then use the cursor to select the four columns. The sensitivity of the NPV to percentage changes in the base case values

As you can see, the line with the steepest slope is the price per unit, followed closely the variable cost per unit. Since the NPV is most sensitive to changes in these two variables, we should concentrate our efforts in determining whether or not our estimates for these two variables are accurate.

-30% -20% -10% 0% 10% 20% 30%

$(400,000.00)

$(300,000.00)

$(200,000.00)

$(100,000.00)

$-

$100,000.00

$200,000.00

$300,000.00

$400,000.00

Sensitivity of NPV to Changes in Inputs

Unit sales

Price per unit


Fixed costs

Percentage Change from Base Case Value

Net

Pre

sent

Val

ue

Scenario SummaryCurrent Values: Best Case Worst Case

Changing Cells:Unit_sales 6,000 6,500 5,500 Price $ 80 $ 85 $ 75 Variable_cost_per_unit $ 60 $ 58 $ 62 Fixed_costs $ 50,000 $ 45,000 $ 55,000

Result Cells:NPV $ 15,566 $ 159,504 $ (111,719)IRR 15.10% 40.88% -14.40%

Notes: Current Values column represents values of changing cells at thetime the Scenario Summary Report was created. Changing cells for eachscenario are highlighted in gray.

Chapter 9Setting a Bid Price

Setting a Bid Price

Equipment $ 3,300,000 Pretax salvage value $ 75,000 Units per year 125,000 Price per unit $ 25.00 VC as a percentage of sales 45%Fixed costs $ 425,000 MACRS Year 1 33.33%MACRS Year 2 44.44%MACRS Year 3 14.82%MACRS Year 4 7.41%Immediate NWC $ 80,000 Tax rate 35%Required return 10%

Pro Forma Income StatementsYear 1 2 3 4Revenues $ 3,125,000 $ 3,125,000 $ 3,125,000 $ 3,125,000 Variable costs 1,406,250 1,406,250 1,406,250 1,406,250 Fixed costs 425,000 425,000 425,000 425,000 Depreciation 1,099,890 1,466,520 489,060 244,530 EBIT $ 193,860 $ (172,770) $ 804,690 $ 1,049,220 Taxes (35%) 67,851 (60,469) 281,642 367,227 Net income $ 126,009 $ (112,301) $ 523,049 $ 681,993 + Depreciation 1,099,890 1,466,520 489,060 244,530 OCF $ 1,225,899 $ 1,354,220 $ 1,012,109 $ 926,523



Suppose you are in a competitive bid situation. If your bid is too high, your company will not get the project, but if your bid is too low, your company will lose money on the project. So, what is the minimum bid price you would submit? The minimum bid price is the price that results in a zero NPV. Suppose we are bidding on the following project. The contract will last for four years, and the equipment will be depreciated on a three-year MACRS schedule. What is the minimum bid price we could submit?

We entered a price in the appropriate cell above. As we will show later, it does not really matter what price we entered. Next, we need to calculate the cash flows and NPV for the project with our hypothetical price. This will be:

The total cash flows for each year of the project are:

Project Cash FlowsYear 0 1 2 3OCF $ 1,225,899 $ 1,354,220 $ 1,012,109 Change in NWC $ (80,000)Capital spending $ (3,300,000)Total cash flow $ (3,380,000) $ 1,225,899 $ 1,354,220 $ 1,012,109

Finally, the NPV of the project at this unit price is:

NPV: $ 334,821.06

The minimum bid price is the price at which the NPV of the project is zero. We can use Solver to find this unit price (and much more.)

RWJ Excel TipTo use Solver, go to the Data tab, then click Solver. The inputs we used for this problem are:

Minimum bid price: $ 22.64

We restored the original unit price so you could use Solver on this problem for practice.

As you see, with Solver you first enter the target cell you would like to set to a specific value, in this case, the NPV cell. Since the lowest bid price is the price that results in a zero NPV, we chose to set the NPV cell equal to a value of zero. Next, we select the cell we would like to change in order to set the target cell equal to the value we chose. In this case, we changed the unit price cell. This is why the original value we entered for the unit price is irrelevant: Solver will change the value when it solves the problem. Note that after we used Solver, we restored the original value. On the next worksheet, you can see the answer report generated by Solver. In this case, the bid price that results in a zero NPV is:

NOTE: There is a bug in Solver that will occur occasionally. In some cases, Solver will not launch, or if you try to save one or more of the reports, you may see "Solver: An unexpected internal error or available memory was exhausted" pop up. In this case, the solution is to uninstall Solver and re-install it. To do this:

1) Go to the Office button on the top left, click Excel options, choose Add-Ins, select Excel Add-Ins in the pulldown menu near the bottom of the box, and click on Go.2) Uncheck the Solver add-in and click OK.

4) Check the Solver add-in and select OK.

3) Go to the Office button on the top left, click Excel options, choose Add-Ins, select Excel Add-Ins in the pulldown menu near the bottom of the box, and click on Go. This is a repeat of Step 1.


Suppose you are in a competitive bid situation. If your bid is too high, your company will not get the project, but if your bid is too low, your company will lose money on the project. So, what is the minimum bid price you would submit? The minimum bid price is the price that results in a zero NPV. Suppose we are bidding on the following project. The contract will last for four years, and the equipment will be depreciated on a three-year MACRS schedule. What is the minimum bid price we could submit?

We entered a price in the appropriate cell above. As we will show later, it does not really matter what price we entered. Next, we need to calculate the cash flows and NPV

The total cash flows for each year of the project are:

Project Cash Flows4

$ 926,523 80,000 48,750 $ 1,055,273

Finally, the NPV of the project at this unit price is:

The minimum bid price is the price at which the NPV of the project is zero. We can use Solver to find this unit price (and much more.)

To use Solver, go to the Data tab, then click Solver. The inputs we used for this problem are:

As you see, with Solver you first enter the target cell you would like to set to a specific value, in this case, the NPV cell. Since the lowest bid price is the price that results in a zero NPV, we chose to set the NPV cell equal to a value of zero. Next, we select the cell we would like to change in order to set the target cell equal to the value we chose. In this case, we changed the unit price cell. This is why the original value we entered for the unit price is irrelevant: Solver will change the value when it solves the problem. Note that after we used Solver, we restored the original value. On the next worksheet, you can see the answer report generated by Solver. In this case, the bid price that

There is a bug in Solver that will occur occasionally. In some cases, Solver will not launch, or if you try to save one or more of the reports, you may see "Solver: An unexpected internal error or available memory was exhausted" pop up. In this case, the solution is to uninstall Solver and re-install it. To do this:

1) Go to the Office button on the top left, click Excel options, choose Add-Ins, select Excel Add-Ins in the pulldown menu near the bottom of the box, and click on Go.

3) Go to the Office button on the top left, click Excel options, choose Add-Ins, select Excel Add-Ins in the pulldown menu near the bottom of the box, and click on Go.

Solver

22.63633524

Microsoft Excel 12.0 Answer ReportWorksheet: [Chapter 9.xlsx]Setting a Bid PriceReport Created: 11/20/2008 5:35:12 PM

Target Cell (Value Of)Cell Name Original Value Final Value

$C$55 NPV: Project Cash Flows $ - $ -

Adjustable CellsCell Name Original Value Final Value

$D$11 Price per unit $ 22.64 $ 22.64

ConstraintsNONE

Chapter 9 - Master it!

a. What is the profitability index of the project?

b. What is the IRR of the project?

c. What is the NPV of the project?

d. How sensitive is the NPV to changes in the price of the new PDA? Construct a one way data table to help you answer this question.

e. How sensitive is the NPV to changes in the quantity sold?

For this Master It! assignment, refer to the Conch Republic Electronics case at the end of Chapter 9. For your convenience, we have entered the relevant values in the case such as the price, variable cost, etc. on the next page. For this project, answer the following questions:

What is the profitability index of the project?

What is the IRR of the project?

What is the NPV of the project?

How sensitive is the NPV to changes in the price of the new PDA? Construct a one way data table to help you answer this question.

How sensitive is the NPV to changes in the quantity sold?

For this Master It! assignment, refer to the Conch Republic Electronics case at the end of Chapter 9. For your convenience, we have entered the relevant values in the case such as the price, variable cost, etc. on the next page. For this project, answer the following questions:

Master it! Solution

Equipment $ 32,500,000 Pretax salvage value $ 3,500,000 R&D $ 750,000 Marketing study $ 200,000

Year 1 Year 2 Year 3 Year 4Sales (units) 65,000 82,000 108,000 94,000 Sales of old PDA 80,000 60,000 Lost sales 15,000 15,000 Depreciation rate 14.29% 24.49% 17.49% 12.49%

Price $ 500 VC $ 215 FC $ 4,300,000 Tax rate 35%NWC percentage 20%Required return 12%

Year 1 Year 2 Year 3 Year 4SalesVCFixed costsDepEBTTaxNI+DepOCF

NWCBegEndNWC CF

Net CF

SalvageBV of equipmentTaxes

Salvage CF

Time Cash flow012345

a. Profitability index

b. IRR

c. NPV

d. Price per unit NPV

$ 400 $ 410 $ 420 $ 430 $ 440 $ 450 $ 460 $ 470 $ 480 $ 490 $ 500 $ 510 $ 520 $ 530 $ 540 $ 550 $ 560 $ 570 $ 580 $ 590 $ 600

e.

NPV

DNPV/DPrice

To find the sensitivity of the NPV to changes in quantity, we need to change the quantity sold manually since the quantity sold is different each year. If we add 100 units to each year's qauntity sold, the NPV is:

DNPV/DQuantity

Year 5 57,000

8.93%

Year 5

To find the sensitivity of the NPV to changes in quantity, we need to change the quantity sold manually since the quantity sold is different each year. If we add 100 units to

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