Chapter 11 Mini Case Cash Flow Estimation Situation a. Define “incremental cash flow.” Analysis of New Expansion Project Part I: Input Data Equipment cost Key Output: NPV = $0 Shipping charge Installation charge Economic Life Salvage Value Tax Rate Cost of Capital Units Sold Sales Price Per Unit Incremental Cost Per Unit NWC/Sales Inflation rate Shrieves Casting Company is considering adding a new line to its product mix, and capital budgeting analysis is being conducted by Sidney Johnson, a recently gradua MBA. The production line would be set up in unused space in Shrieves' main plant. machinery’s invoice price would be approximately $200,000, another $10,000 in ship charges would be required, and it would cost an additional $30,000 to install the equipment. The machinery has an economic life of 4 years, and Shrieves has obtain special tax ruling that places the equipment in the MACRS 3-year class. The machi expected to have a salvage value of $25,000 after 4 years of use. incremental cost of $100 per unit in the first year, excluding depreciation. Each can be sold for $200 in the first year. The sales price and cost are expected to increase by 3% per year due to inflation. Further, to handle the new line, the fi net working capital would have to increase by an amount equal to 12% of sales reve The firm’s tax rate is 40%, and its overall weighted average cost of capital is 10 (1.) Should you subtract interest expense or dividends when calculating proje flow? line site. Should this be included in the analysis? Explain. per year. Should this be included in the analysis? If so, how? (4.) Finally, assume that the new product line is expected to decrease sales o firm’s other lines by $50,000 per year. Should this be considered in the analysis? If so, ho
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1/1/2012
Chapter 11 Mini CaseCash Flow Estimation
Situation
a. Define “incremental cash flow.”
(1.) Should you subtract interest expense or dividends when calculating project cash flow?
Analysis of New Expansion ProjectPart I: Input Data
Equipment cost Key Output: NPV = $0 Shipping chargeInstallation chargeEconomic LifeSalvage ValueTax RateCost of CapitalUnits SoldSales Price Per UnitIncremental Cost Per UnitNWC/SalesInflation rate
Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would be set up in unused space in Shrieves' main plant. The machinery’s invoice price would be approximately $200,000, another $10,000 in shipping charges would be required, and it would cost an additional $30,000 to install the equipment. The machinery has an economic life of 4 years, and Shrieves has obtained a special tax ruling that places the equipment in the MACRS 3-year class. The machinery is expected to have a salvage value of $25,000 after 4 years of use.
The new line would generate incremental sales of 1,250 units per year for 4 years at an incremental cost of $100 per unit in the first year, excluding depreciation. Each unit can be sold for $200 in the first year. The sales price and cost are expected to increase by 3% per year due to inflation. Further, to handle the new line, the firm’s net working capital would have to increase by an amount equal to 12% of sales revenues. The firm’s tax rate is 40%, and its overall weighted average cost of capital is 10%.
(2.) Suppose the firm had spent $100,000 last year to rehabilitate the production line site. Should this be included in the analysis? Explain.
(3.) Now assume that the plant space could be leased out to another firm at $25,000 per year. Should this be included in the analysis? If so, how?
(4.) Finally, assume that the new product line is expected to decrease sales of the firm’s other lines by $50,000 per year. Should this be considered in the analysis? If so, how?
g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR, MIRR, and payback? Do these indicators suggest the project should be undertaken?
To find MIRR, we could now find the discount rate that equates the PV and TV. But it is easier to use the MIRR function.
C113
This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.
(3.) How is each type of risk used in the capital budgeting process?
Evaluating Risk: Sensitivity Analysis
Sensitivity of NPV and to Variations in Input Variablesj. (1.) What is sensitivity analysis?
We summarize the data tables and show the sensitivity analysis graph below:
% Deviation WACC % Deviation 1st YEAR UNIT SALES % Deviation SALVAGEfrom NPV from Units NPV from Variable NPV
Base Case WACC 0 Base Case Sold $0 Base Case Cost $0-30% $0 -30% $0 -30% $0-15% 0 -15% 0 -15% 0
0% 0 0% 0 0% 015% 0 15% 0 15% 030% 0 30% 0 30% 0
h. What does the term ”risk” mean in the context of capital budgeting; to what extent can risk be quantified; and when risk is quantified, is the quantification based primarily on statistical analysis of historical data or on subjective, judgmental estimates?
Risk in capital budgeting really means the probability that the actual outcome will be worse than the expected outcome. For example, if there were a high probability that the expected NPV as calculated above will actually turn out to be negative, then the project would be classified as relatively risky. The reason for a worse-than-expected outcome is, typically, because sales were lower than expected, costs were higher than expected, and/or the project turned out to have a higher than expected initial cost. In other words, if the assumed inputs turn out to be worse than expected then the output will likewise be worse than expected. We use Excel to examine the project's sensitivity to changes in the input variables.
i. (1.) What are the three types of risk that are relevant in capital budgeting?
(2.) How is each of these risk types measured, and how do they relate to one another?
(2.) Perform a sensitivity analysis on the unit sales, salvage value, and cost of capital for the project. Assume that each of these variables can vary from its base-case, or expected, value by plus and minus 10%, 20%, and 30%. Include a sensitivity diagram, and discuss the results.
Here we use an Excel "Data Table" to find the NPVs for changes in unit sales, salvage value, and WACC holding other things constant--changing one variable at a time. This produces the sensitivity analys as shown below.
Evaluating Risk: Sensitivity Analysis
Deviation NPV Deviation from Base Casefrom Units
Base Case WACC Sold Salvage-30% $0 $0 $0 -15% 0 0 0 0% 0 0 0
15% 0 0 0 30% 0 0 0
Range $0 $0 $0
(1.) What is scenario analysis?
(2.) What is the worst-case NPV? The best-case NPV?
(3.) What is the primary weakness of sensitivity analysis? What is its primary usefulness?
k. Assume that Sidney Johnson is confident of her estimates of all the variables that affect the project’s cash flows except unit sales and sales price: If product acceptance is poor, unit sales would be only 900 units a year and the unit price would only be $160; a strong consumer response would produce sales of 1,600 units and a unit price of $240. Sidney believes that there is a 25% chance of poor acceptance, a 25% chance of excellent acceptance, and a 50% chance of average acceptance (the base case).
Scenario analysis extends risk analysis in two ways: (1) It allows us to change more than one variable at a time, hence to see the combined effects of changes in several variables on NPV, and (2) it allows us to bring in the probabilities of changes in the key variables.
(3.) Use the worst-, most likely, and best-case NPVs and probabilities of occurrence to find the project’s expected NPV, standard deviation, and coefficient of variation.
-40% -30% -20% -10% 0% 10% 20% 30% 40%0
1
1
Sensitivity Analysis
Deviation from Base-Case Value
NPV ($)
Salvage Value
Units Sold
WACC
Evaluating Risk: Scenario Analysis
Scenario Analysis Squared Deviation
Scenario Probability Unit Sales Unit Price NPV times Probability
Best Case 25%Base Case 50%
Worst Case 25%Quick calculation:
Expected NPV = $0 $0 Standard Deviation = $0 $0
Coefficient of Variation = Std Dev / Expected NPV = #DIV/0!
Monte Carlo Simulation
Risk Adjusted Cost of Capital
Cost of capital for average projects: 0%Adjustment for risky projects:
Risk adjusted cost of capital:
NPV with risk-adjusted cost of capital: $0
(3.) Are there any subjective risk factors that should be considered before the final decision is made?
We could find the NPV by entering the value of unit sales and price for each scenario and then recording the NPV (this is what we did for the table below). Alternatively, we could use Tools, Scenarios to define the inputs for each scenario, which we did and show in the Scenario Summary Tab below. In fact, you could even use Tools, Scenarios, and then click the Summary button on the dialog box, and it will automatically create a table similar to the one below. This is a powerful feature of Excel, and we encourage you to explore it.
l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and disadvantages.
Monte Carlo simulation is similar to scenario analysis in that different values of key input variables are used. Unlike scenario analysis, Monte Carlo simulation draws the input values from specified probability distributions and then computes the NPV. It repeats this process hundreds, or even thousands, of times. It then averages the NPVs from each repetition.
m. (1.) Assume that Shrieves' average project has a coefficient of variation in the range of 0.2 to 0.4. Would the new line be classified as high risk, average risk, or low risk? What type of risk is being measured here?
(2.) Shrieves typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk. Should the new line be accepted?
The CV of this project is 1.15, which is larger than the CV range of the firm's average project. Consequently, this project is riskier than the firm's average project, so management should add 3% to the WACC to risk adjust.
m. What is a real option? What are some types of real options?
$200,000$10,000$30,000
4$25,000
40%10%1,250$200 $100 12%
3%
$200,000$10,000$30,000
4$25,000
40%10%1,600$240 $100 12%
3%
G49
This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.
C106
This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.
G141
Do not delete or change this cell or row.
$200,000$10,000$30,000
4$25,000
40%10%
900$160 $100 12%
3%
$200,000$10,000$30,000
4$25,000
40%10%1,250$200 $100 12%
0%
Scenario Summary
Current Values: Base Case Best CaseChanging Cells:
Result Cells:$C$113 $88,030 $88,030 $278,965 $C$114 23.9% 23.9% 48.3%
Notes: Current Values column represents values of changing cells attime Scenario Summary Report was created. Changing cells for eachscenario are highlighted in gray.
Worst Case Base-but forget inflation
$200,000 $200,000$10,000 $10,000$30,000 $30,000
4 4$25,000 $25,000
40% 40%10% 10%900 1,250
$160 $200 $100 $100 12% 12%
3% 0%
($48,514) $78,387 1.0% 22.7%
Section 11.7 Scenario Analysis
Analysis of New Expansion ProjectPart I: Input Data
Equipment cost $200,000 Key Output: NPV =Shipping charge $10,000Installation charge $30,000Economic Life 4Salvage Value $25,000 Tax Rate 40%
Cost of Capital 10% Std. Dev.Units Sold Random variable = 1,440 1,250 200Sales Price Per Unit Random variable = $226 $200 $30 Incremental Cost Per Unit $100 NWC/Sales 12%Inflation rate 3%
Year % x Basis = Depr.1 0.33 $240,000 $79,200 2 0.45 240,000 108,000
Monte Carlo simulation is similar to scenario analysis in that different values of key inputs are used Unlike scenario analysis, Monte Carlo simulation draws a trial set of input values from specified probability distributions and then computes the NPV for this trial. This process is repeated for hundreds, or even thousands, of trials, with key results (like NPV) saved from each trial. After running the number of desired trials, the NPVs from the trials can be averaged to estimate the project's expected NPV; the trial results can also be used to provide a histogram showing the project's possible outcomes.
The green area below is the same project as in the mini case, but we have replaced the inputs fro units sold and sales price with random variables drawn from normal distributions with the expected values and means shown next to the inputs. Notice that each time the sheet makes a calculation, the values for unit sales, sales price, and NPV change (Hint: you can make the sheet calculate by hitting the F9 key).
Here is a tip for simulating a project analysis. If you have already done the analysis and it is in a different worksheet, see how many rows it takes. Delete the green area below and add enough rows so that there will be room for your previous analysis. For example, this model was in the "Model" tab in the file Ch 11 Mini Case.xls, rows 33-132. We went into that file, selected Rows 32-135, copied them, and then pasted them into Rows 32-135 of this Worksheet. Because we pasted them into the same row numbers from which we copied them, all the formula references remained correct. We then edited this worksheet.
Expected Value
b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual depreciation expenses?
3 0.15 240,000 36,000 4 0.07 240,000 16,800
d. Construct annual incremental operating cash flow statements.
Annual Operating Cash FlowsYear 1 Year 2 Year 3
Units 1,440 1,440 1,440Unit price $226.30 $233.09 $240.09 Unit cost $100.00 $103.00 $106.09
Annual Cash Flows due to Investments in Net Working Capital
Year 0 Year 1 Year 2 Year 3Sales $325,806 $335,580 $345,655 NWC (% of sales) 39,097 40,270 41,479 42,722 CF due to investment in NOWC) (39,097) (1,173) (1,209) (1,243)
f. Calculate the after-tax salvage cash flow.After-tax Salvage Value
$25,000 $10,000 Salvage value $25,000 $25,000 $10,000 Book value 0 16,800 16,800 Gain or loss $25,000 $8,200 ($6,800)Tax on salvage value 10,000 3,280 (2,720)Net terminal cash flow $15,000 $21,720 $12,720
Projected Net Cash FlowsYear 0 Year 1 Year 2
Investment Outlay: Long Term Assets ($240,000)Operating Cash Flows $140,782 $155,575 CF due to investment in NWC (39,097) (1,173) (1,209)
Salvage Cash Flows
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include inflation when estimating cash flows? See answer to part d.
EBIT (1 – T)
e. Estimate the required net working capital for each year, and the cash flow due to investments in net working capital.
Hypothetical: If sold after 3 years for
Based on facts in case:
g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR, MIRR, and payback? Do these indicators suggest the project should be undertaken?
Column input cell to "trick" Excel into updating random variables in Data Table: 1
Figure 11-27 Summary of Simulation Results (Thousands of Dollars)
We use a Data Table to perform the simulation (the Data Table is below, shaded bright yellow). When the Data Table is updated, it will insert new random variables for each of the inputs we allow to change in Panel A above, run the analysis is Panel C above, and then save the NPV for each trial (we also save the input variables for each trial so that we can verify that they are behaving as we expect). We set the first column of the Data Table (the variable to be changed in each row) to numbers from 1-100. We don't really use these numbers anywhere in the analyis, but if we tell the Data Table to treat these as the Column inputs, Excel will recalculate all items in the Data Table, including the random inputs and the resulting NPV. In other words, we "trick" Excel into doing a simulation. We tell Excel to insert each of the Column inputs in the Data Table into the cell immediately below this box. This cell isn't linked to anything else, but each time Excel updates a row of the Data Table, all the random values will be updated.
Excel normally updates all values in a Data Table each time any cell that is related to the Data Table changes. In our case, we have random variables in the Data Table, so each time any cell in the worksheet makes a calculation, the Data Table is updated. If the Data Table has many rows, updating it can take up to 20 or 30 seconds. With only 100 rows, it updates very quickly. But if it bothers you, you can set the worksheet to do automatic calculation except for data tables.
You don't need to change anything in this section. It will be updated automatically if you do a simulation. The summary of the simulation results and the histogram are based on the simulation trials n the Data Table below and are updated automatically when you do a simulation. You can do an updated simulation by hitting the F9 key.
Number of Trials = 100Simulated Input Variables and Key Results
Monte Carlo simulation is similar to scenario analysis in that different values of key inputs are used Unlike scenario analysis, Monte Carlo simulation draws a trial set of input values from specified probability distributions and then computes the NPV for this trial. This process is repeated for hundreds, or even thousands, of trials, with key results (like NPV) saved from each trial. After running the number of desired trials, the NPVs from the trials can be averaged to estimate the project's expected NPV; the trial results can also be used to provide a histogram showing the project's
The green area below is the same project as in the mini case, but we have replaced the inputs fro units sold and sales price with random variables drawn from normal distributions with the expected values and means shown next to the inputs. Notice that each time the sheet makes a calculation, the values for unit sales, sales price, and NPV change (Hint:
Here is a tip for simulating a project analysis. If you have already done the analysis and it is in a different worksheet, see how many rows it takes. Delete the green area below and add enough rows so that there will be room for your previous
, rows 33-132. We went into that file, selected Rows 32-135, copied them, and then pasted them into Rows 32-135 of this Worksheet. Because we pasted them into the same row numbers from which we copied them, all the formula references remained correct. We then
b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual
Remaining Book Value
16,8000
d. Construct annual incremental operating cash flow statements.
Year 41,440
$247.29 $109.27
$356,020 157,315
16,800 $181,905
72,762 $109,143
16,800 $125,943
Year 4$356,020
42,722
Year 3 Year 4
$130,151 $125,943 (1,243) 42,722
15,000
c. Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include
e. Estimate the required net working capital for each year, and the cash flow due to investments in net working
g. Calculate the net cash flows for each year. Based on these cash flows, what are the project’s NPV, IRR,
$128,908 $183,665
Years
3 4$128,908 $183,665
141,799 186,783
185,820 TV = $698,067
To find MIRR, we could now find the discount rate that equates the PV and TV. But it is easier to use the MIRR function.
Years3 4
$128,908 $183,665 $143,787 $327,452
Don't change the the red cell.
Figure 11-27 Summary of Simulation Results (Thousands of Dollars)
We use a Data Table to perform the simulation (the Data Table is below, shaded bright yellow). When the Data Table is updated, it will insert new random variables for each of the inputs we allow to change in Panel A above, run the analysis is Panel C above, and then save the NPV for each trial (we also save the input variables for each trial so that we can verify that they are behaving as we expect). We set the first column of the Data Table (the variable to be changed in each row) to numbers from 1-100. We don't really use these numbers anywhere in the analyis, but if we tell the Data Table to treat these as the Column inputs, Excel will recalculate all items in the Data Table, including the random inputs and the resulting NPV. In other words, we "trick" Excel into doing a simulation. We tell Excel to insert each of the Column inputs in the Data Table into the cell immediately below this box. This cell isn't linked to anything else, but each time Excel
Excel normally updates all values in a Data Table each time any cell that is related to the Data Table changes. In our case, we have random variables in the Data Table, so each time any cell in the worksheet makes a calculation, the Data Table is updated. If the Data Table has many rows, updating it can take up to 20 or 30 seconds. With only 100 rows, it updates very quickly. But if it bothers you, you can set the worksheet to do automatic calculation except for data tables.
You don't need to change anything in this section. It will be updated automatically if you do a simulation. The summary of the simulation results and the histogram are based on the simulation trials n the Data Table below and are updated automatically when you do a simulation. You can do an updated simulation by hitting the F9 key.
Simulated Input Variables and Key Results
Scratch work for chart: see comments.Count
Range bottom 0 Percent-$290,674 0 0%-$269,911 0 0%