Shrieves Casting Company is considering adding a new line to its product mix, an
ID: 2783973 • Letter: S
Question
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 the 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 both 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, which is the risk-adjusted cost of capital for an average project (r), is 10%. d. Construct annual incremental operating cash flow statements. e. Estimate the required net working capital for each year and the cash flow due to investments in net working capital. f. Calculate the after-tax salvage cash flow. g. Calculate the net cash flows for each year. Based on these cash flows and the average project cost of capital, what are the project’s NPV, IRR, MIRR, PI, payback, and discounted payback? Do these indicators suggest that the project should be undertaken? 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? 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? (3) How is each type of risk used in the capital budgeting process? j. (1) What is sensitivity analysis? (2) Perform a sensitivity analysis on the unit sales, salvage value, and cost of capital for the project. Assume each of these variables can vary from its base-case, or expected, value by 10%, 20%, and 30%. Include a sensitivity diagram, and discuss the results. (3) What is the primary weakness of sensitivity analysis? What is its primary usefulness? k. Assume that Sidney Johnson is confident in 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. Johnson believes there is a 25% chance of poor acceptance, a 25% chance of excellent acceptance, and a 50% chance of average acceptance (the base case). (1) What is scenario analysis? (2) What is the worst-case NPV? The best-case NPV? (3) Use the worst-, base-, and best-case NPVs and probabilities of occurrence to find the project’s expected NPV, as well as the NPV’s standard deviation and coefficient of variation. l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and disadvantages. m. (1) Assume the company’s 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? (3) Are there any subjective risk factors that should be considered before the final decision is made? n. What is a real option? What are some types of real options?
Explanation / Answer
d. Annual incremental operating cash flow statement
Year 1
Year 2
Year 3
Year 4
Sales
$250,000
$257,500
$265,225
$273,188
Costs
$125,000
$128,750
$132,613
$136,588
Depreciation
$79,200
$108,000
$36,000
$16,800
Op. EBIT
$45,800
$20,750
$96,612
$119,800
Taxes (40%)
$18,320
$8,300
$38,645
$47,920
NOPAT
$27,480
$12,450
$57,967
$71,880
Depreciation
$79,200
$108,000
$36,000
$16,800
Net Operating CF
$106,680
$120,450
$93,967
$88,680
e. Estimate the required net operating working capital for each year, and the cash flow due to investments in net operating working capital.
The project requires a level of net operating working capital in the amount equal to 12% of the next year’s sales. Any increase in NOWC is a negative cash flow, and any decrease is a positive cash flow.
Year 0
Year 1
Year 2
Year 3
Year 4
Sales
$250,000
$257,500
$265,225
$273,188
NOWC (% of sales)
$30,000
$30,900
$31,827
$32,783
$0
CF due to NOWC)
($30,000)
($900)
($927)
($956)
$32,783
f. Calculate the after-tax salvage cash flow.
When the project is terminated at the end of year 4, the equipment can be sold for $25,000. But, since it has been depreciated to a $0 book value, taxes must be paid on the full salvage value. For this project, the after-tax salvage cash flow is:
Salvage Value $25,000
Tax On Salvage Value (10,000)
Net After-Tax Salvage Cash Flow $15,000
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 that the project should be undertaken?
The net cash flows are
Year 0
Year 1
Year 2
Year 3
Year 4
Initial Outlay
($240,000)
Operating Cash Flows
$106,680
$120,450
$93,967
$88,680
CF Due To NOWC
($30,000)
($900)
($927)
($956)
$32,783
Salvage Cash Flows
$15,000
Net Cash Flows
($270,000)
$105,780
$119,523
$93,011
$136,463
NPV =
$88,030
IRR =
23.9%
MIRR =
18.0%
Payback =
2.5
h. What does the term “risk” mean in the context of capital budgeting, to what extent can risk being quantified, and when risk is quantified, is the quantification based primarily on statistical analysis of historical data or on subjective, judgmental estimates?
Risk throughout finance relates to uncertainty about future events, and in capital budgeting, this means the future profitability of a project. For certain types of projects, it is possible to look back at historical data and to statistically analyze the riskiness of the investment. This is often true when the investment involves an expansion decision; for example, if Sears were opening a new store, if Citibank were opening a new branch, or if GM were expanding its Chevrolet plant, then past experience could be a useful guide to future risk. Similarly, a company that is considering going into a new business might be able to look at historical data on existing firms in that industry to get an idea about the riskiness of its proposed investment. However, there are times when it is impossible to obtain historical data regarding proposed investments; for example, if GM were considering the development of an electric auto, not much relevant historical data for assessing the riskiness of the project would be available. Rather, GM would have to rely primarily on the judgment of its executives, and they, in turn, would have to rely on their experience in developing, manufacturing, and marketing new products. We will try to quantify risk analysis, but you must recognize at the outset that some of the data used in the analysis will necessarily be based on subjective judgments rather than on hard statistical observations.
i. 1. What are the three types of risk that are relevant to capital budgeting?
2. How is each of these risk types measured, and how do they relate to one another?
Here are the three types of project risk:
3. How is each type of risk used in the capital budgeting process?
Because management’s primary goal is shareholder wealth maximization, the most relevant risk for capital projects is a market risk. However, creditors, customers, suppliers, and employees are all affected by a firm’s total risk. Since these parties influence the firm’s profitability, a project’s within-firm risk should not be completely ignored.
Unfortunately, by far the easiest type of risk to measure is a project’s stand-alone risk. Thus, firms often focus on this type of risk when making capital budgeting decisions. However, this focus does not necessarily lead to poor decisions, because most projects that a firm undertakes are in its core business. In this situation, a project’s stand-alone risk is likely to be highly correlated with its within-firm risk, which in turn is likely to be highly correlated with its market risk.
J. 1. What is sensitivity analysis?
Sensitivity analysis measures the effect of changes in a particular variable, say revenues, on a project’s NPV. To perform a sensitivity analysis, all variables are fixed at their expected values except one. This one variable is then changed, often by specified percentages, and the resulting effect on NPV is noted. (One could allow more than one variable to change, but this then merges sensitivity analysis into scenario analysis.)
2. Perform a sensitivity analysis of 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 percent. Include a sensitivity diagram, and discuss the results.
The sensitivity data are given here in tabular form (in thousands of dollars):
Deviation
NPV Deviation From Base Case
From
Units
Base Case
WACC
Sold
Salvage
-30%
$113,288
$16,668
$84,956
-15%
$100,310
$52,348
$86,493
0%
$88,030
$88,030
$88,030
15%
$76,398
$123,711
$89,567
30%
$65,371
$159,392
$91,103
Range
47,916
176,060
6,147
The sensitivity lines intersect at 0% change and the base case NPV, $81,573. Since all other variables are set at their base case, or expected values, the zero change situation is the base case.
B. The plots for unit sales and salvage value are upward sloping, indicating that higher variable values lead to higher NPVs. Conversely, the plot for cost of capital is downward sloping, because a higher cost of capital leads to a lower NPV.
C. The plot of unit sales is much steeper than that for salvage value. This indicates that NPV is more sensitive to changes in unit sales than to changes in salvage value.
D. Steeper sensitivity lines indicate greater risk. Thus, in comparing two projects, the one with the steeper lines is considered to be riskier.
3. What is the primary weakness of sensitivity analysis? What is its primary usefulness?
The two primary disadvantages of sensitivity analysis are
(1) that it does not reflect the effects of diversification and
(2) that it does not incorporate any information about the possible magnitudes of the forecast errors.
Thus, a sensitivity analysis might indicate that a project’s NPV is highly sensitive to the sales forecast, hence that the project is quite risky, but if the project’s sales, hence its revenues, are fixed by a long-term contract, then sales variations may actually contribute little to the project’s risk. It also ignores any relationships between variables, such as unit sales and sales price.Therefore, in many situations, sensitivity analysis is not a particularly good indicator of risk. However, sensitivity analysis does identify those variables which potentially have the greatest impact on profitability, and this helps management focus its attention on those variables that are probably most important.
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 percent chance of poor acceptance, a 25 percent chance of excellent acceptance, and a 50 percent chance of average acceptance (the base case).
1. What is scenario analysis?
Scenario analysis examines several possible situations, usually worst case, most likely case, and best case. It provides a range of possible outcomes.
2. What is the worst-case NPV? The best-case NPV?
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.
We used a spreadsheet model to develop the scenarios (in thousands of dollars), which are summarized below:
Scenario
Probability
Unit Sales
Unit Price
NPV
Best Case
25%
1600
$240
$278,965
Base Case
50%
1250
$200
$88,030
Worst Case
25%
900
$160
($48,514)
Expected NPV =
$101,628
Standard Deviation =
$75,684
Coefficient Of Variation =
Std Dev / Expected NPV =
0.74
L. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and disadvantages.
Scenario analysis examines several possible scenarios, usually worst case, most likely case, and best case. Thus, it usually considers only 3 possible outcomes. Obviously, the world is much more complex, and most projects have an almost infinite number of possible outcomes.
Simulation analysis is a type of scenario analysis which uses a relatively powerful financial planning software such as interactive financial planning system (IFPs) or @risk (a spreadsheet add-in). Simple simulations can also be conducted with other spreadsheet add-ins, such as Simtools. Here the uncertain cash flow variables (such as unit sales) are entered as continuous probability distribution parameters rather than as point values. Then, the computer uses a random number generator to select values for the uncertain variables on the basis of their designated distributions. Once all of the variable values have been selected, they are combined, and an NPV is calculated. The process is repeated many times, say 1,000, with new values selected from the distributions for each run. The end result is a probability distribution of NPV based on a sample of 1,000 values. The software can graph the distribution as well as print out summary statistics such as expected NPV and NPV. Simulation provides the decision maker with a better idea of the profitability of a project that does scenario analysis because it incorporates many more possible outcomes.
Although simulation analysis is technically refined, its usefulness is limited because managers are often unable to accurately specify the variables’ probability distributions. Further, the correlations among the uncertain variables must be specified, along with the correlations over time. If managers are unable to do this with much confidence, then the results of simulation analyses are of limited value.
Recognize also that neither sensitivity, scenario, nor simulation analysis provides a decision rule--they may indicate that a project is relatively risky, but they do not indicate whether the project’s expected return is sufficient to compensate for its risk.
Finally, remember that sensitivity, scenario, and simulation analyses all focus on stand-alone risk, which is not the most relevant risk in capital budgeting analysis.
M. 1. Assume that Shrieves’ average project has a coefficient of variation in the range of 0.2-0.4. Would the new line be classified as high risk, average risk, or low risk? What type of risk is being measured here?
The project has a CV of 0.57, which is above the average range of 0.2-0.4, so it falls into the high-risk category. The CV measures a project’s stand-alone risk-it is merely a measure of the variability of returns (as measured by NPV) about the expected return.
2. Shrieves typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk. Should the new furniture line be accepted?
Since the project is judged to have an above-average risk, its differential risk-adjusted, or project, cost of capital would be 13 percent. At this discount rate, its NPV would be $60,541, so it would still be acceptable. If it were a low-risk project, its cost of capital would be 7 percent, its NPV would be $104,975, and it would be an even more profitable project on a risk-adjusted basis.
3. Are there any subjective risk factors that should be considered before the final decision is made?
A numerical analysis such as this one may not capture all of the risk factors inherent in the project. If the project has a potential for bringing on harmful lawsuits, then it might be riskier than first assessed. Also, if the project’s assets can be redeployed within the firm or can be easily sold, then, as a result of “abandonment possibilities,” the project may be less risky than the analysis indicates
Year 1
Year 2
Year 3
Year 4
Sales
$250,000
$257,500
$265,225
$273,188
Costs
$125,000
$128,750
$132,613
$136,588
Depreciation
$79,200
$108,000
$36,000
$16,800
Op. EBIT
$45,800
$20,750
$96,612
$119,800
Taxes (40%)
$18,320
$8,300
$38,645
$47,920
NOPAT
$27,480
$12,450
$57,967
$71,880
Depreciation
$79,200
$108,000
$36,000
$16,800
Net Operating CF
$106,680
$120,450
$93,967
$88,680
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