ch. 13 mini case (2)

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Model

2/1/12
Chapter 13 Mini Case
Situation
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%.
a. Define “incremental cash flow.” Answer: See Chapter 13 Mini Case Show
(1.) Should you subtract interest expense or dividends when calculating project cash flow? Answer: See Chapter 13 Mini Case Show
(2.) Suppose the firm had spent $100,000 last year to rehabilitate the production line site. Should this be included in the analysis? Explain. Answer: See Chapter 13 Mini Case Show
(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? Answer: See Chapter 13 Mini Case Show
(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? Answer: See Chapter 13 Mini Case Show
Analysis of New Expansion Project
Part I: Input Data
Equipment cost	$200,000	Key Output: NPV =	$88,010
Shipping charge	$10,000
Installation charge	$30,000
Economic Life	4
Salvage Value	$25,000
Tax Rate	40%
Cost of Capital	10%
Units Sold	1,250
Sales Price Per Unit	$200
Incremental Cost Per Unit	$100
NWC/Sales	12%
Inflation rate	3%
b. Disregard the assumptions in Part a. What is Shrieves' depreciable basis? What are the annual depreciation expenses?
Annual Depreciation Expense
Depreciable Basis = Equipment + Freight + Installation
Depreciable Basis =	$240,000
Year	%	x	Basis	=	Depr. Michael C. Ehrhardt: This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.	Remaining Book Value
1	0.3333	$240,000	$79,992	$160,008
2	0.4445	240,000	106,680	53,328
3	0.1481	240,000	35,544	17,784
4	0.0741	240,000	17,784	0
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.
d. Construct annual incremental operating cash flow statements.
Annual Operating Cash Flows
Year 1	Year 2	Year 3	Year 4
Units	1,250	1,250	1,250	1,250
Unit price	$200.00	$206.00	$212.18	$218.55
Unit cost	$100.00	$103.00	$106.09	$109.27
Sales	$250,000	$257,500	$265,225	$273,182
Costs	125,000	128,750	132,613	136,591
Depreciation	79,992	106,680	35,544	17,784
Operating income before taxes (EBIT)	$45,008	$22,070	$97,069	$118,807
Taxes (40%)	18,003	8,828	38,827	47,523
EBIT (1 – T)	$27,005	$13,242	$58,241	$71,284
Depreciation	79,992	106,680	35,544	17,784
Net operating CF	$106,997	$119,922	$93,785	$89,068
e. Estimate the required net working capital for each year, and the cash flow due to investments in net working capital.
Annual Cash Flows due to Investments in Net Working Capital
Year 0	Year 1	Year 2	Year 3	Year 4
Sales	$250,000	$257,500	$265,225	$273,182
NWC (% of sales)	30,000	30,900	31,827	32,782
CF due to investment in NOWC)	(30,000)	(900)	(927)	(955)	32,782
f. Calculate the after-tax salvage cash flow.
After-tax Salvage Value	Hypothetical: If sold after 3 years for
Based on facts in case:	$25,000	$10,000
Salvage value	$25,000	$25,000	$10,000
Book value	0	17,784	17,784
Gain or loss	$25,000	$7,216	($7,784)
Tax on salvage value	10,000	2,886	(3,114)
Net terminal cash flow	$15,000	$22,114	$13,114
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?
Projected Net Cash Flows
Year 0	Year 1	Year 2	Year 3	Year 4
Investment Outlay: Long Term Assets	($240,000)
Operating Cash Flows	$106,997	$119,922	$93,785	$89,068
CF due to investment in NWC	(30,000)	(900)	(927)	(955)	32,782
Salvage Cash Flows	15,000
Net Cash Flows	($270,000)	$106,097	$118,995	$92,830	$136,850
NPV	$88,010 Michael C. Ehrhardt: This differs slightly from the Powerpoint solution due to rounding in intermediate steps in the Powerpoint solution.
IRR	23.9%	PV of Inflows	TV of Inflows
$358,010	$524,162
Years
Find MIRR	0	1	2	3	4
Net Cash Flows	($270,000)	$106,097	$118,995	$92,830	$136,850	$358,009.72
102,113	($524,162.03)
143,984
141,215
PV=	($270,000)	TV =	$524,162
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.
MIRR =	18.0%
Find Payback	Years
0	1	2	3	4
Cash Flow	($270,000)	$106,097	$118,995	$92,830	$136,850
Cumulative Cash Flow for Payback	($270,000)	($163,903)	($44,908)	$47,922	$184,772
Payback =	2.5
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? Answer: See Chapter 13 Mini Case Show
(2.) How is each of these risk types measured, and how do they relate to one another? Answer: See Chapter 13 Mini Case Show
(3.) How is each type of risk used in the capital budgeting process? Answer: See Chapter 13 Mini Case Show
Evaluating Risk: Sensitivity Analysis
Sensitivity of NPV and to Variations in Input Variables
j. (1.) What is sensitivity analysis? Answer: See Chapter 13 Mini Case Show
(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.
We summarize the data tables and show the sensitivity analysis graph below:
% Deviation	WACC	% Deviation	1st YEAR UNIT SALES	% Deviation	SALVAGE
from	NPV	from	Units	NPV	from	Variable	NPV
Base Case	WACC	88,010	Base Case	Sold	$88,010	Base Case	Cost	$88,010
-30%	7.0%	$113,270	-30%	875	$16,649	-30%	$17,500	$84,936
-15%	8.5%	100,291	-15%	1,063	52,329	-15%	21,250	86,473
0%	10.0%	88,010	0%	1,250	88,010	0%	25,000	88,010
15%	11.5%	76,378	15%	1,438	123,690	15%	28,750	89,546
30%	13.0%	65,350	30%	1,625	159,371	30%	32,500	91,083
Evaluating Risk: Sensitivity Analysis
Deviation	NPV Deviation from Base Case
from	Units
Base Case	WACC	Sold	Salvage
-30%	$113,270	$16,649	$84,936
-15%	100,291	52,329	86,473
0%	88,010	88,010	88,010
15%	76,378	123,690	89,546
30%	65,350	159,371	91,083
Range	$47,920	$176,020	$6,147
(3.) What is the primary weakness of sensitivity analysis? What is its primary usefulness? Answer: See Chapter 13 Mini Case Show
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).
(1.) What is scenario analysis?
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.
(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.
Evaluating Risk: Scenario Analysis
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.
Scenario Analysis
Squared Deviation
Scenario	Probability	Unit Sales	Unit Price	NPV	times Probability
Best Case	25%	1,600	$240	$278,940	$7,861,657,811.87
Base Case	50%	1,250	$200	$88,010	$92,456,383.34
Worst Case	25%	900	$160	($48,527)	$5,635,163,606.11
Quick calculation:
Expected NPV =	$101,608	$101,608
Standard Deviation =	$116,573	$116,573
Coefficient of Variation = Std Dev / Expected NPV =	1.15
l. Are there problems with scenario analysis? Define simulation analysis, and discuss its principal advantages and disadvantages. Answer: See Chapter 13 Mini Case Show
Monte Carlo Simulation
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.
Risk Adjusted Cost of Capital
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? Answer: See Chapter 13 Mini Case Show
(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.
Cost of capital for average projects:	10%
Adjustment for risky projects:	3%
Risk adjusted cost of capital:	13%
NPV with risk-adjusted cost of capital:	$65,350	(See the +30% WACC in the sensitivity analysis above.)
(3.) Are there any subjective risk factors that should be considered before the final decision is made? Answer: See Chapter 13 Mini Case Show
n. What is a real option? What are some types of real options? Answer: See Chapter 13 Mini Case Show

Sensitivity Analysis

WACC -0.3 -0.15 0.0 0.15 0.3 113270.0479935089 100290.9690438629 88009.71641281329 76377.64110832603 65350.1734564107 Units Sold -0.3 -0.15 0.0 0.15 0.3 16648.78990506107 52329.21900826442 88009.71641281329 123690.2138173621 159370.711221911 Salvage -0.3 -0.15 0.0 0.15 0.3 84936.15586367046 86472.93613824184 88009.71641281329 89546.49668738467 91083.27696195611