Iron Ore What? (IOW) Casting Company is considering adding a new line to its pro
ID: 2721417 • Letter: I
Question
Iron Ore What? (IOW) Casting Company is considering adding a new line to its product mix. Sydney Johnson, a recently minted MBA, will be conducting the capital budgeting analysis. The new production line would be set up in unused space in IOW’s main plant. The machinery invoice price totals approximately $250,000, with another $20,000 in shipping charges and $30,000 to install the equipment, for a total requirement estimated at $300,000. The machinery has an economic life of 4 years, and IOW has obtained a special tax ruling that places the equipment in the Modified Accelerated Cost Recovery System (MACRS) 3-year class. After 4 years of use the machinery is expected to have a salvage value of $25,000. The new product line would generate incremental sales of 1,350 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 each 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 15% of sales revenues. The firm’s tax rate is 40%, and its overall weighted average cost of capital is 12%.
1. Assume that Sydney 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 could be only approximately 1,000 units a year and the unit price would be set at $150. Conversely, an excellent consumer response could produce sales of 2,000 units and a unit price of $220. 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). What is the worst-case NPV? The best-case NPV? Use the worst-, base-, and best-case NPVs and probabilities of occurrence to find the project’s expected NPV, standard deviation, and coefficient of variation.
Explanation / Answer
Initial investment = $300,000
After tax salvage value = $25,000 x (1-tax rate) => $25,000 x 0.6 = $15,000
3 Year Schedule
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$250,000.00
33.333%
$83,333.35
$83,333.35
$166,666.65
2
$250,000.00
44.444%
$111,111.13
$194,444.48
$55,555.53
3
$250,000.00
14.815%
$37,038.00
$231,482.48
$18,517.53
4
$250,000.00
7.407%
$18,517.53
$250,000.00
$0.00
Average Scenario:
Year
1
2
3
4
Sales
$270,000.00
$278,100.00
$286,443.00
$295,036.29
Less: Variable Cost
$135,000.00
$139,050.00
$143,221.50
$147,518.15
Less: Depreciation
$83,333.35
$111,111.13
$37,038.00
$18,517.53
EBT
$51,666.65
$27,938.87
$106,183.50
$129,000.62
Less: Tax @ 40%
$20,666.66
$11,175.55
$42,473.40
$51,600.25
Net Income
$30,999.99
$16,763.32
$63,710.10
$77,400.37
Add: Depreciation
$83,333.35
$111,111.13
$37,038.00
$18,517.53
Less: NWC
$40,500.00
$41,715.00
$42,966.45
$44,255.44
Add: After tax salvage value
$0.00
$0.00
$0.00
$15,000.00
Operating Cash flow
$73,833.34
$86,159.45
$57,781.65
$66,662.46
NPV = -$300,000 + [($73,833.34)/(1.12)] + [($86,159.45)/(1.12)2] + [($57,781.65)/(1.10)3] + [($66,662.46)/(1.12)4] = -$81,898.55
Best Case Scenario:
Year
1
2
3
4
Sales
$440,000.00
$453,200.00
$466,796.00
$480,799.88
Less: Variable Cost
$200,000.00
$206,000.00
$212,180.00
$218,545.40
Less: Depreciation
$83,333.35
$111,111.13
$37,038.00
$18,517.53
EBT
$156,666.65
$136,088.87
$217,578.00
$243,736.95
Less: Tax @ 40%
$62,666.66
$54,435.55
$87,031.20
$97,494.78
Net Income
$93,999.99
$81,653.32
$130,546.80
$146,242.17
Add: Depreciation
$83,333.35
$111,111.13
$37,038.00
$18,517.53
Less: NWC
$66,000.00
$67,980.00
$70,019.40
$72,119.98
Add: After tax salvage value
$0.00
$0.00
$0.00
$15,000.00
Operating Cash flow
$111,333.34
$124,784.45
$97,565.40
$107,639.72
NPV = -$300,000 + [($111,333.34)/(1.12)] + [($124,784.45)/(1.12)2] + [($97,565.60)/(1.10)3] + [($107,639.72)/(1.12)4] = $36,734.28
Worst Case Scenario:
Year
1
2
3
4
Sales
$150,000.00
$154,500.00
$159,135.00
$163,909.05
Less: Variable Cost
$100,000.00
$103,000.00
$106,090.00
$109,272.70
Less: Depreciation
$83,333.35
$111,111.13
$37,038.00
$18,517.53
EBT
-$33,333.35
-$59,611.13
$16,007.00
$36,118.82
Less: Tax @ 40%
-$13,333.34
-$23,844.45
$6,402.80
$14,447.53
Net Income
-$20,000.01
-$35,766.68
$9,604.20
$21,671.29
Add: Depreciation
$83,333.35
$111,111.13
$37,038.00
$18,517.53
Less: NWC
$22,500.00
$23,175.00
$23,870.25
$24,586.36
Add: After tax salvage value
$0.00
$0.00
$0.00
$15,000.00
Operating Cash flow
$40,833.34
$52,169.45
$22,771.95
$30,602.46
NPV = -$300,000 + [($40,833.34)/(1.12)] + [($52,169.45)/(1.12)2] + [($22,771.95)/(1.10)3] + [($30,602.46)/(1.12)4] = -$186,295.45
Expected NPV = (-$81,898.55 x 0.50) + ($36,734.28 x 0.25) + (-$186,295.45 x 0.25) = -$78,339.57
Standard Deviation of NPV = (Variance of NPV)1/2
= > [(-$81,898.55 + $78,339.57)2 x 0.50) + (-$36,734.28 + $78,339.57)2 x 0.25) + (-$186,295.45 + $78,339.57)2 x 0.25)]1/2 = $78,933.19
Coefficient of Variation = Standard Deviation / Expected Return
=> $78,933.19/-$78,339.57 = -1.0075
3 Year Schedule
Year
Basis
%
Depreciation Expense
Accumulated Depreciation
Ending Book Value
1
$250,000.00
33.333%
$83,333.35
$83,333.35
$166,666.65
2
$250,000.00
44.444%
$111,111.13
$194,444.48
$55,555.53
3
$250,000.00
14.815%
$37,038.00
$231,482.48
$18,517.53
4
$250,000.00
7.407%
$18,517.53
$250,000.00
$0.00
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