We are evaluating a project that costs $1,446,000, has a six-year life, and has
ID: 2731069 • Letter: W
Question
We are evaluating a project that costs $1,446,000, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 88,600 units per year. Price per unit is $35.05, variable cost per unit is $21.30, and fixed costs are $766,000 per year. The tax rate is 30 percent, and we require a return of 11 percent on this project.
Calculate the base-case cash flow and NPV. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)
What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations.Round your answer to 3 decimal places (e.g., 32.161).)
If there is a 500-unit decrease in projected sales, how much would the NPV drop? (Do not round intermediate calculations. Input your answer as a positive value. Round your answer to 2 decimal places (e.g., 32.16).)
What is the sensitivity of OCF to changes in the variable cost figure? (A negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)
If there is $1 decrease in estimated variable costs, how much would the increase in OCF be? (Round your answer to the nearest whole dollar amount (e.g., 1,234,567).)
We are evaluating a project that costs $1,446,000, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 88,600 units per year. Price per unit is $35.05, variable cost per unit is $21.30, and fixed costs are $766,000 per year. The tax rate is 30 percent, and we require a return of 11 percent on this project.
Explanation / Answer
Requirement 1:
Calculation of Base Case Cash Flow:
Depreciation = Cost of the project / useful life
= $1446000 / 6
= $241000
Tax Shield on depreciation = Depreciation * Tax rate
= $241000 * 0.30
= $72300
Contribution Margin = (Selling Price – Variable Cost) * Units
= (35.05 – 21.30) * 88600
= $1218250
Profit = Contribution margin – Fixed costs
= $1218250 - $766000
= $452250
Base Cash Flows = Profits after tax + Tax Shield on depreciation
= $452250 (1-0.30) + $72300
= $388875
Base Cash Flows = $388875
Calculation of NPV:
Year
Cash Flow
PVF (11%)
PV of Cash Flow
0
-$1446000
1
-$1446000
1-6
$388875
4.2305
$1645135.6875
$199135.6875
NPV = $199135.69
Requirement 2:
Calculation of sensitivity of NPV:
Sales figure = $35.05 * 88600
= $3105430
Let Sales figure at which NPV is 0 be x
Variable Cost = $21.3 * 88600
= $1887180
Profit after tax = (x - 1887180) (1-0.3)
= 0.7x – 566154
Base Cash Flows = 0.7x – 566154 + 72300
= 0.7x – 493854
Calculation of NPV:
Year
Cash Flow
PVF (11%)
PV of Cash Flow
0
-$1446000
1
-$1446000
1-6
0.7x – 493854
4.2305
0.7x-2089249.347
$0.7x – 3535249.347
NPV should be equal to 0
Therefore,
0.7x – 3535249.347 = 0
0.7x = 3535249.347
x = $5050356.21
Change in sales = 3105430 – 5050356.21
= -1944926.21
Sensitivity = 1944926.21 / 3105430
= 62.63%
Sensitivity of NPV to changes in sales figure = 62.63%
Requirement 3:
Calculation of NPV drop:
Decrease in Sales units = 500
Revised Sales units = 88600 – 500 = 88100
Base Cash Flows:
Contribution Margin = (Selling Price – Variable Cost) * Units
= (35.05 – 21.30) * 88100
= $1211375
Profit = Contribution margin – Fixed costs
= $1211375 - $766000
= $445375
Base Cash Flows = Profits after tax + Tax Shield on depreciation
= $445375 (1-0.30) + $72300
= $384062.50
Base Cash Flows = $384062.50
NPV:
Year
Cash Flow
PVF (11%)
PV of Cash Flow
0
-$1446000
1
-$1446000
1-6
$384062.50
4.2305
$1624776.40625
$178776.40625
NPV drop = NPV at 88600 units – NPV AT 88100 units
= $199135.69 - $178776.40625
= $20359.28375
NPV drop = $20359.28
Requirement 4:
Calculation of Sensitivity of OCF to changes in variable cost figure:
Variable cost = $21.3 * 88600
= $1887180
Let Variable cost at which NPV is 0 be x
Variable Cost = $21.3 * x
= $21.3x
Profit after tax = (3105430 – 21.3x) (1-0.3)
= 2173801 – 14.91x
Base Cash Flows = 2173801 – 14.91x + 72300
= 2246101 – 14.91x
Calculation of NPV:
Year
Cash Flow
PVF (11%)
PV of Cash Flow
0
-$1446000
1
-$1446000
1-6
2246101 – 14.91x
4.2305
$9502130.2805 – 63.076755x
8056130.2805 – 63.076755x
NPV should be equal to 0
Therefore,
8056130.2805 – 63.076755x = 0
63.076755x = 8056130.2805
x = 127719.4789
Change in Variable Cost = 1887180 – 127719.4789
= 1759460.5211
Sensitivity = 1759460.5211 / 1887180
= 93.23%
Sensitivity of OCF = 93.23%
Requirement 5:
Calculation of Increase in NPV:
Decrease in Variable cost = $1
Revised Variable cost = 21.3 – 1 = $20.3
Base Cash Flows:
Contribution Margin = (Selling Price – Variable Cost) * Units
= (35.05 – 20.30) * 88600
= $1306850
Profit = Contribution margin – Fixed costs
= $1306850 - $766000
= $540850
Base Cash Flows = Profits after tax + Tax Shield on depreciation
= $540850 (1-0.30) + $72300
= $450895
Base Cash Flows = $450895
NPV:
Year
Cash Flow
PVF (11%)
PV of Cash Flow
0
-$1446000
1
-$1446000
1-6
$450895
4.2305
$1907511.2975
$461511.2975
Increase in NPV
= $461511.2975 - $199135.69
= $262375.6075
Increase in NPV = $262375.6075
Year
Cash Flow
PVF (11%)
PV of Cash Flow
0
-$1446000
1
-$1446000
1-6
$388875
4.2305
$1645135.6875
$199135.6875
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