We are evaluating a project that costs $874,000, has a thirteen-year life, and h
ID: 2740999 • Letter: W
Question
We are evaluating a project that costs $874,000, has a thirteen-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 114,000 units per year. Price per unit is $43, variable cost per unit is $20, and fixed costs are $880,118 per year. The tax rate is 34 percent, and we require a 12 percent return on this project.
Requirement 1:
Calculate the accounting break-even point.(Round your answer to the nearest whole number. (e.g., 32))
Requirement 2:
Calculate the base-case cash flow and NPV.(Do not include the dollar signs ($). 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 include the dollar sign ($). Round your answer to 3 decimal places. (e.g., 32.161))
Calculate the change in NPV If there is a 500-unit decrease in projected sales. (Do not include the dollar sign ($). Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16))
Requirement 3:
What is the sensitivity of OCF to changes in the variable cost figure? (Do not include the dollar sign ($). Negative amount should be indicated by a minus sign. Round your answer to the nearest whole number. (e.g., 32))
Calculate the change in OCF if there is a $1 decrease in estimated variable costs. (Do not include the dollar sign ($). Round your answer to the nearest whole number. (e.g., 32))
We are evaluating a project that costs $874,000, has a thirteen-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 114,000 units per year. Price per unit is $43, variable cost per unit is $20, and fixed costs are $880,118 per year. The tax rate is 34 percent, and we require a 12 percent return on this project.
Explanation / Answer
Requirement -1:
Calculate the accounting break-even point:
= Fixed cost / Contribution per unit
= $880,118 / ($43 -$20)
= 38,266 units
Requirement -2:
a.
Calculate the base-case cash flow and NPV:
Base cash flow:
= Sales value – variable cost – Fixed cost
= (114,000 *$43) – ($114,000 *$20) -$880,118
= $1,741,882
After tax = $1,741,882 * (1- 0.34)
= $1,149,642
Therefore, cash flow of every year is $1,149,642.
NPV:
Year
Cash flows
Discounting factor
@12%
Discounting
cash flows
0
$ (874,000)
1.000000
$ (874,000.00)
1
$ 1,149,642
0.892860
$ 1,026,469.36
2
$ 1,149,642
0.797190
$ 916,483.11
3
$ 1,149,642
0.711780
$ 818,292.18
4
$ 1,149,642
0.635520
$ 730,620.48
5
$ 1,149,642
0.567430
$ 652,341.36
6
$ 1,149,642
0.506630
$ 582,443.13
7
$ 1,149,642
0.452350
$ 520,040.56
8
$ 1,149,642
0.403880
$ 464,317.41
9
$ 1,149,642
0.360610
$ 414,572.40
10
$ 1,149,642
0.321970
$ 370,150.23
11
$ 1,149,642
0.287476
$ 330,494.48
12
$ 1,149,642
0.256680
$ 295,090.11
13
$ 1,149,642
0.229170
$ 263,463.46
NPV
$ 6,510,778.27
b.
Calculate the sensitivity of NPV to changes in the sales figure:
If sales units are increased to 115,000 units
= Sales value – variable cost – Fixed cost
= (115,000 *$43) – ($115,000 *$20) -$880,118
= $1,764,882
After tax = $1,764,882 * (1- 0.34)
= $1,164,822
Therefore, cash flow of every year is $1,164,822.
Year
Cash flows
Discounting factor
@12%
Discounting
cash flows
0
$ (874,000)
1.000000
$ (874,000.00)
1
$ 1,164,822
0.892860
$ 1,040,022.97
2
$ 1,164,822
0.797190
$ 928,584.45
3
$ 1,164,822
0.711780
$ 829,097.00
4
$ 1,164,822
0.635520
$ 740,267.68
5
$ 1,164,822
0.567430
$ 660,954.95
6
$ 1,164,822
0.506630
$ 590,133.77
7
$ 1,164,822
0.452350
$ 526,907.23
8
$ 1,164,822
0.403880
$ 470,448.31
9
$ 1,164,822
0.360610
$ 420,046.46
10
$ 1,164,822
0.321970
$ 375,037.74
11
$ 1,164,822
0.287476
$ 334,858.37
12
$ 1,164,822
0.256680
$ 298,986.51
13
$ 1,164,822
0.229170
$ 266,942.26
NPV
$ 6,608,287.70
Note: Assume sales units increased to 115,000 units.
c.
Calculate the change in NPV If there is a 500-unit decrease in projected sales:
If sales units are decreased by 500 units
= Sales value – variable cost – Fixed cost
= (113,500 *$43) – ($113,500 *$20) -$880,118
= $1,730,382
After tax = $1,730,382 * (1- 0.34)
= $1,142,052
Therefore, cash flow of every year is $1,142,052.
Year
Cash flows
Discounting factor
@12%
Discounting
cash flows
0
$ (874,000)
1.000000
$ (874,000.00)
1
$ 1,142,052
0.892860
$ 1,019,692.55
2
$ 1,142,052
0.797190
$ 910,432.43
3
$ 1,142,052
0.711780
$ 812,889.77
4
$ 1,142,052
0.635520
$ 725,796.89
5
$ 1,142,052
0.567430
$ 648,034.57
6
$ 1,142,052
0.506630
$ 578,597.80
7
$ 1,142,052
0.452350
$ 516,607.22
8
$ 1,142,052
0.403880
$ 461,251.96
9
$ 1,142,052
0.360610
$ 411,835.37
10
$ 1,142,052
0.321970
$ 367,706.48
11
$ 1,142,052
0.287476
$ 328,312.54
12
$ 1,142,052
0.256680
$ 293,141.91
13
$ 1,142,052
0.229170
$ 261,724.06
NPV
$ 6,462,023.56
Requirement 3:
a.
Calculate the sensitivity of OCF to changes in the variable cost figure:
If the variable cost $1 increase
= Sales value – variable cost – Fixed cost
= (114,000 *$43) – ($114,000 *$21) -$880,118
= $1,627,882
After tax = $1,627,882 * (1- 0.34)
= $1,074,402
Year
Cash flows
Discounting factor
@12%
Discounting
cash flows
0
$ (874,000)
1.000000
$ (874,000.00)
1
$ 1,074,402
0.892860
$ 959,290.57
2
$ 1,074,402
0.797190
$ 856,502.53
3
$ 1,074,402
0.711780
$ 764,737.86
4
$ 1,074,402
0.635520
$ 682,803.96
5
$ 1,074,402
0.567430
$ 609,647.93
6
$ 1,074,402
0.506630
$ 544,324.29
7
$ 1,074,402
0.452350
$ 486,005.74
8
$ 1,074,402
0.403880
$ 433,929.48
9
$ 1,074,402
0.360610
$ 387,440.11
10
$ 1,074,402
0.321970
$ 345,925.21
11
$ 1,074,402
0.287476
$ 308,864.79
12
$ 1,074,402
0.256680
$ 275,777.51
13
$ 1,074,402
0.229170
$ 246,220.71
NPV
$ 6,027,470.67
b.
Calculate the change in OCF if there is a $1 decrease in estimated variable costs:
If the variable cost $1 decrease
= Sales value – variable cost – Fixed cost
= (114,000 *$43) – ($114,000 *$19) -$880,118
= $1,855,882
After tax = $1,855,882 * (1- 0.34)
= $1,224,882
Year
Cash flows
Discounting factor
@12%
Discounting
cash flows
0
$ (874,000)
1.000000
$ (874,000.00)
1
$ 1,224,882
0.892860
$ 1,093,648.14
2
$ 1,224,882
0.797190
$ 976,463.68
3
$ 1,224,882
0.711780
$ 871,846.51
4
$ 1,224,882
0.635520
$ 778,437.01
5
$ 1,224,882
0.567430
$ 695,034.79
6
$ 1,224,882
0.506630
$ 620,561.97
7
$ 1,224,882
0.452350
$ 554,075.37
8
$ 1,224,882
0.403880
$ 494,705.34
9
$ 1,224,882
0.360610
$ 441,704.70
10
$ 1,224,882
0.321970
$ 394,375.26
11
$ 1,224,882
0.287476
$ 352,124.18
12
$ 1,224,882
0.256680
$ 314,402.71
13
$ 1,224,882
0.229170
$ 280,706.21
NPV
$ 6,994,085.87
Year
Cash flows
Discounting factor
@12%
Discounting
cash flows
0
$ (874,000)
1.000000
$ (874,000.00)
1
$ 1,149,642
0.892860
$ 1,026,469.36
2
$ 1,149,642
0.797190
$ 916,483.11
3
$ 1,149,642
0.711780
$ 818,292.18
4
$ 1,149,642
0.635520
$ 730,620.48
5
$ 1,149,642
0.567430
$ 652,341.36
6
$ 1,149,642
0.506630
$ 582,443.13
7
$ 1,149,642
0.452350
$ 520,040.56
8
$ 1,149,642
0.403880
$ 464,317.41
9
$ 1,149,642
0.360610
$ 414,572.40
10
$ 1,149,642
0.321970
$ 370,150.23
11
$ 1,149,642
0.287476
$ 330,494.48
12
$ 1,149,642
0.256680
$ 295,090.11
13
$ 1,149,642
0.229170
$ 263,463.46
NPV
$ 6,510,778.27
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