Consider a project to supply Detroit with 40,000 tons of machine screws annually
ID: 2651611 • Letter: C
Question
Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,400,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $850,000 and that variable costs should be $450 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-year project life. It also estimates a salvage value of $380,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $560 per ton. The engineering department estimates you will need an initial net working capital investment of $540,000. You require a 12 percent return and face a marginal tax rate of 38 percent on this project.
Suppose you’re confident about your own projections, but you’re a little unsure about Detroit’s actual machine screw requirement. What is the sensitivity of the project OCF to changes in the quantity supplied? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What is the sensitivity of NPV to changes in quantity supplied? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
Given the sensitivity number you calculated, what is the minimum level of output below which you wouldn’t want to operate? (Do not round intermediate calculations and round your final answer to the nearest whole number.)
Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,400,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $850,000 and that variable costs should be $450 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-year project life. It also estimates a salvage value of $380,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $560 per ton. The engineering department estimates you will need an initial net working capital investment of $540,000. You require a 12 percent return and face a marginal tax rate of 38 percent on this project.
Explanation / Answer
Answer
Base case NPV
Years
Quantity
Selling price
Variable cost
Contribution
Total contribution
Fixed cost
Profit
Salvage value
Depreciation tax benefit
Cost of investment
Working capital
Cashflow
Disc rate : 12%
Present value
per ton
per ton
Per ton
before tax
After tax
after tax
(Cost/ no of years) * tax rate
Salvage value( 1-tax rate)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
B-C
A*D
E-F
G*(1-tax rate)
H+I+J+K+L
M*N
0
0
0
0
0
0
0
0
0
0
0
-5400000
-540000
-5940000
1
-5940000
1
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.89
2270535.71
2
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.80
2027264.03
3
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.71
1810057.17
4
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.64
1616122.47
5
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.57
1442966.49
6
40000
560
-450
110
4400000
-850000
3550000
2201000
235600
342000
0
540000
3318600
0.51
1681306.04
Net present value
4908251.92
a. Suppose you’re confident about your own projections, but you’re a little unsure about Detroit’s actual machine screw requirement. What is the sensitivity of the project OCF to changes in the quantity supplied?
OCF means Operating Cashflow. So initial cost of investment and its salvage value will not be taken.
Base case Operating NPV
Years
Quantity
Selling price
Variable cost
Contribution
Total contribution
Fixed cost
Profit
Salvage value
Depreciation tax benefit
Cost of investment
Working capital
Cashflow
Disc rate : 12%
Present value
per ton
per ton
Per ton
before tax
After tax
after tax
(Cost/ no of years) * tax rate
Salvage value( 1-tax rate)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
B-C
A*D
E-F
G*(1-tax rate)
H+I+J+K+L
M*N
0
0
0
0
0
0
0
0
0
0
0
0
-540000
-540000
1
-540000
1
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.89
2270535.71
2
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.80
2027264.03
3
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.71
1810057.17
4
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.64
1616122.47
5
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.57
1442966.49
6
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
540000
3083000
0.51
1561943.75
Net present value of operating cashflow
10188889.63
Operating NPV if Quantity is reduced by 10%
Years
Quantity
Selling price
Variable cost
Contribution
Total contribution
Fixed cost
Profit
Salvage value
Depreciation tax benefit
Cost of investment
Working capital
Cashflow
Disc rate : 12%
Present value
per ton
per ton
Per ton
before tax
After tax
after tax
(Cost/ no of years) * tax rate
Salvage value( 1-tax rate)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
B-C
A*D
E-F
G*(1-tax rate)
H+I+J+K+L
M*N
0
0
0
0
0
0
0
0
0
0
0
0
-540000
-540000
1
-540000
1
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.89
2026964.29
2
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.80
1809789.54
3
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.71
1615883.52
4
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.64
1442753.14
5
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.57
1288172.45
6
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
540000
2810200
0.51
1423734.78
Net present value of operating cashflow
9067297.71
Particulars
Amount
operating NPV if quantity is reduced by 10%
a
9067297.711
Base case Operating NPV
b
10188889.63
Change (a-b)
c
-1121591.92
operating NPV decrease in % (c/b)*100
-11.01
b. What is the sensitivity of NPV to changes in quantity supplied?
Suppose sales quantity is reduced by 10% i.e. 36000 tonnes ( 40000 tonnes * 0.9)
Years
Quantity
Selling price
Variable cost
Contribution
Total contribution
Fixed cost
Profit
Salvage value
Depreciation tax benefit
Cost of investment
Working capital
Cashflow
Disc rate : 12%
Present value
per ton
per ton
Per ton
before tax
After tax
after tax
(Cost/ no of years) * tax rate
Salvage value( 1-tax rate)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
B-C
A*D
E-F
G*(1-tax rate)
H+I+J+K+L
M*N
0
0
0
0
0
0
0
0
0
0
0
-5400000
-540000
-5940000
1
-5940000
1
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.89
2026964.29
2
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.80
1809789.54
3
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.71
1615883.52
4
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.64
1442753.14
5
36000
560
-450
110
3960000
-850000
3110000
1928200
0
342000
0
0
2270200
0.57
1288172.45
6
36000
560
-450
110
3960000
-850000
3110000
1928200
235600
342000
0
540000
3045800
0.51
1543097.07
Net present value
3786660.00
Particulars
Amount
NPV if quantity is reduced by 10%
a
3786660.003
Base case NPV
b
4908251.92
Change (a-b)
c
-1121591.92
NPV decrease in % (c/b)*100
-22.85
c. Given the sensitivity number you calculated, what is the minimum level of output below which you wouldn’t want to operate?
We wouldn’t operate if Project gives nagative NPV. So minimum NPV is zero.
Particulars
Amount
NPV
a
0
Base case NPV
b
4908251.92
Change (a-b)
c
-4908251.92
NPV decrease in % (c/b)*100
d
-100.00
If NPV decrease in % (Answer b)
e
-22.85
then Quantity decrease in % (answer b)
f
10
Decrease in quantity in % when NPV is 0
43.76148
(d/e)*f
Quantity below which we won’t operate
22495.408
40000*(1-0.4376148)
Years
Quantity
Selling price
Variable cost
Contribution
Total contribution
Fixed cost
Profit
Salvage value
Depreciation tax benefit
Cost of investment
Working capital
Cashflow
Disc rate : 12%
Present value
per ton
per ton
Per ton
before tax
After tax
after tax
(Cost/ no of years) * tax rate
Salvage value( 1-tax rate)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
B-C
A*D
E-F
G*(1-tax rate)
H+I+J+K+L
M*N
0
0
0
0
0
0
0
0
0
0
0
-5400000
-540000
-5940000
1
-5940000
1
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.89
2270535.71
2
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.80
2027264.03
3
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.71
1810057.17
4
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.64
1616122.47
5
40000
560
-450
110
4400000
-850000
3550000
2201000
0
342000
0
0
2543000
0.57
1442966.49
6
40000
560
-450
110
4400000
-850000
3550000
2201000
235600
342000
0
540000
3318600
0.51
1681306.04
Net present value
4908251.92
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