Student Name: __________________________
Spring 2023
Finance – Problem Set 6
Cash Flow Analysis
This problem set can be done in group, but individual submission is required. The problem set is due on
Wednesday, 3/29/2023 in class.
The problem set is graded on a completion basis. Points will be taken off from a total of 100 for any
unfinished work.
---------------------------------------1. Tubby Toys is considering investing in a new machine for $10m that allows it to produce a new line
of rubber ducks. It estimates that this new line will generate sales of $7m and operating costs of $4m.
It thinks that the machine will work for 5 years and can be sold for $2m after that.
a. If the tax rate is 35% and the company’s required rate of return is 12%, what is the NPV of
the project?
b. After the initial proposal, Tubby Toys’ managers realized that in order for sustain the project,
they need to make an investment in working capital of $1m in the same year that they
purchase the machine. This level of working capital will stay the same in subsequent years.
This investment in working capital will be recovered when they sell the machine. What will
the new NPV be?
Answer: a. $182,842; b. -$249,731
Part a.
Year
Capital Investment (1)
0
1
2
3
4
5
2m
(10m)
Working Capital
Change in Working Capital (WCt – WCt-1) (2)
Operating Cash Flow
Revenue
7m
7m
Depreciation
4m
1.6m
4m
1.6m
Pre-tax Income (Revenue – Costs – Depreciation)
1.4m
Costs
Taxes (35% pretax income)
.490m
After-tax Income (Pre-tax income – Taxes)
.910m
OCF (added Depreciation) (3)
2.510m
Total Cash Flow (1 + 2 + 3)
(10m)
Present Values of Cash Flows
(10m)
NPV (sum of all Present Values)
.183m
2.510m
2.241m
7m
7m
7m
4m
1.6m
4m
4m
1.6m
1.6m
1.4m
1.4m
1.4m
1.4m
.490m
.490m
.490m
.490m
.910m
2.510m
.910m
.910m
.910m
2.510m
2.510m
2.510m
2.510m
2.510m
2.510m
4.510m
2.001m
1.787m
1.595m
2.559m
Student Name: __________________________
Spring 2023
Part b.
Year
Capital Investment (1)
Working Capital
Change in Working Capital (WCt – WCt-1) (2)
0
1
2
3
4
(10m)
5
2m
(1m)
(1m)
(1m)
-
(1m)
-
(1m)
-
(1m)
7m
7m
7m
-
1m
Operating Cash Flow
Revenue
7m
Costs
4m
Depreciation
1.6m
4m
4m
7m
4m
4m
1.6m
1.6m
1.6m
1.6m
Pre-tax Income (Revenue – Costs – Depreciation)
1.4m
1.4m
1.4m
1.4m
Taxes (35% pretax income)
.490m
.490m
.490m
.490m
After-tax Income (Pre-tax income – Taxes)
.910m
.910m
.910m
.910m
.910m
OCF (added Depreciation) (3)
2.510m
2.510m
2.510m
2.510m
2.510m
2.510m
2.510m
5.510m
1.787m
1.595m
Total Cash Flow (1 + 2 + 3)
(11m)
2.510m
Present Values of Cash Flows
(11m)
2.241m
NPV (sum of all Present Values)
(.250m)
2.510m
2.001m
1.4m
.490m
3.127m
Student Name: __________________________
Spring 2023
2. Kinky Copies may buy a high-volume copier. The machine costs $100,000 and will be depreciated
straight-line over 5 years to a salvage value of $20,000. Kinky anticipates that the machine can
actually be sold in 5 years for an after-tax amount of $30,000. The machine will save $20,000 a year
in labor costs, but will require an increase in working capital initially, mainly paper supplies, of
$10,000. The firm’s marginal tax rate is 35%, and the discount rate is 8%. Should Kinky buy the
machine?
Answer: −$8,512
Hint: Depreciation is calculated based on salvage value of $20,000  depreciation = (100,000 –
20,000)/5 = 16,000, while the actual amount sold is 30,000 (in year 5). Also, since the machine save labor
cost, we assume that it is the revenue and there is no cost from the project.
Year
0
Capital Investment (1)
(100,000)
Working Capital
(10,000)
Change in Working Capital (WCt – WCt-1) (2)
(10,000)
1
2
3
4
(10,000)
(10,000)
(10,000)
(10,000)
-
-
-
-
5
30,000
10,000
Operating Cash Flow
Revenue
20,000
20,000
16,000
16,000
Pre-tax Income (Revenue – Costs – Depreciation)
4,000
4,000
Taxes (35% pretax income)
1,400
1,400
After-tax Income (Pre-tax income – Taxes)
2,600
2,600
2,600
18,600
18,600
18,600
20,000
20,000
20,000
16,000
16,000
16,000
4,000
4,000
4,000
1,400
1,400
2,600
2,600
18,600
18,600
Costs
Depreciation
OCF (added Depreciation) (3)
Total Cash Flow (1 + 2 + 3)
(110,000)
18,600
18,600
Present Values of Cash Flows
(110,000)
17,222
15,947
NPV (sum of all Present Values)
(8,512)
1,400
18,600
14,765
18,600
58,600
13,672
39,882
Student Name: __________________________
Spring 2023
3. The Marx Brewing Company recently installed a new bottling machine. The machine’s initial cost is
$120,000, and can be depreciated on a straight-line basis to zero salvage in 5 years. The machine’s
fixed cost per year is $1,800, and its variable cost is $0.50 per unit. The selling price per unit is $1.50.
Marx estimated that they will be able to sell 60,000 units per year. Additionally, they have to invest in
$20,000 of working capital initially to set up the machine, and this level of working capital stays the
same in subsequent years. Marx’s tax rate is 34%, and it uses a 16% discount rate. Calculate the NPV
of the new machine.
Answer: $22,013
Hint: Please note that the costs now include both fixed cost of $1,800 per year and variable cost
($0.50 per unit x 60,000 units per year).
Year
0
Capital Investment (1)
(120,000)
Working Capital
(20,000)
Change in Working Capital (WCt – WCt-1) (2)
1
(20,000)
2
3
(20,000) (20,000)
4
5
(20,000)
(20,000)
20,000
Operating Cash Flow
Revenue
90,000
90,000
90,000
90,000
90,000
30,000
30,000
Costs
30,000
30,000
Depreciation
24,000
24,000
24,000
24,000
24,000
Pre-tax Income (Revenue – Costs – Depreciation)
34,200
34,200
34,200
34,200
34,200
Taxes (34% pretax income)
11,628
11,628
11,628
11,628
After-tax Income (Pre-tax income – Taxes)
22,572
22,572
22,572
22,572
22,572
OCF (added Depreciation) (3)
46,572
46,572
46,572
46,572
46,572
11,628
30,000
Total Cash Flow (1 + 2 + 3)
(140,000)
46,572
46,572
46,572
Present Values of Cash Flows
(140,000)
40,148
34,611
29,837
NPV (sum of all Present Values)
22,013
46,572
25,721
66,572
31,696