HW03 Solution: Lec 022: Cash Flows
Total 90 pt
1. (20 pt) NuBattery Inc. just developed a new battery for electric cars. Tesla has offered to buy
the technology from NuBattery for $120m (after-tax). However, NuBattery wants to explore the
feasibility of commercializing the technology on its own. The commercialization project will last
3 years.
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NuBattery has spent $20m on research and development (R&D) so far, which cannot be
recovered.
The commercialization project requires an investment of $90m on equipment at the
beginning of the project.
o The equipment will be depreciated according to the MACRS 3-year schedule over
the project’s 3-year life.
o The salvage value is $15m.
The sales are projected to be $100m, $120m, $210m for years 1, 2, and 3 respectively. Cash
operating costs are estimated to be 50% of sales.
Net working capital (NWC) requires an initial investment of $5m. Afterwards, the amount of
NWC (end of year balance) is estimated to be 10% of annual sales. At the end of the project,
all net working capital will be recovered.
At the end of the project, the technology is estimated to be worth $30m (after-tax) only in
the market (vs. $120m now) because competitors should have caught up by then.
NuBattery's current marginal tax rate is 30% and its cost of capital is 10%.
(i) Is the $20m spent on R&D so far an incremental cash flow that should be included in the NPV
analysis? Why? (1 pt)
No, it’s sunk cost.
(ii) What are the annual depreciation expenses? (1 pt)
0
Depreciation
1
2
3
30.00
40.01
13.33
Annual Dep = Initial Equipment Cost * Depreciation Schedule
(iii) What is the capital gain tax that the company has to pay when they sell the equipment at
the end of the project’s life? (3 pt)
BV = Initial Equip. Cost – Acc. Dep = 90 – (30+40.01+13.33) = 90 – 83.33 =6.67 (1 pt)
CG tax = (MV – BV)(T) = (15 – 6.67)(0.3) = 2.50 (1 pt)
(iv) Use the (a) NPV and (b) IRR decision rules to determine whether NuBattery should take on
the commercialization project or not. (15 pt)
(all in $m)
Year
(1) Operating Cash Flows (OCF):
Sales
- Operating costs
-Depreciation
= EBIT
(1) OCF = EBIT(1-T)+Dep (4 pt)
(2) Other CFs:
Equipment (2 pt)
NWC Cash Flow (2 pt)
Opportunity cost (2 pt)
(2) Other CFs
(3) Total Incremental Cash Flows = (1)+(2) (1 pt)
MACRS
Operating expenses (% Sales)
Operating expenses
NWC (% Sales)
NWC
CG taxes:
Accumulated depreciation
BV = Capex - Accum. Dep
MV (salvage)
CG tax = (MV - BV)*T
Tax rate
Discount rate
NPV (2 pt)
IRR (2 pt)
0
1
2
3
0
100
50
30.00
20.00
44.00
120
60
40.01
20.00
54.00
210
105
13.33
91.67
77.50
-5
-2
-5
-2
12.50
12
30
54.50
-215.00
39.00
52.00
132.00
0.4445
50%
60
10%
12
0.1481
50%
105
5
0.3333
50%
50
10%
10
-90
-5
-120
-215
0
83.33
6.67
15.00
2.50
30%
10%
-37.40 < 0
1.53% <10%
=> Reject!
=> Reject!
2. (15 pt) The GreenBall Inc. is evaluating the possibility of entering the golf ball manufacturing
business. Last month the company spent $15m to rent the equipment for a small scale test run.
Based on the results of the test run, the company came up with the following estimates:
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The equipment has to be purchased at the beginning of the project (year 0). The original
cost of the equipment is $105m, but the company can deduct the $15m payment it
made to the equipment supplier last month for the test run if the company decides to
purchase the equipment. The original cost of the equipment, $105m, will be
depreciated straight line to zero over the project's 3-year life. The end-of-life salvage
value is $30m.
The planned factory site is currently rented out to a neighboring company. If the
company decides to enter the golf ball manufacturing business, it will lose $25m in
after-tax rental income every year during the project's 3-year life.
Sales of golf balls are projected to be $90m, 210m, and $160m, for years 1,2, and 3
respectively; operating expenses are estimated to be 50% of sales.
Net working capital (NWC) investment of $3m is needed at the beginning of the project
(year 0). Afterwards, an additional annual investment (or spending) of $5m is necessary
for years 1-2. At the end of the project, all NWC will be recovered.
The company's average tax rate is 25% and its marginal tax rate is 30%
The company’s cost of capital is 10%.
Use the NPV decision rule to determine whether GreenBall Inc. should enter the golf ball
manufacturing business or not. (15 pt)
(all in $m)
Year
(1) OCF
Sales
- Operating expenses
- Depreciation
= EBIT
(1) OCF = (EBIT)*(1-T)+Dep (4 pt)
(2) Other CFs
Equipment (4 pt)
NWC Cash Flow (2 pt)
Opportunity cost (2 pt)
(2) Other CFs
(3) Total Incremental Cash Flow (1 pt)
Operating expenses (% Sales)
0
1
2
3
0
90
45
35
10
42
210
105
35
70
84
160
80
35
45
66.5
-93
-5
-25
-30
-5
-25
-30
21
13
-25
9
-93
12
54
75.5
50%
50%
50%
-90
-3
Tax rate
30%
Discount rate
10%
NPV (1 pt)
19.26
NPV > 0, the company should enter the golf ball manufacturing business (1 pt)
3. (all numbers are in thousands; 8 pt)
Jaffrey Inc. is considering the purchase of an automation machine with a cost of $350. The
machine has an economic life of 5 years. It will be fully depreciated over the 5-year life using
the straight-line method, and then be sold at $70 at the end of the 5-year life. The machine will
replace 2 workers whose combined annual salaries are $100. However, this machine also
requires additional investment in net working capital of $30 in the beginning, which will be fully
recovered at the end of the machine’s life. The marginal tax rate is 30%.
Is it worthwhile to purchase this automation machine if the company’s required rate of return
is 10%?
(all in $000s)
(1) OCF
Sales
Operating costs
Depreciation
EBIT
(1) OCF = EBIT(1-t) + Dep (4 pt)
0
1
2
3
4
5
0
0
-100
70
30
91
0
-100
70
30
91
0
-100
70
30
91
0
-100
70
30
91
0
-100
70
30
91
(2) Other CFs
Equipment (2 pt)
NWC CF (1 pt)
(2) Other CFs
-350
-30
-380
0
0
0
0
49
30
79
(3) Total Incremental CFs
-380
91
91
91
91
170
Tax rate
Discount rate
30%
10%
NPV (1 pt)
14.01
>0
==> Accept!
4. The Locker Co. has $250,000 in taxable income. (10 pt)
(i) What are the company’s income taxes according to the tax rate table below? (5 pt)
Taxable Income Bracket
0 – $50,000
$50,000 - $75,000
$75,000 - $100,000
$100,000 - $335,000
Marginal Tax Rate (%)
15
25
34
39
(in thousands)
Taxes = (50)(0.15) + (75-50)(0.25) + (100-75)(0.34) + (250-100)(0.39)
= 7.5 + 6.25 + 8.5 + 58.5 = 80.75
(ii) What is the company’s average tax rate? (2 pt)
Average tax rate = 80.75/250 = 32.3%
(ii) Locker Co is evaluating a new project, which is projected to increase the company’s taxable
income from its current level of $250,000 to $330,000. What is the tax rate the company
should use in estimating the incremental free cash flows of the new project? Briefly
describe your reasoning. (3 pt)
$250,000 - $330,000 falls in the 39% tax bracket, so the company should use 39%, i.e. its
marginal tax rate, in estimating the new project’s incremental cash flows.
5. (7 pt) Your boss is evaluating two printers for the office.
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Printer A costs $500, has an annual operating cost of $60, and will last 5 years.
Printer B costs $300, has an annual cost of $150, and will last 3 years.
One of your colleagues conducts an NPV analysis based on your company's cost of capital of
10%. (cash flows and NPVs shown in the following table). He thinks that since NPV of Printer B >
NPV of Printer A, the office should purchase Printer B.
Year
Printer A Cash Flows
Printer A NPV
0
-500
-727.45
1
-60
2
-60
3
-60
Printer B Cash Flows
Printer B NPV
-300
-673.03
-150
-150
-150
4
-60
(i) Do you agree with your colleague's analysis and recommendation? Why? (2 pt)
These two printers have different lives, so looking at the NPV of the project's life is not
appropriate. (2 pt)
5
-60
(ii) If you were to analyze this problem, what would be your recommendation? Show your
analysis and the numbers that help you reach your recommendation. (5 pt)
We should look at EAC (equivalent annual cost) instead. The EACs are as follows:
Year
A's CF for EAC
A's NPV of EAC
0
1
-191.90
2
-191.90
3
-191.90
-270.63
-270.63
-270.63
4
-191.90
5
-191.90
-727.45
B's CF for EAC
B's NPV of EAC
-673.03
Cost of capital
10%
EAC(A) = 191.90 (since it's a cost, the sign in the table above is negative) (2 pt)
EAC(A): N=5, I=10%, PV=-727.45, FV=0 => PMT=191.90
EAC(B) = 270.63 (2 pt).
EAC(A): N=3, I=10%, PV= -673.03, FV=0 => PMT=270.63
=> Printer A's cost is cheaper on an annual basis, so we should choose Printer A. (1 pt)
6. (10 pt) Could you think of one example in real life where you apply the knowledge you
acquired in this lecture to analyze the problem and come up with a decision? Illustrate with
numbers and calculations. If you cannot think of any example, you can make up a problem
based on the material in this lecture and then perform an analysis to solve it.
7. (5 pt) Which concepts in this lecture do you find most interesting? Why?
8. (5 pt) Which concepts in this lecture do you find a bit difficult to comprehend? What can the
professor do to help you better under them?
Formula Sheet
Lec 022
(1) Cash Flow of the Firm = Operating Cash Flows (OCF) + Other Cash flows (equipment
buy/sale, NWC, opportunity cost etc.)
(2) OCF (top-down) = Sales – Costs – Taxes
(3) OCF (bottom-up) = (EBIT – Taxes) + Depreciation = EBIT*(1-T) + Depreciation
(4) EBIT = Sales – Costs – Depreciation
(5) Taxes = EBIT*T = (Sales – Costs – Depreciation)*T
(6) Salvage after-tax = MV - Capital gain taxes = MV - (MV - BV)*T
(7) BV = Initial Cost of Equipment – Accumulated Depreciation
(8) 1 + nominal rate = (1 + real rate) * (1 + inflation)
(9) Real CF = Nominal CF / (1 + inflation)
(10)
MACRS Schedule