Canyon Tours showed the following components of working capital last year:
Beginning of Year End of
Year
Accounts receivable $ 27,800 $24,900
Inventory 13,900 16,300
Accounts payable 16,400 20,300
a. What was the change in net working capital during the year? (A
negative amount should be indicated by a minus sign.)
b. If sales were $37,900 and costs were $25,900, what was cash flow for the
year? Ignore taxes.
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should
be used for actual calculations.
a.
ΔNWC = Ending NWC – Beginning NWC
= (Ending current assets – Ending current liabilities) – (Beginning current assets – Beginning current liabilities)
= ($24,900 + $16,300 – $20,300) – ($27,800 + $13,900 – $16,400)
= –$4,400
b.
Cash flow = $37,900 – $25,900 – (–$4,400)
= $16,400
The firm reduced its investment in net working capital during the year which increased the firm’s
cash flow.
A firm had after-tax income last year of $1.4 million. Its depreciation expenses
were $0.6 million, and its total cash flow was $1.4 million. What happened to
net working capital during the year? (Enter your answer in millions
rounded to 1 decimal place.)
Explanation
Cash flow = Net income + Depreciation – Increase in net working capital
$1.4m = $1.4m + 0.6m – ΔNWC
ΔNWC = $0.6 million
The efficiency gains resulting from a just-in-time inventory management
system will allow a firm to reduce its level of inventories permanently by
$379,000. What is the most the firm should be willing to pay for installing the
system?
Explanation
If the savings are permanent, then the inventory system is worth $379,000 to the firm. The firm can
take $379,000 out of the project now without ever having to replace it. So the most the firm should
be willing to pay is $379,000.
Better Mousetraps has developed a new trap. It can go into production for an
initial investment in equipment of $6.6 million. The equipment will be
depreciated straight-line over 6 years, but, in fact, it can be sold after 6 years
for $643,000. The firm believes that working capital at each date must be
maintained at a level of 15% of next year’s forecast sales. The firm estimates
production costs equal to $1.90 per trap and believes that the traps can be
sold for $6 each. Sales forecasts are given in the following table. The project
will come to an end in 6 years, when the trap becomes technologically
obsolete. The firm’s tax bracket is 40%, and the required rate of return on the
project is 12%.
Year: 0 1 2 3 4 5 6 Thereafter
Sales (millions of traps)0 0.4 0.5 0.7 0.7 0.5 0.3 0
Suppose the firm can cut its requirements for working capital in half by using
better inventory control systems. By how much will this increase project
NPV? (Do not round your intermediate calculations. Enter
your answer in millions rounded to 4 decimal places.)
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should
be used for actual calculations.
All cash flows are in millions of dollars.
Year 0 1 2 3 4 5 6
Sales units $ 0.400 $ 0.500 $0.700 $0.700 $0.500 $0.300
NWC $ 0.360 $ 0.450 $ 0.630 $0.630 $0.450 $0.270 $ 0.00
Cash flow
NWC $–
0.360 $ –
0.090 $ –
0.180 $ 0.00 $0.180 $0.180 $0.270
If working capital requirements were only one-half of the expected amount, then the working capital
cash-flow forecasts would change as follows:
Year 0 1 2 3 4 5 6
New NWC $ 0.180 $ 0.225 $ 0.315 $0.315 $ 0.225 $ 0.135 $ 0.00
New cash
flow NWC $–
0.180 $ –
0.045 $ –
0.090 $ 0.00 $ 0.090 $ 0.090 $ 0.135
Change in
cash flow $ 0.180 $ 0.045 $ 0.090 $ 0.00 $ –
0.090 $ –
0.090 $ –
0.135
Change in NPV = $0.1153 million
Quick Computing currently sells 16 million computer chips each year at a
price of $30 per chip. It is about to introduce a new chip, and it forecasts
annual sales of 18 million of these improved chips at a price of $38 each.
However, demand for the old chip will decrease, and sales of the old chip are
expected to fall to 2 million per year. The old chips cost $15 each to
manufacture, and the new ones will cost $18 each. What is the proper cash
flow to use to evaluate the present value of the introduction of the new
chip? (Enter your answer in millions.)
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should
be used for actual calculations.
Gross revenues from new chip = 18 million × $38 = $684 million
Cost of new chip = 18 million × $18 = $324 million
Lost sales of old chip = 14 million × $30 = $420 million
Saved costs of old chip = 14 million × $15 = $210 million
Increase in cash flow = ($684 − $324) − ($420 − $210) = $150 million
Tubby Toys estimates that its new line of rubber ducks will generate sales of
$6.30 million, operating costs of $3.30 million, and a depreciation expense of
$0.30 million. If the tax rate is 30%, what is the firm’s operating cash
flow? (Do not round your intermediate calculations. Enter
your answer in millions rounded to 2 decimal places.)
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should
be used for actual calculations.
Net income = ($6.30 − $3.30 − $0.30) − [0.30 × ($6.30 − $3.30 − $0.30)] = $2.70 − $0.81 = $1.89
million
Revenues − cash expenses − taxes paid = $3.00 − $0.81 = $2.19 million
Alternatively,
After-tax profit + depreciation = $1.89 + $0.30 = $2.19 million
Alternatively,
(Revenues − cash expenses) × (1 − tax rate) + (depreciation × tax rate) = ($3.00 × 0.70) +
($0.30 × 0.30) = $2.19 million
The owner of a bicycle repair shop forecasts revenues of $172,000 a year.
Variable costs will be $53,000, and rental costs for the shop are $33,000 a
year. Depreciation on the repair tools will be $13,000.
a. Prepare an income statement for the shop based on these estimates. The
tax rate is 20%.
b. Calculate the operating cash flow for the repair shop using the three
methods given below:
Now calculate the operating cash flow.
i. Dollars in minus dollars out.
ii. Adjusted accounting profits.
iii. Add back depreciation tax shield.
rev: 11_13_2019_QC_CS-189854
Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should
be used for actual calculations.
a.
Pretax
profit = Revenue – Rental costs – Variable costs – Depreciation
= $172,000 – $33,000 – $53,000 – $13,000
= $73,000
Taxes = Tax rate × Pretax profit
= 0.20 × $73,000
= $14,600
Net income = Pretax profit – Taxes
= $73,000 – $14,600
= $58,400
b.
The Cash Flows:
i. Revenue − rental costs − variable costs − taxes
= $172,000 − $33,000 − $53,000 − $14,600 = $71,400
ii. Net income + depreciation = $58,400 + $13,000 = $71,400
iii. [(Revenue − rental costs − variable costs) × (1 − 0.20)] + (depreciation × 0.20)
= [($172,000 − $33,000 − $53,000) × 0.80] + ($13,000 × 0.20)
= $68,800 + $2,600 = $71,400
Laurel’s Lawn Care Ltd., has a new mower line that can generate revenues of
$129,000 per year. Direct production costs are $43,000, and the fixed costs of
maintaining the lawn mower factory are $16,500 a year. The factory originally
cost $0.86 million and is being depreciated for tax purposes over 20 years
using straight-line depreciation. Calculate the operating cash flows of the
project if the firm’s tax bracket is 25%. (Enter your answer in dollars
not in millions.)
Explanation
Revenue $129,000
Variable costs 43,000
Fixed costs 16,500
Depreciation 43,000
Pretax profit 26,500
Taxes (25%) 6,625
Net income 19,875
Depreciation 43,000
Operating cash flow $ 62,875
Gluon Inc. is considering the purchase of a new high pressure glueball. It can
purchase the glueball for $70,000 and sell its old low-pressure glueball, which
is fully depreciated, for $12,000. The new equipment has a 10-year useful life
and will save $16,000 a year in expenses. The opportunity cost of capital is
9%, and the firm’s tax rate is 21%. What is the equivalent annual saving from
the purchase if Gluon can depreciate 100% of the investment
immediately. (Do not round intermediate calculations. Round
your answer to 2 decimal places.)
Explanation
The EAC (Equivalent Annual Cost) is composed of the sum of the initial expense, the after-tax
proceeds of the sale of the old unit, and the Present Value of the annual ongoing cost spread over
each of the 10 years of the operating life of the unit.
If the firm can depreciate 100% of the investment immediately, then all the Depreciation Tax Shield
benefit falls in the first year. ,
Initial Expense: Cost − Tax Shield = −$70k + ($70k × 0.21) = −$55.30k
Sale of Old Unit: Sale price − Tax on fully depreciated gain = $12k − ($12k × 0.21) = +$9.48k
PV of Operating Savings:
The annual savings:
+$16k Reduced Expenses (although higher taxable income)
−$(16k × 0.21) Increase in taxes due to higher taxable income
= +$12.64k
The Present Value (today) of the annual savings:
[$12.64k × annuity factor (9%, 10 years)] = +$81,119.19
Adding those 3 elements = +$35,299.19, which is the Net Present Value of the purchase.
Calculating the EAC means we have to find the amount which, if saved every year for 10 years,
would have a Present Value of that same amount.
So we know: $35,299.19 = Χ annuity factor (9%, 10 years)]
C = EAC = $5,500.32
Johnny’s Lunches is considering purchasing a new, energy-efficient grill. The
grill will cost $38,000 and will be depreciated straight-line over 3 years. It will
be sold for scrap metal after 5 years for $9,500. The grill will have no effect on
revenues but will save Johnny’s $19,000 in energy expenses. The tax rate is
30%.
Required:
a. What are the operating cash flows in each year?
b. What are the total cash flows in each year?
c. Assuming the discount rate is 12%, calculate the net present value (NPV)
of the cash flow stream. Should the grill be purchased?
Explanation
Some values below may show as rounded for display purposes, though unrounded
numbers should be used for actual calculations.
a.
In the following table, we compute the impact on operating cash flows by summing the
value of the depreciation tax shield (depreciation × tax rate) plus the net-of-tax
improvement in operating income [$19,000 × (1 – tax rate)].
(SEE CHART IN DEHK CH9 to 13 WORKING PAPERS, Excel worksheet for Q11)
Depreciation
% Depreciation Depreciation × 0.30
ΔOperating
Income(1 –
0.30)
Contribution to
Operating Cash flow
0.3333 $12,667 $3,800.00 $13,300 $17,100.00
0.3333 12,667 $3,800.00 13,300 $17,100.00
0.3333 12,667 $3,800.00 13,300 $17,100.00
0 0 $ 0.00 13,300 $13,300.00
0 0 $ 0.00 13,300 $13,300.00
b.
Total cash flow = operating cash flow + cash flow associated with investments.
At time 0, the cash flow from the investment is –$38,000.
When the grill is sold at the end of year 5, its book value will be $0, so the sales price,
net of tax, will be $9,500 – [0.30 × $9,500] = $6,650.
Therefore, total cash flows are:
Time Cash Flow
0 -$38,000.00
1 17,100.00
2 17,100.00
3 17,100.00
4 13,300.00
5 19,950.00
[ = 13,300 operating delta + 6,650 net from sale of grill]
c.
The net present value of this cash-flow stream, at a discount rate of 12%, is $22,843.94,
which is positive. So the grill should be purchased.
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