Assignment #1 Solution (Chapters 3 and 5)
8.
a.
Cash will increase. The sale of a non-cash current asset (inventory) generates cash.
Working capital may not change if the cash received for the inventory equals the
recorded value of the inventory.
b.
Cash will increase. The machine will bring in cash when it is sold, but the lease
payments will be made over several years.
c.
The firm will use cash to buy back the shares from existing shareholders. Cash
balance will decrease.
16. a.
Assume that depreciation equals CCA. If the firm paid taxes of $2,000, and the
average tax rate was 20%, then taxable income must have been $2,000/.20 = $10,000.
Therefore:
net income = taxable income  taxes = $8,000.
b.
Revenues
- Cost of goods sold
- Administrative expenses
- Depreciation expense
- Interest expense
Taxable income
???
8,000
3,000
1,000
1,000
$10,000 [from (a)]
We conclude that revenues were $23,000.
c.
17. a.
Revenue
 Cost of goods sold
 Administrative expenses
 Depreciation expense
EBIT
$23,000
8,000
3,000
1,000
$11,000
Note: assume depreciation equals CCA
Sales
 Cost of goods sold
 Interest expense
 Depreciation expense
Taxable income
 Taxes (35%)
Net income
$14 million
8
1
2
3
1.05
$ 1.95 million
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Cash flow from operations = NI + depreciation
– change in non-cash net working capital = $3.95 million
Cash flow from assets = Cash flow from operations – capital expenditures
= 3.95 – 1 = $2.95 million
b.
If depreciation were $1 million higher, taxable income would be $2 million,
taxes would be .35  2, or $.7 million and net income would be 2 – .7, or $1.3
million. Thus, net income would be lower by $0.65 million. Cash flow from
operations (= net income + depreciation) would be 1.3 + 3, or $4.3 million,
higher by 4.3 – 3.95, or $0.35 million. Cash flow from assets (= net income +
depreciation – increase in net working capital – capital expenditures) would
also increase by $0.35 million. Cash flow increases because depreciation is not
a cash outflow, but increasing the depreciation expense for tax purposes
reduces taxes paid by $0.35 million.
c.
The impact on stock price is likely to be positive. Cash available to the firm
would increase. The reduction in net income would be recognized as due
purely to accounting changes, and not as reflecting any changes in the
underlying profitability of the firm.
d.
If interest expense were $1 million higher, net income, operating cash flow
and cash flow from assets would decrease by $0.65 million, i.e., by the $1
million increase in expenses less the $0.35 million reduction in taxes. This
differs from part (b) because, in contrast to depreciation, interest expense
represents an actual cash outlay.
19. a.
Cash flow to bondholders = interest + debt repayment – new debt issued
= 500,000 + 3,700,000 – 2,000,000 = $2,200,000
b.
Cash flow to shareholders = dividends + share repurchases – new shares issued
= 425,000 – 1,750,000 = –$1,325,000
c.
Financing flow = cash flow to bondholders + cash flow to shareholders + increase in
cash in the bank = $2,200,000 –$1,325,000 + $300,000 = $1,175,000
Since cash flow from assets must equal financing flow, the cash flow from assets also
equals $1,175,000.
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Chapter 4
21.
a.
PV = 100  annuity factor(6%, 3 periods)
= 100  Ошибка!= $267.30
b.
26.
a.
If the payment stream is deferred by an extra year, each payment will be
discounted by an additional factor of 1.06. Therefore, the present value is
reduced by a factor of 1.06 to 267.30/1.06 = $252.17.
Compare the present value of the lease to cost of buying the truck.
PV lease = 8,000 × PVIFA(7%, 6) = -$38,132.32
It is cheaper to lease than buy because by leasing the truck will cost only
$38,132.32, rather than $40,000. Of course, the crucial assumption here is that the
truck is worthless after 6 years. If you buy the truck, you can still operate it after 6
years. If you lease it, you must return the truck and replace it.
b.
If the lease payments are payable at the start of each year, then the present value of
the lease payments are:
PV annuity due lease = 8,000 + 8,000 × PVIFA(7%, 5) = 8,000 + 32,801.58 =
$40,801.58. Note too that PV of an annuity due = PV of ordinary annuity  (1 +
r). Therefore, with immediate payment, the value of the lease payments increases
from its value in the previous problem to $38,132  1.07 = $40,801 which is
greater than $40,000 (the cost of buying a truck). Therefore, if the first payment on
the lease is due immediately, it is cheaper to buy the truck than to lease it.
39. The PV of the payments under option (a) is 11,000, assuming the $1,000 rebate is paid
immediately. The PV of the payments under option (b) is
$250  annuity factor(1%, 48 months) = $9,493.49
Option (b) is the better deal.
53. a.
The present value of the ultimate sales price is 4 million/(1.08)5 = $2.722
million.
b.
The present value of the sales price is less than the cost of the property, so this
would not be an attractive opportunity.
c.
The value of the total cash flows from the property is now
PV = .2  annuity factor(8%, 5 years) + 4/(1.08)5
= .80 + 2.72 = $3.52 million
To solve with a calculator, enter: PMT = .2, FV = 4, i = 8%, n = 5 and compute
PV.
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Therefore, the property is an attractive investment if you can buy it for $3
million.
73. a.
$30,000  annuity factor(10%, 15 years) = $228,182
b.
Fin the annual payment, PMT, such that PMT × future value annuity
factor(10%, 30 years) = 228,182. Using the calculator, PV = 0, n=30, i= 10%,
FV= (-) 228,182. Compute PMT = 1,387. You must save $1,387 annually.
c.
1.00  (1.04)30 = $3.24
d.
We repeat part (a) using the real rate of 1.10/1.04 – 1 = .0577 or 5.77%
The retirement goal in real terms is
$30,000  annuity factor(5.77%, 15 years) = $295,797
e.
The future value of your 30-year saving stream must equal this value. So we
solve for payment (PMT) in the following equation
PMT  future value annuity factor(5.77%, 30 years) = $295,797
PMT  75.930 = $295,797
PMT = 3,896
You must save $3896 per year in real terms. This value is much higher than
the answer to (b) because the rate at which purchasing power grows is less
than the nominal interest rate, 10%.
f.
78.
If the real amount saved is $3,896 and prices rise at 4 percent per year, then
the amount saved at the end of one year in nominal terms will be $3,896 
1.04 = $4,052. The thirtieth year will require nominal savings of 3,896 
(1.04)30 = $12,636.
The answer to this question can be found in various ways. The key is to pick a
common point in time to measure all cash flows. Here we pick today as the common
reference point.
Monthly interest rate = 1.061/12 – 1 = .004868 = .4868%.
Present value today of the funds need for boat: 150,000/(1.06)4 = 118,814
Funds need for monthly expenses (this is an annuity due)
= (2200 + 2200×annuity factor(.4868%, 23 months))/ (1.06)5
= 37,333.29
Funds need for emergencies = 45,000/(1.06)5 = 33,626.62
Total funds needed = 118,814 + 37,333.29 + 33,626.62 = 189,774
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The present value of the savings stream must equal the present value of the
expenditures:
PMT × annuity factor (.4868%,60 months) = 189,774
The monthly savings must be $3,654.9. (Expect slight variations due to rounding)
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