Solutions to Chapter 3 - University of Windsor
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 8,000
- Administrative expenses 3,000
- Depreciation expense 1,000
- Interest expense 1,000
Taxable income $10,000 [from (a)]
We conclude that revenues were $23,000.
c. Revenue $23,000
( Cost of goods sold 8,000
( Administrative expenses 3,000
( Depreciation expense 1,000
EBIT $11,000
17. a. Note: assume depreciation equals CCA
Sales $14 million
( Cost of goods sold 8
( Interest expense 1
( Depreciation expense 2
Taxable income 3
( Taxes (35%) 1.05
Net income $ 1.95 million
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.
Chapter 4
21. a. PV = 100 ( annuity factor(6%, 3 periods)
= 100 ( = $267.30
b. 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.
26. a. 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.
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. 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.
78. 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
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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