P2-3.
LG 1: Income statement preparation
a.
Cathy Chen, CPA
Income Statement
for the Year Ended December 31, 2009
Sales revenue
Less: Operating expenses
Salaries
Employment taxes and benefits
Supplies
Travel & entertainment
Lease payment
Depreciation expense
Total operating expense
Operating profits
Less: Interest expense
Net profits before taxes
Less: Taxes (30%)
Net profits after taxes
$360,000
180,000
34,600
10,400
17,000
32,400
15,600
290,000
$ 70,000
15,000
$ 55,000
16,500
$ 38,500
b. In her first year of business, Cathy Chen covered all her operating expenses and
earned a net profit of $38,500 on revenues of $360,000.
P2-5.
LG 1: Calculation of EPS and retained earnings
a.
Earnings per share:
Net profit before taxes
Less: Taxes at 40%
Net profit after tax
Less: Preferred stock dividends
Earnings available to common stockholders
Earnings per share 
$218,000
87,200
$130,800
32,000
$ 98,800
Earning available to common stockholders $98,800

 $1.162
Total shares outstanding
85,000
b. Amount to retained earnings:
85,000 shares  $0.80  $68,000 common stock dividends
Earnings available to common shareholders
Less: Common stock dividends
To retained earnings
$98,800
68,000
$30,800
P2-6.
LG 1: Balance sheet preparation
Owen Davis Company
Balance Sheet
December 31, 2009
Assets
Current assets:
Cash
Marketable securities
Accounts receivable
Inventories
Total current assets
Gross fixed assets
Land and buildings
Machinery and equipment
Furniture and fixtures
Vehicles
Total gross fixed assets
Less: Accumulated depreciation
Net fixed assets
Total assets
Liabilities and stockholders’
equity
Current liabilities:
Accounts payable
Notes payable
Accruals
Total current liabilities
Long-term debt
Total liabilities
Stockholders’ equity
Preferred stock
Common stock (at par)
Paid-in capital in excess of par
Retained earnings
Total stockholders’ equity
Total liabilities and stockholders’
equity
$ 215,000
75,000
450,000
375,000
$1,115,000
$ 325,000
560,000
170,000
25,000
$1,080,000
265,000
$ 815,000
$1,930,000
$ 220,000
475,000
55,000
$ 750,000
420,000
$1,170,000
$ 100,000
90,000
360,000
210,000
$ 760,000
$1,930,000
P2-10. LG 1: Statement of retained earnings
a.
Cash dividends paid on common stock Net profits after taxes – preferred
dividends – change in retained earnings
$377,000 – $47,000 – (1,048,000 – $928,000)
$210,000
Hayes Enterprises
Statement of Retained Earnings
for the Year Ended December 31, 2009
Retained earnings balance (January 1, 2009)
Plus: Net profits after taxes (for 2009)
Less: Cash dividends (paid during 2009)
Preferred stock
Common stock
Retained earnings (December 31, 2009)
b.
$ 928,000
377,000
(47,000)
(210,000)
$1,048,000
Earnings per share 
Net profit after tax  Preferred dividends (EACS* )
Number of common shares outstanding
Earnings per share 
$377,000  $47,000
 $2.36
140,000
*
Earnings available to common stockholders
c.
Cash dividend per share 
Total cash dividend
# shares
Cash dividend per share 
$210,000 (from part (a))
 $1.50
140,000
P2-23. LG 6: Financial statement analysis
a.
Zach Industries
Ratio Analysis
Industry
Average
Current ratio
Quick ratio
Inventory turnover
Average collection period
Debt ratio
Times interest earned
Gross profit margin
Net profit margin
Return on total assets
1.80
0.70
2.50
37.5 days
65%
3.8
38%
3.5%
4.0%
Actual
2008
1.84
0.78
2.59
36.5 days
67%
4.0
40%
3.6%
4.0%
Actual
2009
1.04
0.38
2.33
57 days
61.3%
2.8
34%
4.1%
4.4%
Return on common equity
Market/book ratio
9.5%
1.1
8.0%
1.2
11.3%
1.3
b. Liquidity: Zach Industries’ liquidity position has deteriorated from 2008 to 2009 and is
inferior to the industry average. The firm may not be able to satisfy short-term obligations as
they come due.
Activity: Zach Industries’ ability to convert assets into cash has deteriorated from 2008 to
2009. Examination into the cause of the 20.5-day increase in the average collection period is
warranted. Inventory turnover has also decreased for the period under review and is fair
compared to industry. The firm may be holding slightly excessive inventory.
Debt: Zach Industries’ debt position has improved since 2008 and is below average. Zach
Industries’ ability to service interest payments has deteriorated and is below the industry
average.
Profitability: Although Zach Industries’ gross profit margin is below its industry average,
indicating high cost of goods sold, the firm has a superior net profit margin in comparison to
average. The firm has lower than average operating expenses. The firm has a superior return
on investment and return on equity in comparison to the industry and shows an upward trend.
Market: Zach Industries’ increase in their market price relative to their book value per share
indicates that the firm’s performance has been interpreted as more positive in 2009 than in
2008 and it is a little higher than the industry.
Overall, the firm maintains superior profitability at the risk of illiquidity. Investigation into the
management of accounts receivable and inventory is warranted.
P3-6.
LG 2: Finding operating and free cash flows
a. Cash flow from operations  net profits after taxes  depreciation
Cash flow from operations  $1,400  1,600
Cash flow from operations  $3,000
b. NOPAT  EBIT  (1  t)
NOPAT  $2,700  (1  0.40)  $1,620
c. OCF  EBIT  taxes  depreciation
OCF  $2,700  $933  $1,600
OCF  $3,367
d. FCF  OCF  net fixed asset investment*  net current asset investment**
FCF  $3,367  $1,400  $1,400
FCF  $567
Net fixed asset investment  change in net fixed assets  depreciation
Net fixed asset investment  ($14,800  $15,000)  ($14,700  $13,100)
Net fixed asset investment  –$200  $1,600  $1,400
** Net current asset investment  change in current assets  change in
(accounts payable and accruals)
Net current asset investment  ($8,200  $6,800)  ($100  $100)
Net current asset investment  $1,400  0  $1,400
*
e. Keith Corporation has positive cash flows from operating activities. The accounting cash
flows are a little less than the operating and free cash flows (FCF). The FCF value is very
meaningful since it shows that the cash flows from operations are adequate to cover both
operating expense plus investment in fixed and current assets.
P3-11. LG 4: Cash budget
a.
Xenocore, Inc.
($000)
Sept.
Oct.
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
Forecast Sales
$210 $250
Cash sales (0.20)
Collections
Lag 1 month (0.40)
Lag 2 months (0.40)
Other cash receipts
Total cash receipts
Forecast Purchases
$120 $150
Cash purchases
Payments
Lag 1 month (0.50)
Lag 2 months (0.40)
Salaries & wages
Rent
Interest payments
Principal payments
Dividends
Taxes
Purchases of fixed assets
Total cash disbursements
Total cash receipts
Less: Total cash
disbursements
Net cash flow
Add: Beginning cash
Ending cash
Less: Minimum cash
balance
b.
Required total financing
(notes payable)
Excess cash balance
(marketable securities)
$170
$ 34
$160
$ 32
$140
$ 28
$180
$ 36
$200
$ 40
$250
$ 50
100
84
68
100
$218
$140
$ 14
$200
$100
$ 10
64
68
15
$175
$ 80
$ 8
56
64
27
$183
$110
$ 11
72
56
15
$183
$100
$ 10
80
72
12
$214
$ 90
$ 9
75
48
50
20
70
60
34
20
50
56
32
20
10
40
40
28
20
55
32
36
20
50
44
40
20
10
30
20
80
$139
$183
$153
$183
$303
$214
c.
20
$207
$218
25
$219
$200
$196
$175
207
11
22
33
219
(19)
33
14
196
(21)
14
(7)
139
44
(7)
37
153
30
37
67
303
(89)
67
(22)
15
15
15
15
15
15
1
22
18
37
22
52
The line of credit should be at least $37,000 to cover the maximum borrowing needs for the
month of April.
P3-15. LG 5: Pro forma income statement
a.
Pro Forma Income Statement
Metroline Manufacturing, Inc.
for the Year Ended December 31, 2010
(percent-of-sales method)
Sales
Less: Cost of goods sold (0.65  sales)
Gross profits
Less: Operating expenses (0.086  sales)
Operating profits
Less: Interest expense
Net profits before taxes
Less: Taxes (0.40  NPBT)
Net profits after taxes
Less: Cash dividends
To retained earnings
$1,500,000
975,000
$ 525,000
129,000
$ 396,000
35,000
$ 361,000
144,400
$ 216,600
70,000
$ 146,600
b.
Pro Forma Income Statement
Metroline Manufacturing, Inc.
for the Year Ended December 31, 2010
(based on fixed and variable cost data)
Sales
Less: Cost of goods sold
Fixed cost
Variable cost (0.50  sales)
Gross profits
Less: Operating expense:
Fixed expense
Variable expense (0.06  sales)
Operating profits
Less: Interest expense
Net profits before taxes
Less: Taxes (0.40  NPBT)
Net profits after taxes
Less: Cash dividends
To retained earnings
c.
$1,500,000
210,000
750,000
$ 540,000
$
$
$
$
36,000
90,000
414,000
35,000
379,000
151,600
227,400
70,000
157,400
The pro forma income statement developed using the fixed and variable cost data projects a
higher net profit after taxes due to lower cost of goods sold and operating expenses. Although
the percent-of-sales method projects a more conservative estimate of net profit after taxes, the
pro forma income statement that classifies fixed and variable cost is more accurate.
P3-17. LG 5: Pro forma balance sheet–basic
a.
Pro Forma Balance Sheet
Leonard Industries
December 31, 2010
Assets
Current assets
Cash
Marketable securities
Accounts receivable
Inventories
Total current assets
Net fixed assets
Total assets
Liabilities and stockholders’ equity
Current liabilities
Accounts payable
Accruals
Other current liabilities
Total current liabilities
Long-term debts
Total liabilities
Common stock
Retained earnings
Total stockholders’ equity
External funds required
Total liabilities and stockholders’ equity
1
Beginning gross fixed assets
$
50,000
15,000
300,000
360,000
$725,000
658,0001
$1,383,000
$ 420,000
60,000
30,000
$ 510,000
350,000
$ 860,000
200,000
270,0002
$ 470,000
53,0003
$1,383,000
$ 600,000
Plus: Fixed asset outlays
90,000
Less: Depreciation expense
2
3
(32,000)
Ending net fixed assets
$ 658,000
Beginning retained earnings (Jan. 1, 2010)
$ 220,000
Plus: Net profit after taxes ($3,000,000  0.04)
120,000
Less: Dividends paid
(70,000)
Ending retained earnings (Dec. 31, 2010)
$ 270,000
Total assets
$1,383,000
Less: Total liabilities and equity
External funds required
1,330,000
$
53,000
b. Based on the forecast and desired level of certain accounts, the financial manager should
arrange for credit of $53,000. Of course, if financing cannot be obtained, one or more of the
constraints may be changed.
c.
If Leonard Industries reduced its 2010 dividend to $17,000 or less, the firm would not
need any additional financing. By reducing the dividend, more cash is retained by the firm to
cover the growth in other asset accounts.
P3-19
LG 5: Integrative–pro forma statements
a.
Pro Forma Income Statement
Red Queen Restaurants
for the Year Ended December 31, 2010
(percent-of-sales method)
Sales
Less: Cost of goods sold (0.75  sales)
Gross profits
Less: Operating expenses (0.125  sales)
Net profits before taxes
Less: Taxes (0.40  NPBT)
Net profits after taxes
Less: Cash dividends
To Retained earnings
$900,000
675,000
$225,000
112,500
$112,500
45,000
$ 67,500
35,000
$ 32,500
b.
Pro Forma Balance Sheet
Red Queen Restaurants
December 31, 2010
(Judgmental Method)
Assets
Liabilities and Equity
Cash
Marketable securities
Accounts receivable
Inventories
Current assets
Net fixed assets
$ 30,000
18,000
162,000
112,500
$322,500
375,000
Total assets
$697,500
*Beginning retained earnings (January 1, 2010)
$175,000
Plus: Net profit after taxes
67,500
Less: Dividends paid
(35,000)
Ending retained earnings (December 31, 2010)
c.
Accounts payable
Taxes payable
Other current liabilities
Current liabilities
Long-term debt
Common stock
Retained earnings
External funds required
Total liabilities and
stockholders’ equity
$207,500
Using the judgmental approach, the external funds requirement is $11,250.
$112,500
11,250
5,000
$128,750
200,000
150,000
207,500*
11,250
$697,500
P4-4.
LG 2: Future values: FVn  PV  (1  I)n or FVn  PV  (FVIFi%,n)
Case
A
FV20  PV  FVIF5%,20 yrs.
FV20  $200  (2.653)
FV20  $530.60
Calculator solution: $530.66
Case
B
FV7  PV  FVIF8%,7 yrs.
FV7  $4,500  (1.714)
FV7  $7,713
Calculator solution: $7,712.21
C
FV10  PV  FVIF9%,10 yrs.
FV10  $10,000  (2.367)
FV10  $23,670
Calculator solution: $23,673.64
D
FV12  PV  FVIF10%,12 yrs.
FV12  $25,000  (3.138)
FV12  $78,450
Calculator solution: $78,460.71
E
FV5  PV  FVIF11%,5 yrs.
FV5  $37,000  (1.685)
FV5  $62,345
Calculator solution: $62,347.15
F
FV9  PV  FVIF12%,9 yrs.
FV9  $40,000  (2.773)
FV9  $110,920
Calculator solution: $110,923.15
P4-11. LG 2: Present values: PV  FVn(PVIFi%,n)
Case
A
B
C
D
E
Calculator Solution
PV12%,4yrs  $7,000
PV8%, 20yrs  $28,000
PV14%,12yrs
PV11%,6yrs  $150,000
PV20%,8yrs  $45,000
 0.636  $4,452
 0.215  $6,020
 $10,000  0.208  $2,080
 0.535  $80,250
 0.233  $10,485
$4,448.63
$6,007.35
$2,075.59
$80,196.13
$10,465.56
P4-18. LG 3: Future value of an annuity
a.
Future value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity
(2) Annuity Due
FVAk%,n  PMT(FVIFAk%,n)
FVAdue  PMT[(FVIFAk%,n(1  k)]
A
FVA8%,10  $2,50014.487
FVA8%,10  $36,217.50
Calculator solution: $36,216.41
FVAdue  $2,500(14.4871.08)
FVAdue  $39,114.90
Calculator solution: $39,113.72
B
FVA12%,6  $5008.115
FVA12%,6  $4,057.50
Calculator solution: $4,057.59
FVAdue  $500 ( 8.1151.12)
FVAdue  $4,544.40
Calculator solution: $4,544.51
C
FVA20%,5  $30,0007.442
FVA20%,5  $223,260
Calculator solution: $223,248
FVAdue  $30,000(7.4421.20)
FVAdue  $267,912
Calculator solution: $267,897.60
D
FVA9%,8  $11,50011.028
FVA9%,8  $126,822
Calculator solution: $126,827.45
FVAdue  $11,500(11.0281.09)
FVAdue  $138,235.98
Calculator solution: $138,241.92
E
FVA14%,30  $6,000356.787
FVA14%,30  $2,140,722
Calculator solution: $2,140,721.08
FVAdue  $6,000(356.7871.14)
FVAdue  $2,440,422.00
Calculator solution: $2,440,422.03
b. The annuity due results in a greater future value in each case. By depositing the payment at
the beginning rather than at the end of the year, it has one additional year of compounding.
P4-19. LG 3: Present value of an annuity: PVn  PMT(PVIFAi%,n)
a.
Present value of an ordinary annuity vs. annuity due
(1) Ordinary Annuity
(2) Annuity Due
PVAk%,n  PMT(PVIFAi%,n)
PVAdue  PMT[(PVIFAi%,n(1  k)]
A
PVA7%,3  $12,0002.624
PVA7%,3  $31,488
Calculator solution: $31,491.79
PVAdue  $12,000(2.6241.07)
PVAdue  $33,692
Calculator solution: $33,696.22
B
PVA12%15  $55,0006.811
PVA12%,15  $374,605
Calculator solution: $374,597.55
PVAdue  $55,000(6.8111.12)
PVAdue  $419,557.60
Calculator solution: $419,549.25
C
PVA20%,9  $7004.031
PVA20%,9  $2,821.70
Calculator solution: $2,821.68
PVAdue  $700(4.0311.20)
PVAdue  $3,386.04
Calculator solution: $3,386.01
D
PVA5%,7  $140,0005.786
PVA5%,7  $810,040
Calculator solution: $810,092.28
PVAdue  $140,000(5.7861.05)
PVAdue  $850,542
Calculator solution: $850,596.89
E
PVA10%,5  $22,5003.791
PVA10%,5  $85,297.50
Calculator solution: $85,292.70
PVAdue  $22,500(2.7911.10)
PVAdue  $93,827.25
Calculator solution: $93,821.97
b. The annuity due results in a greater present value in each case. By depositing the payment at
the beginning rather than at the end of the year, it has one less year to discount back.
P4-25. LG 3: Perpetuities: PVn  PMT(PVIFAi%,)
a.
b.
Case
PMT(PVIFAi%,)  PMT(1  i)
PV Factor
A
1  0.08  12.50
$20,000
 12.50  $250,000
B
1  0.10  10.00
$100,000  10.00  $1,000,000
C
1  0.06  16.67
$3,000
 16.67  $50,000
D
1  0.05  20.00
$60,000
 20.00  $1,200,000
P4-30. LG 4: PV-mixed stream
a.
Cash Flow
Stream
A
Year
1
2
3
4
5
CF
$50,000
40,000
30,000
20,000
10,000


PVIF15%,n







0.870
0.756
0.658
0.572
0.497





Calculator solution:
B
1
$10,000
2
3
4
5
20,000
30,000
40,000
50,000





0.870
0.756
0.658
0.572
0.497





Calculator solution:
Present Value
$43,500
30,240
19,740
11,440
4,970
$109,890
$109,856.33
$ 8,700
15,120
19,740
22,880
24,850
$ 91,290
$ 91,272.98
b. Cash flow stream A, with a present value of $109,890, is higher than cash flow stream B’s
present value of $91,290 because the larger cash inflows occur in A in the early years when
their present value is greater, while the smaller cash flows are received further in the future.
P4-35. LG 5: Compounding frequency, time value, and effective annual rates
a.
Compounding frequency: FVn  PVFVIFi%,n
A
FV5  $2,500(FVIF3%,10)
FV5  $2,500(1.344)
FV5  $3,360
Calculator solution: $3,359.79
C
FV10  $1,000(FVIF5%,10)
FV10  $1,000  (1.629)
FV10  $16,290
Calculator solution: $1,628.89
b. Effective interest rate: ieff  (1  i%/m)m – 1
A
ieff  (1  0.06/2)2 – 1
ieff f  (1  0.03)2 – 1
ieff  (1.061) – 1
ieff  0.061  06.1%
C
ieff  (1  0.05/1)1 – 1
ieff  (1  0.05)1 – 1
ieff  (1.05) – 1
ieff  0.05  5%
B
FV3  $50,000(FVIF2%,18)
FV3  $50,000(1.428)
FV3  $71,400
Calculator solution: $71,412.31
D
FV6  $20,000(FVIF4%,24)
FV6  $20,000(2.563)
FV6  $51,260
Calculator solution: $51,266.08
B
ieff  (1  0.12/6)6 – 1
ieff  (1  0.02)6 – 1
ieff  (1.126) – 1
ieff  0.126  12.6%
D
ieff  (1  0.16/4)4 – 1
ieff  (1  0.04)4 – 1
ieff  (1.170) – 1
ieff  0.17  17%
c. The effective rates of interest rise relative to the stated nominal rate with increasing
compounding frequency.
P4-40. LG 6: Deposits to accumulate growing future sum: PMT 
Case
Terms
FVAn
FVIFAi %,n
Calculation
Payment
A
12%, 3 yrs.
PMT  $5,000  3.374
B
7%, 20 yrs.
PMT  $100,000  40.995
$1,481.92

Calculator solution: $1,481.74

$2,439.32
Calculator solution:
10%, 8 yrs.
C
PMT  $30,000  11.436

$2,623.29
Calculator solution:
8%, 12 yrs.
D
$2,439.29
$2,623.32
PMT  $15,000  18.977
$ 790.43

Calculator solution: $ 790.43
P4-47. LG 6: Loan interest deductions
a.
PMT  $10,000  (PVIFA13%,3)
PMT  $10,000  (2.361)
PMT  $4,235.49
Calculator solution: $4,235.22
b.
End of
Year
Loan
Payment
Beginning of
Year Principal
1
$4,235.49
$10,000.00
2
3
4,235.49
4,235.49
7,064.51
3,747.41
Payments
Interest Principal
End of Year
Principal
$1,300.00 $2,935.49
$7,064.51
918.39
487.16
3,317.10
3,748.33
3,747.41
0
(The difference in the last year’s beginning and ending principal is due to rounding.)
P4-49. LG 6: Growth rates
a.
PV  FVnPVIFi%,n
Case
A
PV  FV4PVIFk%,4yrs.
$500  $800PVIFk%,4yrs
0.625  PVIFk%,4yrs
B
PV
 FV9PVIFi%,9yrs.
$1,500  $2,280PVIFk%,9yrs.
0.658  PVIFk%,9yrs.
12%  k  13%
Calculator solution: 12.47%
C
4% k 5%
Calculator solution: 4.76%
PV
 FV6PVIFi%,6
$2,500  $2,900PVIFk%,6 yrs.
0.862  PVIFk%,6yrs.
2%  k  3%
Calculator solution: 2.50%
b.
c.
Case
A Same as in a
B Same as in a
C Same as in a
The growth rate and the interest rate should be equal, since they represent the same thing.
P4-56. LG 6: Number of years to equal future amount
A
FV
 PV(FVIF7%,n yrs.)
$1,000  $300(FVIF7%,n yrs.)
3.333  FVIF7%,n yrs.
17  n  18
Calculator solution: 17.79 years
B
FV
 $12,000(FVIF5%,n yrs.)
$15,000  $12,000(FVIF5%,n yrs.)
1.250  FVIF5%,n yrs.
4n5
Calculator solution: 4.573 years
C
FV
 PV(FVIF10%,n yrs.)
$20,000  $9,000(FVIF10%,n yrs.)
2.222  FVIF10%,n yrs.
8n9
Calculator solution: 8.38 years
D
FV  $100(FVIF9%,n yrs.)
$500  $100(FVIF9%,n yrs.)
5.00  FVIF9%,n yrs.
18  n  19
Calculator solution: 18.68 years
E
FV
 PV(FVIF15%,n yrs.)
$30,000  $7,500(FVIF15%,n yrs.)
4.000  FVIF15%,n yrs.
9  n  10
Calculator solution: 9.92 years
P4-58. LG 6: Number of years to provide a given return
A
PVA  PMT(PVIFA11%,n yrs.)
$1,000  $250(PVIFA11%,n yrs.)
yrs.)
4.000  PVIFA11%,n yrs.
5n6
Calculator solution: 5.56 years
B
PVA
 PMT(PVIFA15%,n yrs.)
$150,000  $30,000(PVIFA15%,n
5.000
 PVIFA15%,n yrs.
9  n  10
Calculator solution: 9.92 years
P5-2.
LG 1: Return calculations: rt =
(Pt  Pt 1  Ct )
Pt1
Investment
P5-4.
Calculation
rt(%)
A
($1,100  $800  $100)  $800
25.00
B
($118,000  $120,000  $15,000)  $120,000
10.83
C
($48,000  $45,000  $7,000)  $45,000
22.22
D
($500  $600  $80)  $600
E
($12,400  $12,500  $1,500)  $12,500
3.33
11.20
LG 2: Risk analysis
a.
Expansion
Range
A
24%  16%  8%
B
30%  10%  20%
b. Project A is less risky, since the range of outcomes for A is smaller than the range for
Project B.
c. Since the most likely return for both projects is 20% and the initial investments are equal, the
answer depends on your risk preference.
d. The answer is no longer clear, since it now involves a risk–return tradeoff. Project B has a
slightly higher return but more risk, while A has both lower return and lower risk.
P5-11. LG 2: Integrative–expected return, standard deviation, and coefficient of variation
a.
n
Expected return: r   ri  Pri
i 1
Expected Return
Rate of Return
ri
Probability
Pr i
Weighted Value
ri Pri
0.40
0.10
0.04
0.10
0.20
0.02
0.00
0.40
0.00

0.05
0.20
0.01

0.10
0.10
0.01
Asset F
n
r   ri  Pri
i 1
0.04
Asset G

0.35
0.40
0.14
0.10
0.30
0.03
0.20
0.30
0.06
0.11
Asset H

0.40
0.10
0.04
0.20
0.20
0.04
0.10
0.40
0.04
0.00
0.20
0.00
0.20
0.10
0.02
0.10
Asset G provides the largest expected return.
b. Standard deviation:  
n
 (r  r )
i 1
Asset F
i
2
xPri
ri  r
( ri  r ) 2
Pr i
2
0.40  0.04  0.36
0.1296
0.10
0.01296
0.10  0.04  0.06
0.0036
0.20
0.00072
0.00  0.04 0.04
0.0016
0.40
0.00064
0.05  0.04 0.09
0.0081
0.20
0.00162
0.10  0.04 0.14
0.0196
0.10
0.00196
0.01790
Asset G
0.35  0.11  .24
0.0576
0.40
0.02304
0.10  0.11 0.01
0.0001
0.30
0.00003
0.20  0.11 0.31
0.0961
0.30
0.02883
0.05190
Asset H
0.40  0.10  .30
0.0900
0.10
0.009
0.20  0.10  .10
0.0100
0.20
0.002
0.10  0.10  0.00
0.0000
0.40
0.000
0.00  0.10 0.10
0.0100
0.20
0.002
0.20  0.10 0.30
0.0900
0.10
0.009
0.022
r
0.1338
0.2278
0.1483
Based on standard deviation, Asset G appears to have the greatest risk, but it must be
measured against its expected return with the statistical measure coefficient of variation, since
the three assets have differing expected values. An incorrect conclusion about the risk of the
assets could be drawn using only the standard deviation.
c.
Coefficient of variation =
standard deviation ( )
expected value
0.1338
 3.345
0.04
0.2278
Asset G: CV 
 2.071
0.11
0.1483
Asset H: CV 
 1.483
0.10
As measured by the coefficient of variation, Asset F has the largest relative risk.
Asset F:
CV 
P5-14. LG 3: Portfolio analysis
a.
Expected portfolio return:
Alternative 1: 100% Asset F
rp 
16%  17%  18%  19%
 17.5%
4
Alternative 2: 50% Asset F  50% Asset G
Year
Asset F
(wFrF)
Asset G
(wGrG)

Portfolio Return
rp
2010
(16%0.50  8.0%)

(17%0.50  8.5%)

16.5%
2011
(17%0.50  8.5%)

(16%0.50  8.0%)

16.5%
2012
(18%0.50  9.0%)

(15%0.50  7.5%)

16.5%
2013
(19%0.50  9.5%)

(14%0.50  7.0%)

16.5%
rp 
16.5%  16.5%  16.5%  16.5%
 16.5%
4
Alternative 3: 50% Asset F  50% Asset H
Year
Asset F
(wFrF)

Asset H
(wHrH)
Portfolio Return
rp
2010
(16%0.50  8.0%)

(14%0.50  7.0%)
15.0%
2011
(17%0.50  8.5%)

(15%0.50  7.5%)
16.0%
2012
(18%0.50  9.0%)

(16%0.50  8.0%)
17.0%
2013
(19%0.50  9.5%)

(17%0.50  8.5%)
18.0%
rp 
15.0%  16.0%  17.0%  18.0%
 16.5%
4
b. Standard deviation:  rp 
(ri  r )2

i 1 ( n  1)
n
(1)
F 
[(16.0%  17.5%)2  (17.0%  17.5%)2  (18.0%  17.5%) 2  (19.0%  17.5%)2 ]
4 1
F 
[(1.5%)2  (0.5%)2  (0.5%)2  (1.5%)2 ]
3
F 
(0.000225  0.000025  0.000025  0.000225)
3
F 
0.0005
 .000167  0.01291  1.291%
3
(2)
 FG 
[(16.5%  16.5%)2  (16.5%  16.5%)2  (16.5%  16.5%)2  (16.5%  16.5%)2 ]
4 1
 FG 
[(0)2  (0)2  (0)2  (0)2 ]
3
 FG  0
(3)
c.
 FH 
[(15.0%  16.5%)2  (16.0%  16.5%)2  (17.0%  16.5%)2  (18.0%  16.5%)2 ]
4 1
 FH 
[(1.5%)2  (0.5%)2  (0.5%)2  (1.5%)2 ]
3
 FH 
[(0.000225  0.000025  0.000025  0.000225)]
3
 FH 
0.0005
 0.000167  0.012910  1.291%
3
Coefficient of variation: CV   r  r
1.291%
 0.0738
17.5%
0
CVFG 
0
16.5%
1.291%
CVFH 
 0.0782
16.5%
d. Summary:
CVF 
rp: Expected Value
of Portfolio
rp
CVp
Alternative 1 (F)
17.5%
1.291%
0.0738
Alternative 2 (FG)
16.5%
0
Alternative 3 (FH)
16.5%
1.291%
0.0
0.0782
Since the assets have different expected returns, the coefficient of variation should be used to
determine the best portfolio. Alternative 3, with positively correlated assets, has the highest
coefficient of variation and therefore is the riskiest. Alternative 2 is the best choice; it is
perfectly negatively correlated and therefore has the lowest coefficient of variation.
P5-18. LG 5: Graphic derivation of beta
Intermediate
a.
b. To estimate beta, the “rise over run” method can be used: Beta 
c.
Rise Y

Run X
Taking the points shown on the graph:
Y 12  9 3
Beta A 

  0.75
X 8  4 4
Y 26  22 4
Beta B 

  1.33
X 13  10 3
A financial calculator with statistical functions can be used to perform linear regression
analysis. The beta (slope) of line A is 0.79; of line B, 1.379.
With a higher beta of 1.33, Asset B is more risky. Its return will move 1.33 times for each one
point the market moves. Asset A’s return will move at a lower rate, as indicated by its beta
coefficient of 0.75.
P5-23. LG 6: Capital asset pricing model (CAPM): rj  RF  [bj(rm  RF)]
rj

A
8.9%

5%  [1.30(8%  5%)]
B
12.5%

8%  [0.90(13%  8%)]
Case
RF  [bj(rm  RF)]
C
8.4%

9%  [0.20(12%  9%)]
D
15.0%

10%  [1.00(15%  10%)]
E
8.4%

6%  [0.60(10%  6%)]
P5-27. LG 6: Security market line, SML
a, b, and d
rj  RF  [bj(rm  RF)]
Asset A
rj  0.09  [0.80(0.13  0.09)]
rj  0.122
Asset B
rj  0.09  [1.30(0.13  0.09)]
rj  0.142
d. Asset A has a smaller required return than Asset B because it is less risky, based on the beta
of 0.80 for Asset A versus 1.30 for Asset B. The market risk premium for Asset A is 3.2%
(12.2%  9%), which is lower than Asset B’s market risk premium (14.2%  9%  5.2%).
c.
P5-29. LG 6: Integrative-risk, return, and CAPM
a.
Project
rj
 RF  [bj(rm  RF)]
A
rj
 9%  [1.5(14%  9%)]
B
rj
 9%  [0.75(14%  9%)]
C
rj
 9%  [2.0(14%  9%)]
D
rj
 9%  [0(14%  9%)]
 16.5%
 12.75%
 19.0%
 9.0%
E
rj
 9%  [(0.5)(14%  9%)]

6.5%
b and d
c.
Project A is 150% as responsive as the market.
Project B is 75% as responsive as the market.
Project C is twice as responsive as the market.
Project D is unaffected by market movement.
Project E is only half as responsive as the market, but moves in the opposite direction as the
market.
d. See graph for new SML.
rA  9%  [1.5(12%  9%)] 13.50%
rB  9%  [0.75(12%  9%)] 11.25%
rC  9%  [2.0(12%  9%)] 15.00%
rD  9%  [0(12%  9%)]
9.00%
rE  9%  [0.5(12%  9%)] 7.50%
e.
The steeper slope of SMLb indicates a higher risk premium than SMLd for these market
conditions. When investor risk aversion declines, investors require lower returns for any
given risk level (beta).
P6-11. LG 4: Bond prices and yields
a. 0.97708  $1,000 = $977.08
b. (0.05700  $1,000)  $977.08 = $57.000  $977.08 = 0.0583 = 5.83%
c. The bond is selling at a discount to its $1,000 par value.
d. The yield to maturity is higher than the current yield, because the former includes $22.92 in
price appreciation between today and the May 15, 2017 bond maturity.
P6-13. LG 4: Valuation of assets
Asset
A
End of Year
Amount
1
2
3
$ 5000
$ 5000
$ 5000
PVIF or
PVIFAr%,n
2.174
$10,870.00
Calculator solution:
B
1–
C
1
2
3
4
5
D
E
1–5
6
1
2
3
4
5
6
$
300
0
0
0
0
$35,000
$ 1,500
8,500
$ 2,000
3,000
5,000
7,000
4,000
1,000
PV of
Cash Flow
1  0.15
$10,871.36
$2,000
0.476
$16,660.00
Calculator solution:
$16,663.96
3.605
0.507
$ 5,407.50
4,309.50
$ 9,717.00
Calculator solution:
$ 9,713.53
0.877
0.769
0.675
0.592
0.519
0.456
$ 1,754.00
2,307.00
3,375.00
4,144.00
2,076.00
456.00
$14,112.00
Calculator solution:
$14,115.27
P6-16. LG 5: Bond valuation–annual interest
B0  I  (PVIFArd%,n)  M  (PVIFrd%,n)
Bond
Table Values
Calculator Solution
A
B0  $140  (7.469)  $1,000  (0.104)  $1,149.66
$1,149.39
B
B0  $80  (8.851)  $1,000  (0.292)  $1,000.00
$1,000.00
C
B0  $10  (4.799)  $100  (0.376)

$
D
B0  $80  (4.910)  $500  (0.116)
$ 450.80
$ 450.90
E
B0  $120  (6.145)  $1,000  (0.386)  $1,123.40
$1,122.89
$85.59
85.60
P6-24. LG 6: Bond valuation–semiannual interest
B0  I(PVIFArd%,n)  M(PVIFrd%,n)
B0  $50(PVIFA7%,12)  M(PVIF7%,12)
B0  $50(7.943)  $1,000(0.444)
B0  $397.15  $444
B0  $841.15
Calculator solution: $841.15
P7-6.
LG 4: Common stock valuation–zero growth: P0  D1  rs
a.
b.
c.
P7-8.
P0 $2.40  0.12 $20
P0 $2.40  0.20 $12
As perceived risk increases, the required rate of return also increases, causing the stock price
to fall.
LG 4: Preferred stock valuation: PS0  Dp  rp
PS0  $6.40  0.093
PS0  $68.82
b. PS0  $6.40  0.105
PS0  $60.95
The investor would lose $7.87 per share ($68.82  $60.95) because, as the required rate of return
on preferred stock issues increases above the 9.3% return she receives, the value of her stock
declines.
a.
P7-9.
LG 4: Common stock value–constant growth: P0  D1  (rs  g)
Firm
P0  D1  (rs  g)
A
B
C
D
E
P0  $1.20  (0.13  0.08)
P0  $4.00  (0.15  0.05)
P0  $0.65  (0.14  0.10)
P0  $6.00  (0.09  0.08)
P0  $2.25  (0.20  0.08)
Share Price





$ 24.00
$ 40.00
$ 16.25
$600.00
$ 18.75
P7-12. LG 4: Common stock valuevariable growth:
P0 PV of dividends during initial growth period
   PV of price of stock at end of growth period.
Steps 1 and 2: Value of cash dividends and PV of annual dividends
t
D0
FVIF25%, t
Dt
PVIF15%, t
1
2
3
$2.55
2.55
2.55
1.250
1.562
1.953
$3.19
3.98
4.98
0.870
0.756
0.658
PV
of Dividends
$2.78
3.01
3.28
$9.07
Step 3: PV of price of stock at end of initial growth period
D3 1 $4.98  (1  0.10)
D4 $5.48
P3 [D4  (rs  g2)]
P3 $5.48  (0.15  0.10)
P3 $109.60
PV of stock at end of year 3  P3  (PVIF15%,3)
PV $109.60  (0.658)
PV $72.12
Step 4: Sum of PV of dividends during initial growth period and PV price of stock at end of
growth period
P0 $9.07  $72.12
P0 $81.19
Calculator solution: $81.12
P7-16. LG 5: Free cash flow (FCF) valuation
a.
The value of the total firm is accomplished in three steps.
(1) Calculate the PV of FCF from 2015 to infinity.
FCF2115 
$390,000(1.03) $401,700

 $5,021,250
0.11  0.03
0.08
(2) Add the PV of the cash flow obtained in (1) to the cash flow for 2014.
FCF2014  $5,021,250  390,000  $5,411,250
(3) Find the PV of the cash flows for 2010 through 2014.
Year
2010
2011
2012
2013
2014
FCF
PVIF11%,n
PV
$200,000
0.901
250,000
0.812
310,000
0.731
350,000
0.659
5,411,250
0.593
Value of entire company, Vc 
$ 180,200
203,000
226,610
230,650
3,208,871
$ 4,049,331
Calculator solution:
$ 4,051,624
b. Calculate the value of the common stock.
VS  VC  VD  VP
VS  $4,049,331  $1,500,000  $400,000  $2,149,331
c.
Value per share 
$2,149,331
 $10.75
200,000
Calculator solution: $10.76
P7-22. LG 4: 6: Integrative–risk and valuation
a.
b.
c.
rs RF  [b  (rm – RF)]
rs 0.10  [1.20  (0.14 – 0.10)]
rs  0.148
g: FV PV  (1  r)n
$2.45 $1.73  (1  r)6
$2.45
FVIFk%,6
$1.73
1.416 FVIF6%,6
g approximately 6%
P0 D1  (rs  g)
P0 $2.60  (0.148  0.06)
P0  $29.55
Calculator solution: $29.45
A decrease in beta would decrease the required rate of return, which in turn would increase
the price of the stock.
P8-4.
LG 3: Expansion versus replacement cash flows
a.
Year
Initial investment
1
2
3
4
5
b.
Relevant Cash
Flows
($28,000)
4,000
6,000
8,000
10,000
4,000
An expansion project is simply a replacement decision in which all cash flows from the old
asset are zero.
P8-15. LG 4: Calculating initial investment
a.
Book value  ($60,000  0.31)  $18,600
b.
Sales price of old equipment
$35,000
Book value of old equipment
18,600
Recapture of depreciation
$16,400
Taxes on recapture of depreciation  $16,400  0.40  $6,560
Sale price of old roaster
$35,000
Tax on recapture of depreciation
(6,560)
After-tax proceeds from sale of old roaster $28,440
Changes in current asset accounts
Inventory
$ 50,000
Accounts receivable
70,000
Net change
$ 120,000
Changes in current liability accounts
Accruals $ (20,000)
Accounts payable 40,000
Notes payable
15,000
Net change
$ 35,000
Change in net working capital
$ 85,000
c.
d.
Cost of new roaster
$130,000
Less after-tax proceeds from sale of old roaster 28,440
Plus change in net working capital
85,000
Initial investment
$186,560
P8-17. LG 5: Incremental operating cash inflows
a.

b.
Incremental profits before depreciation and tax  $1,200,000  $480,000
 $720,000 each year
Year
(1)
(2)
(3)
(4)
(5)
(6)
PBDT
Depr.
NPBT
Tax
NPAT
$720,000
400,000
320,000
128,000
192,000
$720,000
640,000
80,000
32,000
48,000
$720,000
80,000
340,000
136,000
204,000
$720,000
240,000
480,000
192,000
288,000
$720,000
240,000
480,000
192,000
288,000
$720,000
100,000
620,000
248,000
372,000
c.
Cash
flow
(1)
$592,000
(2)
$688,000
(3)
$584,000
(4)
$528,000
(5)
$528,000
(6)
$472,000
(NPAT  depreciation)
PBDT Profits before depreciation and taxes
NPBT Net profits before taxes
NPAT Net profits after taxes
P8-21. LG 5: Determining incremental operating cash flows
a.
Year
1
Revenues:(000)
New buses
$1,850
Old buses
1,800
Incremental revenue $ 50
Expenses: (000)
New buses
$ 460
Old buses
500
Incremental expense $ (40)
Depreciation: (000)
New buses
$ 600
Old buses
324
Incremental depr.
$ 276
Incremental depr. tax
savings @40%
110
Net Incremental Cash Flows
2
3
4
5
6
$1,850
1,800
$50
$1,830
1,790
$ 40
$1,825
1,785
$ 40
$1,815
1,775
$ 40
$1,800
1,750
$ 50
$ 460
510
$ (50)
$ 468
520
$ (52)
$ 472
520
$ (48)
$ 485
530
$ (45)
$ 500
535
$ (35)
$ 960
135
$ 825
$ 570
0
$ 570
$ 360
0
$ 360
$ 360
0
$ 360
$ 150
0
$ 150
330
228
144
144
60
Cash flows: (000)
Revenues
Expenses
Less taxes @40%
Depr. tax savings
Net operating cash
inflows
$ 50
40
(36)
110
$ 50
50
(40)
330
$ 40
52
(37)
228
$ 40
48
(35)
144
$ 40
45
(34)
144
$ 50
35
(34)
60
$164
$390
$283
$197
$195
$111
P8-23. LG 6: Terminal cash flow–replacement decision
After-tax proceeds from sale of new asset 
Proceeds from sale of new machine
$75,000
l
 Tax on sale of new machine
(14,360)
Total after-tax proceeds-new asset
   After-tax proceeds from sale of old asset
Proceeds from sale of old machine
(15,000)
2
 Tax on sale of old machine
6,000
Total after-tax proceeds-old asset
 Change in net working capital
Terminal cash flow
l
2
Book value of new machine at end of year.4:
[1  (0.20  0.32 0.19  0.12)  ($230,000)]
$75,000  $39,100
$35,900  (0.40)
Book value of old machine at end of year 4:
$0
$15,000  $0
$15,000  (0.40)
$60,640
(9,000)
25,000
$76,640
 $39,100
 $35,900 recaptured depreciation
 $14,360 tax liability
 $15,000 recaptured depreciation
 $6,000 tax benefit
P8-24. LG 4, 5, 6: Relevant cash flows for a marketing campaign
Marcus Tube
Calculation of Relevant Cash Flow
($000)
Calculation of Net Profits after Taxes and Operating Cash Flow:
with Marketing Campaign
Sales
CGS (@ 80%)
Gross profit
Less: Less: Operating expenses
General and
2010
2011
2012
2013
2014
$20,500
16,400
$ 4,100
$21,000
16,800
$ 4,200
$21,500
17,200
$ 4,300
$22,500
18,000
$ 4,500
$23,500
18,800
$ 4,700
administrative
(10% of sales)
Marketing campaign
Depreciation
Total operating
expenses
Net profit
before taxes
Less: Taxes 40%
Net profit
after taxes
Depreciation
Operating CF
$ 2,050
150
500
$ 2,100
150
500
$ 2,150
150
500
$ 2,250
150
500
$ 2,350
150
500
2,700
2,750
2,800
2,900
3,000
$ 1,400
560
$ 1,450
580
$ 1,500
600
$ 1,600
640
$ 1,700
680
$
$
$
$
$ 1,020
500
$ 1,520
840
500
$ 1,340
870
500
$ 1,370
900
500
$ 1,400
960
500
$ 1,460
Without Marketing Campaign
Years 2007–2011
Net profit after taxes
 Depreciation
Operating cash flow
$ 900
500
$1,400
Relevant Cash Flow
($000)
Year
2010
2011
2012
2013
2014
With Marketing
Campaign
$1,340
1,370
1,400
1,460
1,520
Without Marketing Incremental
Campaign
Cash Flow
$1,400
1,400
1,400
1,400
1,400
$(60)
(30)
0
60
120
P8-26. LG 4, 5, 6: Integrative—determining relevant cash flows
a.



Initial investment:
Installed cost of new asset 
Cost of new asset
$105,000

 Installation costs
5,000
Total cost of new asset
 After-tax proceeds from sale of old asset 
Proceeds from sale of old asset
(70,000)
*

 Tax on sale of old asset
16,480
Total proceeds from sale of old asset

 Change in working capital
$110,000
(53,520)
12,000
Initial investment
*
$ 68,480
Book value of old asset:
[1  (0.20  0.32)]  $60,000
 $28,800
$70,000  $28,800  $41,200 gain on sale of asset
$31,200 recaptured depreciation  0.40  $12,480
$10,000 capital gain  0.40
 4,000
Total tax of sale of asset
 $16,480
b.
Calculation of Operating Cash Inflows
Year
Profits before
Depreciation
Net Profits
Net Profits
and Taxes Depreciation before Taxes Taxes after Taxes
New Grinder
1
$43,000
2
43,000
3
43,000
4
43,000
5
43,000
6
0
$22,000
35,200
20,900
13,200
13,200
5,500
$21,000
7,800
22,100
29,800
29,800
5,500
$8,400
3,120
8,840
11,920
11,920
2,200
$12,600
4,680
13,260
17,880
17,880
3,300
$34,600
39,880
34,160
31,080
31,080
2,200
Existing Grinder
1
$26,000
2
24,000
3
22,000
4
20,000
5
18,000
6
0
$11,400
7,200
7,200
3,000
0
0
$14,600
16,800
14,800
17,000
18,000
0
$5,840
6,720
5,920
6,800
7,200
0
$8,760
10,080
8,880
10,200
10,800
0
$20,160
17,280
16,080
13,200
10,800
0
Calculation of Incremental Cash Inflows
Year
1
2
3
4
5
6
c.


Operating
Cash
Inflows
New Grinder Existing Grinder
$34,600
39,880
34,160
31,080
31,080
2,200
$20,160
17,280
16,080
13,200
10,800
0
Incremental Operating
Cash Flow
$14,440
22,600
18,080
17,880
20,280
2,200
Terminal cash flow:
After-tax proceeds from sale of new asset 
Proceeds from sale of new asset
$29,000
*

 Tax on sale of new asset
(9,400)
Total proceeds from sale of new asset

 After-tax proceeds from sale of old asset 
19,600


Proceeds from sale of old asset

 Tax on sale of old asset
Total proceeds from sale of old asset

 Change in net working capital
Terminal cash flow
*
d.
P9-2.
0
0
0
12,000
$31,600
Book value of asset at end of year 5  $5,500
$29,000  $5,500
 $23,500 recaptured depreciation
$23,500  0.40
 $9,400
Year 5 relevant cash flow:
Operating cash flow
Terminal cash flow
Total inflow
$20,280
31,600
$51,880
LG 2: Payback comparisons
Machine 1: $14,000  $3,000  4 years, 8 months
Machine 2: $21,000  $4,000  5 years, 3 months
b. Only Machine 1 has a payback faster than 5 years and is acceptable.
c. The firm will accept the first machine because the payback period of 4 years, 8 months is
less than the 5-year maximum payback required by Nova Products.
d. Machine 2 has returns that last 20 years while Machine 1 has only seven years of returns.
Payback cannot consider this difference; it ignores all cash inflows beyond the payback
period. In this case, the total cash flow from Machine 1 is $59,000 ($80,000  $21,000) less
than Machine 2.
a.
P9-7.
LG 3: NPV–independent projects
Project A
PVn PMT(PVIFA14%,10 yrs.)
PVn $4,000(5.216)
PVn $20,864
NPV $20,864  $26,000
NPV $5,136
Calculator solution: $5,135.54
Reject
Project B—PV of Cash Inflows
Year
1
2
3
4
5
6
CF
PVIF14%,n
PV
$100,000
120,000
140,000
160,000
180,000
200,000
0.877
0.769
0.675
0.592
0.519
0.456
$ 87,700
92,280
94,500
94,720
93,420
91,200
$553,820
NPV PV of cash inflows  initial investment  $553,820  $500,000
NPV $53,820
Calculator solution: $53,887.93
Accept
Project C—PV of Cash Inflows
Year
CF
PVIF14%,n
PV
1
2
3
4
5
6
7
8
9
$20,000
19,000
18,000
17,000
16,000
15,000
14,000
13,000
12,000
0.877
0.769
0.675
0.592
0.519
0.456
0.400
0.351
0.308
$17,540
14,611
12,150
10,064
8,304
6,840
5,600
4,563
3,696
10
11,000
0.270
2,970
$86,338
NPV PV of cash inflows  initial investment  $86,338  $170,000
NPV $83,662
Calculator solution: $83,668.24
Reject
Project D
PVn PMT(PVIFA14%,8 yrs.)
PVn $230,0004.639
PVn $1,066,970
NPV PVn  Initial investment
NPV $1,066,970  $950,000
NPV $116,970
Calculator solution: $116,938.70
Accept
Project E—PV of Cash Inflows
Year
4
5
6
7
8
9
CF
PVIF14%,n
PV
$20,000
30,000
0
50,000
60,000
70,000
0.592
0.519
$11,840
15,570
0
20,000
21,060
21,560
$90,030
0.400
0.351
0.308
NPV PV of cash inflows  initial investment
NPV $90,030  $80,000
NPV $10,030
Calculator solution: $9,963.63
Accept
P9-10. LG 3: NPV–mutually exclusive projects
PVn  PMT(PVIFAk%,n)
a. & b.
Press
A
B
Year
1
2
3
4
5
6
PV of cash inflows; NPV
PVn PMT(PVIFA15%,8 yrs)
PVn $18,0004.487
PVn $80,766
NPV PVn  initial investment
NPV $80,766  $85,000
NPV $4,234
Calculator solution: $4,228.21
Reject
CF
PVIF15%,n
PV
$12,000
14,000
16,000
18,000
20,000
25,000
0.870
0.756
0.658
0.572
0.497
0.432
$10,440
10,584
10,528
10,296
9,940
10,800
$62,588
NPV $62,588  $60,000
NPV $2,588
Calculator solution: $2,584.34
Accept
C
Year
1
2
3
4
5
6
7
8
CF
PVIF15%,n
PV
0.870
0.756
0.658
0.572
0.497
0.432
0.376
0.327
$43,500
22,680
13,160
11,440
9,940
12,960
15,040
16,350
$145,070
$50,000
30,000
20,000
20,000
20,000
30,000
40,000
50,000
NPV  $145,070  $130,000
NPV  $15,070
Calculator solution: $15,043.89
Accept
c.
Ranking–using NPV as criterion
Rank
1
2
3
Press
NPV
C
B
A
$15,070
2,588
4,234
P9-13. LG 4: I
n
 CFt 
IRR is found by solving: $0   
 initial investment
t 
t 1  (1  IRR) 
It can be computed to the nearest whole percent by the estimation method as shown for Project A below or
by using a financial calculator. (Subsequent IRR problems have been solved with a financial
calculator and rounded to the nearest whole percent.)
Project A
Average annuity ($20,000  $25,000  30,000  $35,000  $40,000)  5
Average annuity $150,000  5
Average annuity $30,000
PVIFAk%,5yrs. $90,000  $30,000 3.000
PVIFA19%,5 yrs. 3.0576
PVlFA20%,5 yrs. 2.991
However, try 17% and 18% since cash flows are greater in later years.
Yeart
1
2
3
4
5
CFt
(1)
PVIF17%,t
(2)
$20,000
25,000
30,000
35,000
40,000
0.855
0.731
0.624
0.534
0.456
Initial investment
NPV
PV@17%
[(1)(2)]
(3)
$17,100
18,275
18,720
18,690
18,240
$91,025
90,000
$ 1,025
PVIF18%,t
(4)
0.847
0.718
0.609
0.516
0.437
PV@18%
[(1)(4)]
(5)
$16,940
17,950
18,270
18,060
17,480
$88,700
90,000
$ 1,300
NPV at 17% is closer to $0, so IRR is 17%. If the firm’s cost of capital is below 17%, the project
would be acceptable.
Calculator solution: 17.43%
Project B
PVn PMT(PVIFAk%,4 yrs.)
$490,000 $150,000(PVIFAk%,4 yrs.)
$490,000  $150,000 (PVIFAk%,4 yrs.)
3.27  PVIFAk%,4
8% IRR  9%
Calculator solution: IRR  8.62%
The firm’s maximum cost of capital for project acceptability would be 8% (8.62%).
Project C
PVn PMT(PVIFAk%,5 yrs.)
$20,000 $7,500(PVIFAk%,5 yrs.)
$20,000  $7,500 (PVIFAk%,5 yrs.)
2.67 PVIFAk%,5 yrs.
25% IRR  26%
Calculator solution: IRR  25.41%
The firm’s maximum cost of capital for project acceptability would be 25% (25.41%).
Project D
$120,000 $100,000
$80,000
$60,000
$0 



 $240,000
1
2
3
(1  IRR) (1  IRR)
(1  IRR) (1  IRR)4
IRR  21%; Calculator solution: IRR  21.16%
The firm’s maximum cost of capital for project acceptability would be 21% (21.16%).
P9-14. LG 4: IRR–Mutually exclusive projects
Intermediate
a. and b.
Project X
$0 
$100,000
$120,000 $150,000 $190,000 $250,000




 $500,000
1
(1  IRR)
(1  IRR)2 (1  IRR)3 (1  IRR)4 (1  IRR)5
IRR  16%; since IRR  cost of capital, accept.
Calculator solution: 15.67%
Project Y
$0 
$140,000
$120,000
$95,000
$70,000
$50,000




 $325,000
1
2
3
4
(1  IRR)
(1  IRR) (1  IRR) (1  IRR) (1  IRR)5
IRR  17%; since IRR  cost of capital, accept.
Calculator solution: 17.29%
c.
Project Y, with the higher IRR, is preferred, although both are acceptable.
P9-21. LG 3, 4, 5: NPV, IRR, and NPV profiles
a. and b.
Project A
PV of cash inflows:
Year
1
2
3
4
5
CF
$25,000
35,000
45,000
50,000
55,000
PVIF12%,n
0.893
0.797
0.712
0.636
0.567
PV
$ 22,325
27,895
32,040
31,800
31,185
$145,245
NPV PV of cash inflows  initial investment
NPV $145,245  $130,000
NPV $15,245
Calculator solution: $15,237.71
Based on the NPV the project is acceptable since the NPV is greater than zero.
$0 
$25,000
$35,000
$45,000
$50,000
$55,000




 $130,000
1
2
3
4
(1  IRR) (1  IRR)
(1  IRR) (1  IRR)
(1  IRR)5
IRR 16%
Calculator solution: 16.06%
Based on the IRR the project is acceptable since the IRR of 16% is greater than the 12% cost
of capital.
Project B
PV of cash inflows:
Year
1
2
3
4
5
CF
PVIF12%,n
PV
$40,000
35,000
30,000
10,000
5,000
0.893
0.797
0.712
0.636
0.567
$35,720
27,895
21,360
6,360
2,835
$94,170
NPV $94,170  $85,000
NPV $9,170
Calculator solution: $9,161.79
Based on the NPV the project is acceptable since the NPV is greater than zero.
$0 
$40,000
$35,000
$30,000
$10,000
$5,000




 $85,000
1
2
3
4
(1  IRR) (1  IRR)
(1  IRR) (1  IRR)
(1  IRR)5
IRR 18%
Calculator solution: 17.75%
Based on the IRR the project is acceptable since the IRR of 16% is greater than the 12% cost
of capital.
c.
Data for NPV Profiles
NPV
Discount Rate
0%
12%
15%
16%
18%
A
$80,000
$15,245
—
0
—
B
$35,000
—
$ 9,170
—
0
d. The net present value profile indicates that there are conflicting rankings at a discount rate
less than the intersection point of the two profiles (approximately 15%). The conflict in
rankings is caused by the relative cash flow pattern of the two projects. At discount rates
above approximately 15%, Project B is preferable; below approximately 15%, Project A is
better. Based on Candor Enterprise’s 12% cost of capital, Project A should be chosen.
e. Project A has an increasing cash flow from Year 1 through Year 5, whereas Project B has a
decreasing cash flow from Year 1 through Year 5. Cash flows moving in opposite directions
often cause conflicting rankings. The IRR method reinvests Project B’s larger early cash
flows at the higher IRR rate, not the 12% cost of capital.
P9-24. LG 2, 3, 4: Integrative–complete investment decision
a.
Initial investment:
Installed cost of new press 
Cost of new press
 After-tax proceeds from sale of old asset
Proceeds from sale of existing press
 Taxes on sale of existing press*
Total after-tax proceeds from sale
Initial investment
$2,200,000
(1,200,000)
480,000
(720,000)
$1,480,000
*
Book value $0
$1,200,000  $0  $1,200,000 income from sale of existing press
$1,200,000 income from sale(0.40) $480,000
b.
Year Revenues
Calculation of Operating Cash Flows
Net Profits
Expenses Depreciation before Taxes
Taxes
Net Profits
after Taxes
1
2
3
4
5
6
$800,000
800,000
800,000
800,000
800,000
0
$216,000
57,600
229,200
321,600
321,600
66,000
c.
$1,600,000
1,600,000
1,600,000
1,600,000
1,600,000
0
$440,000
704,000
418,000
264,000
264,000
110,000
$360,000
96,000
382,000
536,000
536,000
110,000
$144,000
38,400
152,800
214,400
214,400
44,000
Cash
Flow
$656,000
761,600
647,200
585,600
585,600
44,000
Payback period  2 years  ($62,400  $647,200)  2.1 years
d. PV of cash inflows:
Year
1
2
3
4
5
6
CF
PVIF11%,n
PV
$656,000
761,000
647,200
585,600
585,600
44,000
0.901
0.812
0.731
0.659
0.593
0.535
$ 591,056
618,419
473,103
385,910
347,261
23,540
$2,439,289
NPV PV of cash inflows  initial investment
NPV $2,439,289  $1,480,000
NPV $959,289
Calculator solution: $959,152
$656,000 $761,600 $647,200 $585,600 $585,600
$44,000
$0 





 $1,480,000
1
2
3
4
5
(1  IRR) (1  IRR)
(1  IRR) (1  IRR)
(1  IRR) (1  IRR)6
e.
IRR 35%
Calculator solution: 35.04%
The NPV is a positive $959,289 and the IRR of 35% is well above the cost of capital of 11%.
Based on both decision criteria, the project should be accepted.
P10-3. LG 2: Breakeven cash inflows and risk
a.
Project X
Project Y
PVn  PMT  (PVIFA15%,5 yrs.)
PVn  PMT  (PVIFA15%,5 yrs.)
PVn  $10,000  (3.352)
PVn $15,000  (3.352)
PVn  $33,520
PVn  $50,280
NPV  PVn  initial investment
NPV  PVn  initial investment
NPV  $33,520  $30,000
NPV  $50,280  $40,000
NPV  $3,520
NPV  $10,280
Calculator solution: $3,521.55
Calculator solution: $10,282.33
b. Project X
Project Y
$CF  3.352  $30,000
$CF  3.352  $40,000
$CF  $30,000  3.352
$CF  $40,000  3.352
$CF  $8,949.88
$CF  $11,933.17
Calculator solution: $8,949.47
Calculator solution: $11,932.62
c. Project X
Project Y
Probability  60%
Probability  25%
d. Project Y is more risky and has a higher potential NPV. Project X has less risk and less return
while Project Y has more risk and more return, thus the risk–return tradeoff.
e. Choose Project X to minimize losses; to achieve higher NPV, choose Project Y.
P10-5. LG 2: Scenario analysis
a.
Range P  $1,000  $500  $500
Range Q  $1,200  $400  $800
b.
NPV
Project P
Outcome
c.
Table Value
Calculator Solution
Project Q
Table Value
Calculator Solution
1,608.43
$542
1,609
$542.17
1,608.43
3,144.57
4,374
4,373.48
Pessimistic
$73
$72.28
Most likely
1,609
Optimistic
3,145
Range P $3,145  $73  $3,072 (Calculator solution: $3,072.29)
Range Q $4,374  ($542)  $4,916 (Calculator solution: $4,915.65)
Each computer has the same most likely result. Computer Q has both a greater potential loss
and a greater potential return. Therefore, the decision will depend on the risk disposition of
management.
P10-8. LG 4: Risk–adjusted discount rates–Basic
a.
Project E
PVn  $6,000  (PVIFA15%,4)
PVn  $6,000  2.855
PVn  $17,130
NPV  $17,130  $15,000
NPV  $2,130
Calculator solution: $2,129.87
Project F
Year
1
2
3
4
CF
PVIF15%,n
$6,000
4,000
5,000
2,000
0.870
0.756
0.658
0.572
PV
$ 5,220
3,024
3,290
1,144
$12,678
NPV  $12,678  $11,000
NPV  $1,678
Calculator solution: $1,673.05
Project G
Year
1
2
3
4
CF
PVIF15%,n
$4,000
6,000
8,000
12,000
0.870
0.756
0.658
0.572
PV
$ 3,480
4,536
5,264
6,864
$20,144
NPV  $20,144  $19,000
NPV  $1,144
Calculator solution: $1,136.29
Project E, with the highest NPV, is preferred.
b. RADRE  0.10  (1.80  (0.15  0.10))  0.19
RADRF  0.10  (1.00  (0.15  0.10))  0.15
RADRG  0.10  (0.60  (0.15  0.10))  0.13
c.
Project E
$6,000  (2.639)  $15,834
NPV  $15,834  $15,000
NPV  $834
Calculator solution: $831.51
Project F
Same as in part a, $1,678 (Calculator solution: $1,673.05)
Project G
Year
CF
PVIF13%,n
PV
1
$4,000
0.885
$3,540
2
6,000
0.783
4,698
3
8,000
0.693
5,544
4
12,000
0.613
7,356
$21,138
NPV  $21,138  $19,000
NPV  $2,138
Calculator solution: $2,142.93
Rank
Project
1
G
2
F
3
E
b. RADRE  0.10  (1.80  (0.15  0.10))  0.19
RADRF  0.10  (1.00  (0.15  0.10))  0.15
RADRG  0.10  (0.60  (0.15  0.10))  0.13
c. Project E
$6,000  (2.639)  $15,834
NPV  $15,834  $15,000
NPV  $834
Calculator solution: $831.51
Project F
Same as in part a, $1,678 (Calculator solution: $1,673.05)
Project G
Year
CF
PVIF13%,n
PV
1
2
$4,000
6,000
0.885
0.783
$ 3,540
4,698
3
8,000
0.693
5,544
4
12,000
0.613
7,356
$21,138
NPV  $21,138  $19,000
NPV  $2,138
Calculator solution: $2,142.93
Rank
Project
1
G
2
F
3
E
d. After adjusting the discount rate, even though all projects are still acceptable, the ranking
changes. Project G has the highest NPV and should be chosen.
P10-11. LG 4: Risk-adjusted rates of return using CAPM
kX  7%  1.2(12%  7%)  7%  6%  13%
kY  7%  1.4(12%  7%)  7%  7%  14%
NPVX  $30,000(PVIFA13%,4)  $70,000
NPVX  $30,000(2.974)  $70,000
NPVX  $89,220  $70,000  $19,220
Calculator solution: $19,234.14
NPVY  $22,000(PVIF14%,1)  $32,000(PVIF14%,2)  $38,000(PVIF14%3)
 $46,000(PVIF14%,4)  $78,000
NPVY  $22,000(0.877)  $32,000(0.769)  $38,000(0.675)  $46,000(0.592)  $78,000
NPVY  $19,294  $24,608  $25,650  $27,232  78,000  $18,805.82
Calculator solution: $18,805.82
b. The RADR approach prefers Project Y over Project X. The RADR approach combines the
risk adjustment and the time adjustment in a single value. The RADR approach is most often
used in business.
a.
P10-12. LG 4: Risk classes and RADR
a.
Project X
Year
CF
PVIF22%,n
PV
1
2
$80,000
70,000
0.820
0.672
$ 65,600
47,040
3
60,000
0.551
33,060
4
60,000
0.451
27,060
5
60,000
0.370
22,200
$194,960
NPV  $194,960  $180,000
NPV  $14,960
Calculator solution: $14,930.45
Project Y
Year
CF
PVIF13%,n
PV
1
$50,000
0.885
$ 44,250
2
60,000
0.783
46,980
3
70,000
0.693
48,510
4
80,000
0.613
49,040
5
90,000
0.543
48,870
$237,650
NPV  $237,650  $235,000
NPV  $2,650
Calculator solution: $2,663.99
Project Z
Year
CF
1
2
$90,000
$90,000
3
$90,000
4
$90,000
5
$90,000
PVIFA15%,5
3.352
PV
$301,680
NPV  $301,680  $310,000
NPV  $8,320
Calculator solution: $8,306.04
b. Projects X and Y are acceptable with positive NPV’s, while Project Z with a negative NPV is
not. Project X with the highest NPV should be undertaken.
P10-14. LG 5: Unequal lives–ANPV approach
a. Project X
Year
CF
PVIF14%,n
PV
1
$17,000
0.877
$14,909
2
25,000
0.769
19,225
3
33,000
0.675
22,275
4
41,000
0.592
24,272
$80,681
NPV  $80,681  $78,000
NPV  $2,681
Calculator solution: $2,698.32
Project Y
Year
CF
PVIF14%,n
PV
1
$28,000
0.877
$24,556
2
38,000
0.769
29,222
$53,778
NPV  $53,778  $52,000
NPV  $1,778
Calculator solution: $1,801.17
Project Z
PVn  PMT  (PVIFA14%,8 yrs.)
PVn  $15,000  4.639
PVn  $69,585
NPV  PVn  initial investment
NPV  $69,585  $66,000
NPV  $3,585
Calculator solution: $3,582.96
Rank
b.
Project
1
Z
2
X
3
Y
ANPV (ANPVj ) 
NPVj
PVIFAr %, nj
Project X
ANPV  $2,681  2.914 (14%, 4 yrs.)
ANPV  $920.04
Calculator solution: $926.08
Project Y
ANPV  $1,778  1.647 (14%, 2 yrs.)
ANPV  $1,079.54
Calculator solution: $1093.83
Project Z
ANPV  $3,585  4.639 (14%, 8 yrs.)
ANPV  $772.80
Calculator solution: $772.38
Rank
Project
1
Y
2
X
3
Z
c.
Project Y should be accepted. The results in Part a and b show the difference in NPV when
differing lives are considered.
P10-18. LG 6: Capital rationing–IRR and NPV approaches
a.
Rank by IRR
Project
F
E
G
C
B
A
D
IRR
Initial Investment
Total Investment
$2,500,000
800,000
1,200,000
$2,500,000
3,300,000
4,500,000
23%
22
20
19
18
17
16
Projects F, E, and G require a total investment of $4,500,000 and provide a total present value
of $5,200,000, and therefore a NPV of $700,000.
b. Rank by NPV (NPV  PV – Initial investment)
Project
F
A
C
B
D
G
E
NPV
$500,000
400,000
300,000
300,000
100,000
100,000
100,000
Initial Investment
$2,500,000
5,000,000
2,000,000
800,000
1,500,000
1,200,000
800,000
Project A can be eliminated because, while it has an acceptable NPV, its initial investment
exceeds the capital budget. Projects F and C require a total initial investment of $4,500,000
and provide a total present value of $5,300,000 and a net present value of $800,000. However,
the best option is to choose Projects B, F, and G, which also use the entire capital budget and
provide an NPV of $900,000.
c.
The internal rate of return approach uses the entire $4,500,000 capital budget but provides
$200,000 less present value ($5,400,000 – $5,200,000) than the NPV approach. Since the
NPV approach maximizes shareholder wealth, it is the superior method.
d. The firm should implement Projects B, F, and G, as explained in Part c.
P11-5. LG 2: Cost of debt using the approximation formula
rd 
$1,000  N d
n
N d  $1,000
2
I
ri  rd  (1T)
Alternative A
rd 
$1,000  $1,220
$76.25
16

 6.87%
$1,220  $1,000
$1,110
2
$90 
ri  6.87%  (10.40)  4.12%
Alternative B
rd 
$1,000  $1,020
$66.00
5

 6.54%
$1,020  $1,000
$1,010
2
$70 
ri  6.54%  (10.40)  3.92%
Alternative C
rd 
$1,000  $970
$64.29
7

 6.53%
$970  $1,000
$985
2
$60 
ri  6.53%  (10.40)  3.92%
Alternative D
rd 
$1,000  $895
$60.50
10

 6.39%
$895  $1,000
$947.50
2
$50 
ri  6.39%  (10.40)  3.83%
P11-7. LG 2: Cost of preferred stock: rp  Dp  Np
a.
rp 
$12.00
 12.63%
$95.00
b.
rp 
$10.00
 11.11%
$90.00
P11-10. LG 3: Cost of common stock equity: kn 
D1  g
Nn
D2009
 FVIFk %,4
D2005
$3.10
g
 1.462
$2.12
From FVIF table, the factor closest to 1.462 occurs at 10% (i.e., 1.464 for 4 years).
Calculator solution: 9.97%
b. Nn  $52 (given in the problem)
D
c. rr  2010  g
P0
a.
g
$3.40
 0.10  15.91%
$57.50
D
rr  2010  g
Nn
rr 
d.
rr 
$3.40
 0.10  16.54%
$52.00
P11-11. LG 3: Retained earnings versus new common stock
rr 
D1
g
P0
Firm
A
rn 
D1
g
Nn
Calculation
rr = ($2.25  $50.00) + 8% = 12.50%
rn = ($2.25  $47.00) + 8% = 12.79%
B
rr = ($1.00  $20.00) + 4% = 9.00%
rn = ($1.00 $18.00) + 4% = 9.56%
C
rr = ($2.00  $42.50) + 6% = 10.71%
rn = ($2.00  $39.50) + 6% = 11.06%
D
rr = ($2.10  $19.00) + 2% = 13.05%
rn = ($2.10  $16.00) + 2% = 15.13%
P11-14. LG 4: WACC–book weights and market weights
a.
Book value weights:
Type of Capital
L-T debt
Preferred stock
Common stock
Book Value
$4,000,000
40,000
1,060,000
$5,100,000
b. Market value weights:
Type of Capital
Market Value
L-T debt
$3,840,000
Preferred stock
60,000
Common stock
3,000,000
$6,900,000
c.
Weight
0.784
0.008
0.208
Cost
6.00%
13.00%
17.00%
Weighted Cost
4.704%
0.104%
3.536%
8.344%
Weight
0.557
0.009
0.435
Cost
6.00%
13.00%
17.00%
Weighted Cost
3.342%
0.117%
7.395%
10.854%
The difference lies in the two different value bases. The market value approach yields the
better value since the costs of the components of the capital structure are calculated using the
prevailing market prices. Since the common stock is selling at a higher value than its book
value, the cost of capital is much higher when using the market value weights. Notice that
the book value weights give the firm a much greater leverage position than when the market
value weights are used.
P11-17. LG 2, 3, 4, 5: Calculation of specific costs, WACC, and WMCC
a.
Cost of debt: (approximate)
rd 
rd 
($1,000  N d )
n
( N d  $1,000)
2
I
($1,000  $950)
$100  $5
10

 10.77%
($950  $1,000)
$975
2
$100 
ri  10.77  (l0.40)
ri  6.46%
Cost of preferred stock: rp 
rp 
Dp
Np
$8
 12.70%
$63
Cost of common stock equity: rs 
g
D2009
 FVIFk %,4
D2005
g
$3.75
 1.316
$2.85
D1
g
P0
From FVIF table, the factor closest to 1.316 occurs at 7% (i.e., 1.311 for 4 years).
Calculator solution: 7.10%
rr 
$4.00
 0.07  15.00%
$50.00
Cost of new common stock equity:
rn 
b.
$4.00
 0.07  16.52%
$42.00
Breaking point 
BPcommon equity 
AFj
Wj
[$7,000,000  (1  0.6* )]
 $5,600,000
0.50
Between $0 and $5,600,000, the cost of common stock equity is 15% because all common
stock equity comes from retained earnings. Above $5,600,000, the cost of common stock
equity is 16.52%. It is higher due to the flotation costs associated with a new issue of
common stock.
*
The firm expects to pay 60% of all earnings available to common shareholders as dividends.
c.
WACC—$0 to $5,600,000:
L-T debt
0.40  6.46%
Preferred stock 0.10  12.70%
Common stock 0.50  15.00%
WACC




2.58%
1.27%
7.50%
11.35%
d.
WACC—above $5,600,000: L-T debt
0.40  6.46%
Preferred stock 0.10  12.70%
Common stock 0.50  16.52%
WACC




2.58%
1.27%
8.26%
12.11%
P11-20. LG 4, 5, 6: Integrative–WACC, WMCC, and IOS
a.
Breaking points and ranges:
Source of
Capital
Long-term debt
b.
c.
Cost
Range of
% New Financing
6
$0$320,000
8
$320,001
and above
Preferred stock
17
$0 and above
Common stock
equity
20
24
$0$200,000
$200,001
and above
Breaking
Point
$320,000  0.40  $800,000
Range of Total
New Financing
$0$800,000
Greater than
$800,000
Greater than $0
$200,000  0.40  $500,000
$0$500,000
Greater than
$500,000
WACC will change at $500,000 and $800,000.
WACC
Source of
Capital
(1)
Debt
Preferred
Common
Target
Proportion
(2)
0.40
0.20
0.40
$500,000$800,000
Debt
Preferred
Common
0.40
0.20
0.40
Greater than
$800,000
Debt
Preferred
Common
0.40
0.20
0.40
Range of Total
New Financing
$0$500,000
Weighted
Cost
Cost %
(2)  (3)
(3)
(4)
6
2.40%
17
3.40%
20
8.00%
WACC  13.80%
6%
2.40%
17%
3.40%
24%
9.60%
WACC  15.40%
8%
3.20%
17%
3.40%
24
9.60%
WACC  16.20%
d.
IOS data for graph
Investment
E
C
G
A
H
I
B
D
F
e.
IRR
23%
22
21
19
17
16
15
14
13
Initial
Investment
$200,000
100,000
300,000
200,000
100,000
400,000
300,000
600,000
100,000
The firm should accept Investments E, C, G, A, and H, since for each of these, the IRR on
the marginal investment exceeds the WMCC. The next project (i.e., I) cannot be accepted
since its return of 16% is below the weighted marginal cost of the available funds of 16.2%.
P12-7. LG 1: Breakeven analysis
a.
Cumulative
Investment
$ 200,000
300,000
600,000
800,000
900,000
1,300,000
1,600,000
2,200,000
2,300,000
Q
FC
$4,000

 2,000 figurines
( P  VC ) $8.00  $6.00
b. Sales
Less:
Fixed costs
Variable costs ($6  1,500)
EBIT
c. Sales
Less:
Fixed costs
$10,000
4,000
9,000
$3,000
$15,000
4,000
Variable costs ($6  1,500)
EBIT
9,000
$2,000
EBIT  FC $4,000  $4,000 $8,000


 4,000 units
P  VC
$8  $6
$2
e. One alternative is to price the units differently based on the variable cost of the unit. Those
more costly to produce will have higher prices than the less expensive production models. If
they wish to maintain the same price for all units they may need to reduce the selection from
the 15 types currently available to a smaller number that includes only those that have an
average variable cost below $5.33 ($8  $4000/1500 units).
P12-9. LG 2: DOL
d.
Q
a.
Q
FC
$380,000

 8,000 units
( P  VC ) $63.50  $16.00
9,000 Units
10,000 Units
11,000 Units
$571,500
$635,000
$698,500
144,000
160,000
176,000
380,000
$ 47,500
380,000
$ 95,000
380,000
$142,500
1,000
0
1,000
% change in sales
1,000  10,000  10%
0
1,000  10,000  10%
Change in EBIT
$47,500
0
$47,500
% Change in EBIT
$47,500  95,000 = 50%
0
$47,500  95,000 = 50%
% change in EBIT
% change in sales
50  10  5
b.
Sales
Less: Variable costs
Less: Fixed costs
EBIT
c.
Change in unit sales
d.
e.
DOL 
[Q  ( P  VC )]
[Q  ( P  VC )]  FC
DOL 
[10,000  ($63.50  $16.00)]
[10,000  ($63.50  $16.00)  $380,000]
DOL 
$475,000
 5.00
$95,000
50  10  5
P12-12. LG 2: DFL
a.
EBIT
$80,000
$120,000
40,000
40,000
$40,000
$ 80,000
16,000
32,000
Net profit after taxes
$24,000
$ 48,000
EPS (2,000 shares)
$ 12.00
$ 24.00
Less: Interest
Net profits before taxes
Less: Taxes (40%)
b.
DFL 
DFL 
EBIT

1 

 EBIT  I   PD 

(1  T )  


$80,000
2
[$80,000  $40,000  0]
c.
EBIT
$80,000
$120,000
16,000
16,000
Less: Interest
Net profits before taxes
$64,000
Less: Taxes (40%)
$104,000
25,600
41,600
Net profit after taxes
$38,400
$ 62,400
EPS (3,000 shares)
$ 12.80
$ 20.80
DFL 
$80,000
 1.25
[$80,000  $16,000  0]
P12-20. LG 3: Debt and financial risk
a.
EBIT Calculation
Probability
Sales
Less: Variable costs (70%)
Less: Fixed costs
EBIT
Less: Interest
Earnings before taxes
Less: Taxes
Earnings after taxes
0.20
0.60
0.20
$200,000
140,000
75,000
$(15,000)
12,000
$(27,000)
(10,800)
$(16,200)
$300,000
210,000
75,000
$ 15,000
12,000
$ 3,000
1,200
$ 1,800
$400,000
280,000
75,000
$ 45,000
12,000
$ 33,000
13,200
$ 19,800
$(16,200)
$ 1,800
$19,800
b. EPS
Earnings after taxes
Number of shares
EPS
10,000
$ (1.62)
10,000
$ 0.18
10,000
$ 1.98
n
Expected EPS   EPSj  Pr j
i 1
Expected EPS  ($1.62  0.20)  ($0.18  0.60)  ($1.98  0.20)
Expected EPS  $0.324  $0.108  $0.396
Expected EPS  $0.18
 EPS 
n
 (EPS  EPS)
i 1
i
2
 Pri
 EPS  [($1.62  $0.18)2  0.20]  [($0.18  $0.18) 2  0.60]  [($1.98  $0.18)2  0.20]
 EPS  ($3.24  0.20)  0  ($3.24  0.20)
 EPS  $0.648  $0.648
 EPS  $1.296  $1.138
 EPS
1.138
CVEPS 
Expected EPS

0.18
 6.32
c.
EBIT *
$(15,000)
$15,000
$45,000
Less: Interest
Net profit before taxes
Less: Taxes
Net profits after taxes
EPS (15,000 shares)
0
$(15,000)
(6,000)
$ (9,000)
$ (0.60)
0
$15,000
6,000
$ 9,000
$ 0.60
0
$45,000
18,000
$27,000
$ 1.80
*
From part a
Expected EPS  ($0.60  0.20)  ($0.60  0.60)  ($1.80  0.20)  $0.60
 EPS  [( $0.60  $0.60)2  0.20]  [($0.60  $0.60)2  0.60]  [($1.80  $0.60)2  0.20]
 EPS  ($1.44  0.20)  0  ($1.44  0.20)
 EPS  $0.576  $0.759
$0.759
 1.265
0.60
d. Summary statistics
CVEPS 
Expected EPS
EPS
CVEPS
With Debt
All Equity
$0.180
$1.138
$0.600
$0.759
6.320
1.265
Including debt in Tower Interiors’ capital structure results in a lower expected EPS, a higher
standard deviation, and a much higher coefficient of variation than the all-equity structure.
Eliminating debt from the firm’s capital structure greatly reduces financial risk, which is
measured by the coefficient of variation.
P12-23. LG 5: EBIT-EPS and preferred stock
a.
EBIT
Less: Interest
Net profits before taxes
Less: Taxes
Net profit after taxes
Less: Preferred dividends
Earnings available for
common shareholders
EPS (8,000 shares)
EPS (10,000 shares)
Structure A
$30,000
12,000
$18,000
7,200
$10,800
1,800
$ 9,000
$ 1.125
$50,000
12,000
$38,000
15,200
$22,800
1,800
$21,000
$ 2.625
Structure B
$30,000
7,500
$22,500
9,000
$13,500
2,700
$50,000
7,500
$42,500
17,000
$25,500
2,700
$10,800
$22,800
$ 1.08
$ 2.28
b.
c. Structure A has greater financial leverage, hence greater financial risk.
d. If EBIT is expected to be below $27,000, Structure B is preferred. If EBIT is expected to be
above $27,000, Structure A is preferred.
e. If EBIT is expected to be $35,000, Structure A is recommended since changes in EPS are
much greater for given values of EBIT.
P12-24. LG 3, 4, 6: Integrative–optimal capital structure
Intermediate
a.
Debt Ratio
0%
15%
EBIT
Less: Interest
EBT
Taxes @40%
Net profit
Less: Preferred
dividends
Profits available to
common stock
# shares outstanding
EPS
30%
45%
60%
$2,000,000
0
$2,000,000
800,000
$1,200,000
$2,000,000
120,000
$1,880,000
752,000
$1,128,000
$2,000,000
270,000
1,730,000
692,000
$1,038,000
$2,000,000
540,000
$1,460,000
584,000
$ 876,000
$2,000,000
900,000
$1,100,000
440,000
$ 660,000
200,000
200,000
200,000
200,000
200,000
$1,000,000
200,000
$
5.00
$ 928,000
170,000
$
5.46
$ 838,000
140,000
$
5.99
$ 676,000
110,000
$
6.15
$ 460,000
80,000
$
5.75
EPS
rs
Debt: 0%
Debt: 15%
$5.00
$5.46
P0 
 $41.67
P0 
 $42.00
0.12
0.13
Debt: 30%
Debt: 45%
$5.99
$6.15
P0 
 $42.79
P0 
 $38.44
0.14
0.16
Debt: 60%
$5.75
P0 
 $28.75
0.20
c. The optimal capital structure would be 30% debt and 70% equity because this is the
debt/equity mix that maximizes the price of the common stock.
b.
P0 
P13-3. LG 2: Residual dividend policy
a.
Residual dividend policy means that the firm will consider its investment opportunities first.
If after meeting these requirements there are funds left, the firm will pay the residual out in
the form of dividends. Thus, if the firm has excellent investment opportunities, the dividend
will be smaller than if investment opportunities are limited.
b. Proposed
Capital budget
Debt portion (40%)
Equity portion (60%)
Available retained earnings
Dividend
$2,000,000
$3,000,000
$4,000,000
800,000
1,200,000
1,600,000
1,200,000
1,800,000
2,400,000
$2,000,000
$2,000,000
$2,000,000
800,000
200,000
0
Dividend payout ratio
c.
40%
10%
0%
The amount of dividends paid is reduced as capital expenditures increase. Thus, if the firm
chooses larger capital investments, dividend payments will be smaller or nonexistent.
P13-6. LG 4: Low-regular-and-extra dividend policy
a.
Year
Payout %
Year
Payout %
2004
2005
25.4
23.3
2007
2008
22.7
20.8
2006
17.9
2009
16.7
b.
c.
Year
25%
Payout
Actual
Payout
$ Diff.
Year
25%
Payout
Actual
Payout
$ Diff.
2004
$0.49
0.50
0.01
2007
0.55
0.50
0.05
2005
0.54
0.50
–0.04
2008
0.60
0.50
0.10
2006
0.70
0.50
–0.20
2009
0.75
0.50
0.25
In this example the firm would not pay any extra dividend since the actual dividend did not
fall below the 25% minimum by $1.00 in any year. When the “extra” dividend is not paid due
to the $1.00 minimum, the extra cash can be used for additional investment by placing the
funds in a short-term investment account.
d. If the firm expects the earnings to remain above the earnings per share (EPS) of $2.20 the
dividend should be raised to $0.55 per share. The 55 cents per share will retain the 25% target
payout but allow the firm to pay a higher regular dividend without jeopardizing the cash
position of the firm by paying too high of a regular dividend.
P13-9. LG 5: Stock dividend–firm
(a) 5%
Stock Dividend
Preferred stock
$100,000
Common stock (xx,xxx shares
@$2.00 par)
21,0001
Paid-in capital in excess of par
Retained earnings
Stockholders’ equity
(b) (1) 10%
Stock Dividend
$100,000
22,0002
(b) (2) 20%
Stock Dividend
$100,000
24,0003
294,000
308,000
336,000
85,000
70,000
40,000
$500,000
$500,000
$500,000
1
10,500 shares
11,000 shares
3
12,000 shares
2
c.
Stockholders’ equity has not changed. Funds have only been redistributed between the
stockholders’ equity accounts.
P13-15. LG 5, 6: Stock split versus stock dividend–firm
a. There would be a decrease in the par value of the stock from $3 to $2 per share. The shares
outstanding would increase to 150,000. The common stock account would still be $300,000
(150,000 shares at $2 par).
b. The stock price would decrease by one-third to $80 per share.
c. Before stock split: $100 per share ($10,000,000  100,000)
After stock split: $66.67 per share ($10,000,000  150,000)
d. (1) A 50% stock dividend would increase the number of shares to 150,000 but would not
entail a decrease in par value. There would be a transfer of $150,000 into the common
stock account and $5,850,000 in the paid-in capital in excess of par account from the
retained earnings account, which decreases to $4,000,000.
(2) The stock price would change to approximately the same level.
(3) Before dividend: $100 per share ($10,000,000  100,000)
After dividend: $26.67 per share ($4,000,000  150,000)
e. Stock splits cause an increase in the number of shares outstanding and a decrease in the par
value of the stock with no alteration of the firm’s equity structure. However, stock dividends
cause an increase in the number of shares outstanding without any decrease in par value.
Stock dividends cause a transfer of funds from the retained earnings account into the common
stock account and paid-in capital in excess of par account.
P13-17. LG 6: Stock repurchase
a. Shares to be repurchased 
b. EPS 
$400,000
 19,047 shares
$21.00
$800,000
$800,000

 $2.10 per share
(400,000  19,047) 380,953
If 19,047 shares are repurchased, the number of common shares outstanding will decrease and
earnings per share will increase.
c. Market price: $2.1010  $21.00 per share
d. The stock repurchase results in an increase in earnings per share from $2.00 to $2.10.
e. The pre-repurchase market price is different from the post-repurchase market price by the
amount of the cash dividend paid. The post-repurchase price is higher because there are fewer
shares outstanding.
Cash dividends are taxable to the stockholder when they are distributed and are taxed at a
maximum 15% tax rate. If the firm repurchases stock, taxes on the increased value resulting
from the purchase are also due at the time of the repurchase. The additional $1 gain would be
taxed at either the long-term capital gains rate of 15%, the same as the dividend, unless the
stock was held for less than 1 year then the gain would be short-term and taxed at the higher
marginal ordinary income rate. Which alternative is preferred by the shareholders would
depend on the investors’ holding period for the stock at the time the repurchase is made.
Taxes would not have to be paid on the repurchase gains until the shares are sold.
P14-1. LG 2: CCC
a.


b.

c.


d.
 Average age of inventories
 Average collection period

 90 days  60 days

 150 days
CCC
 Operating cycle  Average payment period
 150 days  30 days

 120 days
Resources needed
 (total annual outlays  365 days)  CCC

 [$30,000,000  365]  120

 $9,863,013.70
Shortening either the AAI or the ACP, lengthening the APP, or a combination of these can
reduce the CCC.
OC
P14-4. LG 2: Aggressive versus conservative seasonal funding strategy
a.
Total Funds
Requirements
Permanent
Requirements
$2,000,000
2,000,000
$2,000,000
2,000,000
March
2,000,000
2,000,000
0
April
4,000,000
2,000,000
2,000,000
May
6,000,000
2,000,000
4,000,000
June
9,000,000
2,000,000
7,000,000
July
12,000,000
2,000,000
10,000,000
August
14,000,000
2,000,000
12,000,000
September
9,000,000
2,000,000
7,000,000
October
5,000,000
2,000,000
3,000,000
November
4,000,000
2,000,000
2,000,000
December
3,000,000
2,000,000
1,000,000
Month
January
February
b.
c.



d.
Seasonal
Requirements
$
0
0
Average permanent requirement  $2,000,000
Average seasonal requirement  $48,000,000  12

 $4,000,000
(1) Under an aggressive strategy, the firm would borrow from $1,000,000 to $12,000,000
according to the seasonal requirement schedule shown in part a at the prevailing shortterm rate. The firm would borrow $2,000,000, or the permanent portion of its
requirements, at the prevailing long-term rate.
(2) Under a conservative strategy, the firm would borrow at the peak need level of
$14,000,000 at the prevailing long-term rate.
Aggressive  ($2,000,000  0.17)  ($4,000,000  0.12)

 $340,000  $480,000

 $820,000
Conservative  ($14,000,000  0.17)

 $2,380,000
In this case, the large difference in financing costs makes the aggressive strategy more
attractive. Possibly the higher returns warrant higher risks. In general, since the conservative
strategy requires the firm to pay interest on unneeded funds, its cost is higher. Thus, the
aggressive strategy is more profitable but also more risky.
P14-9. LG 4: Accounts receivable changes and bad debts
a.
b.
c.
Bad debts
Proposed plan (60,000  $20  0.04)
$48,000
Present plan (50,000  $20  0.02)
20,000
Cost of marginal bad debts
$28,000
No, since the cost of marginal bad debts exceeds the savings of $3,500.
d.
Additional profit contribution from sales:
10,000 additional units  ($20  $15)
$50,000
Cost of marginal bad debts (from part (b))
(28,000)
Savings
3,500
Net benefit from implementing proposed plan $25,500
This policy change is recommended because the increase in sales and the savings of $3,500
exceed the increased bad debt expense.
e. When the additional sales are ignored, the proposed policy is rejected. However, when all the
benefits are included, the profitability from new sales and savings outweigh the increased cost of
bad debts. Therefore, the policy is recommended
P14-10. LG 4: Relaxation of credit standards
Additional profit contribution from sales  1,000 additional units  ($40  $31)
Cost of marginal investment in AR:
11,000 units  $31
Average investment, proposed plan 
$56,055
365
60
10,000 units  $31
Average investment, present plan 
38,219
365
45
Marginal investment in AR
$17,836
Required return on investment
 0.25
Cost of marginal investment in AR
Cost of marginal bad debts:
Bad debts, proposed plan (0.03  $40  11,000 units)
$13,200
Bad debts, present plan (0.01  $40  10,000 units)
4,000
Cost of marginal bad debts
Net loss from implementing proposed plan
The credit standards should not be relaxed since the proposed plan results in a loss.
$9,000
(4,459)
(9,200)
($ 4,659)
P15-3. LG 1: Credit terms
a.
1/15 net 45 date of invoice
2/10 net 30 EOM
2/7 net 28 date of invoice
1/10 net 60 EOM
b. 45 days
49 days
28 days
79 days
c.
CD
365

100%  CD N
1%
365
Cost of giving up cash discount 

100%  1% 30
Cost of giving up cash discount  0.0101 12.17  0.1229  12.29%
Cost of giving up cash discount 
2%
365

98% (49  10)
Cost of giving up cash discount  0.0204  9.359  0.1909  19.09%
Cost of giving up cash discount 
2%
365

100%  2% 21
Cost of giving up cash discount  0.0204  17.38  0.3646  36.46%
Cost of giving up cash discount 
1%
365

100%  1% (79  10)
Cost of giving up cash discount  0.0101  5.2899  0.0534  5.34%
Cost of giving up cash discount 
d. For the first three purchases the firm would be better off to borrow the funds and take the
discount. The annual cost of not taking the discount is less than the firm’s 8% cost of capital
in the last case
P15-6. LG 1, 2: Cash discount decisions
a.
c.
Supplier
Cost of Forgoing Discount
b.
Decision
J
(0.01  0.99)  (365  20)  18.43%
Borrow
K
(0.02  0.98)  (365  60)  12.42%
Give up
L
(0.01  0.99)  (365  40)  9.22%
Give up
M
(0.03  0.97)  (365  45)  25.09%
Borrow
Prairie would have lower financing costs by giving up Ks and Ls discount since the cost of
forgoing the discount is lower than the 16% cost of borrowing.
Cost of giving up discount from Supplier M  (0.03  0.97)  (365  75)  15.05% In this
case the firm should give up the discount and pay at the end of the extended period.
P15-13. LG 3: Compensating balance vs. discount loan
$150,000  0.09
$13,500

 10.0% This calculation
$150,000  ($150,000  0.10) $135,000
assumes that Weathers does not maintain any normal account balances at State Bank.
$150,000  0.09  6/12
$6,750
Frost finance interest 

 4.71%
$150,000  ($150,000  0.09  6/12) $143,250
Effective annual rate = (1.0471)2 –1 = 0.0964 = 9.46%
b. If Weathers became a regular customer of State Bank and kept its normal deposits at the
bank, then the additional deposit required for the compensating balance would be reduced
and the cost would be lowered.
a.
State Bank interest 
P15-14. LG 3: Integrative–comparison of loan terms
(0.08  0.033)  0.80  14.125%
[$2,000,000  (0.08  0.028)  (0.005  $2,000,000)]
 14.125%
b. Effective annual interest rate 
($2,000,000  0.80)
c. The revolving credit account seems better, since the cost of the two arrangements is the same;
with a revolving loan arrangement, the loan is committed.
a.
P16-3. LG 2: Loan payments and interest
Payment  $117,000  3.889  $30,085 (Calculator solution: $30,087.43)
Year
Beginning
Balance
Interest
Principal
1
2
3
$117,000
103,295
87,671
$16,380
14,461
12,274
$ 13,705
15,624
17,811
4
69,860
9,780
20,305
5
49,555
6,938
23,147
6
26,408
3,697
26,388
$ 26,408
$116,980
$117,000
Note: Due to the present value interest factor of the annuity (PVIFA) tables in the text presenting
factors only to the third decimal place and the rounding of interest and principal payments to the
second decimal place, the summed principal payments over the term of the loan will be slightly
different from the loan amount. To compensate in problems involving amortization schedules, the
adjustment has been made in the last principal payment. The actual amount is shown with the
adjusted figure to its right.
P16-4. LG 2: Lease versus purchase
a. Lease
After-tax cash outflow  $25,200(l – 0.40 )  $15,120/year for 3years  $5,000 purchase
option in year 3 (total for year 3: $20,120)
Purchase
Loan
MainPayment tenance
Year
(1)
(2)
Depreciation
(3)
After-tax
Total
Tax
Cash
Shields
Outflows
Interest Deductions
at 14% (2  3  4) [(0.40)  (5)] [(1  2) – (6)]
(4)
(5)
(6)
(7)
1
$19,800
$8,400
$30,000
$12,000
$15,644
$25,844 $1,800
2
25,844
1,800
27,000
5,958
34,758
13,903
13,741
3
25,844
1,800
9,000
3,174
13,974
5,590
22,054
b.
End of Year
Lease
1
2
3
Purchase
1
2
3
c.
After-tax
Cash Outflows
PVIF8%,n
PV of Outflows
Calculator
Solution
$15,120
15,120
20,120
0.926
0.857
0.794
$14,001
12,958
15,975
$42,934
$42,934.87
$14,486
11,776
17,511
$43,773
$43,773.05
$15,644
13,741
22,054
0.926
0.857
0.794
Since the PV of leasing is less than the PV of purchasing the equipment, the firm should lease
the equipment and save $839 in present value terms.
P16-5. LG 2: Lease versus purchase
a.
Lease
After-tax cash outflows  $19,800  (1 – 0.40)  $11,880/year for 5 years plus $24,000
purchase option in year 5 (total $35,880).
Purchase
Tax
After-tax
Shields
Cash
Outflows
[(0.40) 
(5)]
[(1  2)  (6)]
(6)
(7)
Year
Loan
MainPayment tenance
(1)
(2)
Depreciation
(3)
Total
Interest Deductions
at 14% (2  3  4)
(4)
(5)
1
$23,302
$2,000
$16,000
$11,200
$29,200
$11,680
$13,622
2
3
4
5
23,302
23,302
23,302
23,302
2,000
2,000
2,000
2,000
25,600
15,200
9,600
9,600
9,506
7,574
5,372
2,862
37,106
24,774
16,972
14,462
14,842
9,910
6,789
5,785
10,460
15,392
18,513
19,517
b.
End of Year
Lease
1
2
3
4
5
After-tax
Cash Outflows
PVIF9%,n
$11,880
11,880
11,880
11,880
35,880
0.917
0.842
0.772
0.708
0.650
PV of Outflows
Calculator
Solution
$10,894
10,003
9,171
8,411
23,322
$61,801
$61,807.41
$12,491
8,807
11,883
13,107
12,686
$58,974
$58,986.46
Purchase
1
2
3
4
5
c.
$13,622
10,460
15,392
18,513
19,517
0.917
0.842
0.772
0.708
0.650
The present value of the cash outflows is less with the purchasing plan, so the firm should
purchase the machine. By doing so, it saves $2,827 in present value terms.