# 25 % Interest Rate by vmy19736

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```									                  CHAPTER 2 – Solutions to Assignment Problems
Assignment 2.1:
a.
Freida, Incorporated
Income Statement
For the Year ending December 31, 2006

Gross sales                             462,720
Less Returns and allowances            (10,210)
Net sales                                             452,510

Beginning inventory                      63,210
+ Materials Purchases                   228,580
- Ending inventory                     (68,390)
Cost of goods sold                                    223,400
Gross profit                                        229,110
Management salaries                                    17,950
Lease payments                                         39,270
R&D expenditures                                        4,890
Repairs and maintenance costs                           2,910
Depreciation                                           12,510
Operating profit                                    138,650
Interest expense                                       17,090
Earnings before taxes                               121,560
Taxes                                                   3,270
Net income                                          118,290

b. Net profit margin = net income/net sales = 118,290/452,510 = 26.14%
c. Accumulated depreciation = 212,820 + 12,510 = \$225,330.
Assignment 2.2:
a.

Windcharter Company
Balance Sheet
For the Year ending December 31, 2006

Cash                                     17,600      ST bank loans                       32,570
Accounts receivable, net                105,770      Accounts payable                    50,830
Inventories                             136,500      Accrued expenses                    11,850
Current assets                        259,870      Current portion LT Debt              4,080
Current liabilities                99,330
Gross fixed assets                      284,950      Long-term debt                     134,300
Less Accumulated depreciation           (82,310)      Total liabilities                 233,630
Net fixed assets                        202,640      Preferred stock                      8,000
Common stock (\$0.20 par)            60,000
Retained earnings                   89,280
Total assets                           462,510       Total liabilities & net worth     462,510

b. Assume for this problem that the number given for Net income is actually Net income
available to common stockholders (that is, reported Net income minus preferred dividends).
Thus, Annual addition to Retained earnings = Net income available to common stockholders
– Common stock dividends paid.
Thus, Common stock dividends paid = Net income – Addition to (i.e., change in) Retained
earnings.
Common stock dividends paid = 25,400 – (89,280 – 79,880) = 16,000.

Dividends per share = Dividends divided by number of shares outstanding.
Number of shares outstanding = Common Stock divided by par value per share
= 60,000/.20 = 300,000.

Dividends per share = \$0.053 or 5.3 cents per share.

c. Cash spent on new plant and equipment = Depreciation for the year as listed on the income
statement plus the change in net fixed assets.
Thus, Cash spent on fixed assets in 1999 = 10,260 + (202,640 – 184660) = \$28,240.
Assignment 2.3:
1. \$4,055,740
\$4,100,144
Although Gross sales decreased by 2 percent, net sales (the only number reported) show an
increase of 1.1 percent. Since Returns and allowances are estimates made by management,
there is some chance that the growth in sales conclusion may be misleading.

2. Cost of goods sold = Beginning inventory + Purchases – Ending inventory.
a. \$174,300
b. \$218,500
3. First solve for accumulated depreciation:
2005                 2006
Gross fixed assets                                 3,200,000            4,620,000
Less Accumulated depreciation                     (1,280,000)          (1,540,000)
Net fixed assets                                   1,920,000            3,080,000

Depreciation expense = change in accumulated depreciation = \$260,000.
Problems:
1. Look up definitions in chapter
2. EBIT = \$15,000; Net income = \$6,500
3. a. \$400            b. \$100              c. \$35
4. Gross profit = \$3,120,000; Ending Inventory = 850,000.
5.

Gross Sales              5,000,000
-Returns                   100,000
Net Sales                4,900,000
-COGS                    3,000,000 (250,000 x \$12 per unit)
Gross profit             1,900,000
- Operating expenses     1,000,000
- Depreciation             100,000
Operating income           800,000
- Interest                 500,000
EBT                        300,000
- Taxes                    120,000
Net income                 180,000

6.
Sales                                   32,000
Cost of goods sold                      19,200
Gross profit                           12,800
Operating expenses                       4,000
Depreciation                             3,000
Operating profit                        5,800
Interest expense                         2,800
EBT                                     3,000
Taxes                                      900
Net income                              2,100

7.
Inventory – current asset                     Retained earnings - equity
Accounts receivable – current asset           Accounts payable – current liability
Long-term debt – noncurrent liability         Accrued wages and taxes – current liability
Common stock (par value) - equity             Notes payable (bank loans) – current liability
Plant and equipment – noncurrent asset        Marketable securities – current asset
Cash – current asset                          Prepaid expenses – current asset

8. Total shareholders’ equity = \$1,450,000.
9. In the following solution, the reported number for Gross fixed assets is assumed to exclude
Leasehold improvements.

Quest-Mar, Incorporated
Balance Sheet
For the Year Ending Decemebr 31, 2006

Cash                                         120      ST Bank loan                            20
Net Accounts receivable                      100      Accounts payable                        90
Inventories                                  190      Accrued expenses                        40
Current assets                              410      Current portion LT Debt                 60
Gross fixed assets (exc. Lease. Imp.)        900       Current liabilities                   210
Leasehold improvements                       300      Long-term bank loan                    600
Less Accumulated depreciation              (200)      Total liabilities                     810
Net fixed assets                           1,000      Common stock (\$1.00 par)               400
Retained earnings                      200
Total stockholder's equity            600

Total assets                              1,410      Total liabilities & net worth        1,410

10. a. \$782,200        b. \$54,532,500         c. \$44,465,000

2004           2005            2006
11. CP LT Debt                   280,000        280,000         280,000
LT Debt                    2,240,000      1,960,000       1,680,000

12. a. 75,000 shares (note that all figures for this problem are in thousands).
b. (10,450,000 – 8,700,000) / 75,000 = \$23.33              c. \$1.12 (total dividends paid by the
company = NI(2006) – change in retained earnings = 700,000. Divide this by 625,000
shares outstanding to get \$1.12 per share).
13. Total dividends paid = \$6,000,000 ; Dividends per share = \$1.20
14. a. EPS=\$6.14; DPS = \$1.89           b. \$180,400 c. EPS=\$6.01; DPS=\$1.76 (assumes
3,000 shares issued – typo on problem).

15. a. 5.25             b. Price=8.25         c. 1.57 times
Equity represents shareholder wealth. Book value is historical. Market value is a function of
the expected future cash flows of the company. Book value is approximately what the firm’s
assets are worth if liquidated. Market value is what the company is worth as a functioning
entity. Thus, this company is worth approximately 1.57 times more as an operating company
than if the company stopped operating and sold off all of its assets. The larger this ratio, the
more successful the company is at creating value in operations.
16. a.   Owners equity in 2005 = \$140,000; owners equity in 2006 = \$144,000
b.   \$10,000
c.   \$40,000
d.   \$4,000
e.   \$50,000
17. a.   Owners equity in 2005 = \$100,000; owners equity in 2006 = \$110,000
b.   \$20,000; \$24,000
c.   \$10,000
d.   \$3,000
e.   \$128,000 – note this merely equals the change in net fixed assets + depreciation from I/S
f.   +\$22,000
CHAPTER 3 – Solutions to Assignment Problems
Assignment 3.1:

Net income                                       48,000
+ Depreciation                                   30,000
+ Decrease in Accounts receivable                21,000
- Increase in Inventories                       (10,900)
- Decrease in Accounts payable                  (12,000)
- Decrease in Accruals                          (14,000)
Net Cash Flow from Operating Activities         62,100

Purchase of Gross fixed assets*                 (40,000)
Net Cash Flow from Investing Activities        (40,000)

Increase in Notes payable                       15,000
Change in LT Debt                               6,000
Change in Common Stock                          5,000
Increase in Capital surplus                     1,000
- Payment of dividends**                        (33,200)
Net Cash Flow from Financing Activities        (6,200)

Change in Cash                                  15,900

* Change in Net fixed assets + Depreciation
** Net income - (Change in Retained earnings)
Assignment 3.2:

Net income                                      1,800
+ Depreciation                                  1,600
- Increase in Accounts receivable                (500)
- Increase in Inventories                        (300)
+ Increase in Accounts payable                  1,100
+ Increase in Accruals                            500
Net Cash Flow from Operating Activities        4,200

Purchase of Gross fixed assets*                 (2,400)
Net Cash Flow from Investing Activities        (2,400)

Change in LT Debt                                  -
Change in Common Stock                             -
- Payment of dividends**                        (1,200)
Net Cash Flow from Financing Activities        (1,200)

Change in Cash                                    600

* Change in Net fixed assets + Depreciation
** Net income - (Change in Retained earnings)
Assignment 3.3:
Net income                                        32,000
+ Depreciation*                                   30,000
+ Decrease in Accounts receivable                  7,000
- Increase in Inventories                        (30,900)
+ Increase in Accounts payable                     8,000
- Decrease in Accruals                            (1,000)
Net Cash Flow from Operating Activities         45,100

Purchase of Gross fixed assets**                 (40,000)
Net Cash Flow from Investing Activities         (40,000)

Change in Notes payable                           (3,000)
Change in LT Debt                                 15,000
Change in Common Stock                             2,000
Change in Capital surplus                          4,000
- Payment of dividends***                        (24,900)
Net Cash Flow from Financing Activities          (6,900)

Change in Cash                                    (1,800)

* Change in Accumulated depreciation
** Change in Gross fixed assets
*** Net income - (Change in Retained earnings)
Problems:
1. Raise prices, reduce growth rate, speed up collections, hold smaller inventory levels, etc.

2. A reduction or non-payment of a dividend, the substitution of a stock dividend for a cash
dividend, late payments to suppliers or other creditors, bounced payroll checks, etc.
3.
July Balance Sheet
Cash                             15,000     Debt                                -
Accounts receivable              35,000     Stock                            40,000
Inventories                      28,000     Retained earnings                38,000
Total assets                    78,000       Total claims                   78,000

4. The growth in sales slowed to zero percent per year. Note that outflows for this company are
based on the current month’s sales level. That is, outflows in February are based on February
purchases (which are based on February sales). Outflows in March are based on March
purchases (which are based on March sales). And so on. Conversely, inflows are based on
sales that occurred one month ago. Thus, inflows in February are based on January sales and
inflows in March are based on February sales. In periods of rapid growth, this one-month lag
can cause outflows to exceed inflows even though revenue exceeds costs for that period.
When sales growth slows to zero, the lag effectively disappears since sales in each month are
the same. In this case, inflows minus outflows are essentially the same as revenue minus cost.

5. Depreciation expense (2004) = \$2,000.
Depreciation expense (2005) = \$4,000.
Depreciation expense (2006) = \$2,000.

6. Change in gross fixed assets (2004) = \$20,000.
Change in gross fixed assets (2005) = \$40,000.
Change in gross fixed assets (2006) = \$20,000.
7. Change in Net fixed assets + Depreciation (2004) = 18,000 + 2,000 = \$20,000.
Change in Net fixed assets + Depreciation (2005) = 36,000 + 4,000 = \$40,000.
Change in Net fixed assets + Depreciation (2006) = 18,000 + 2,000 = \$20,000.
8.
Net income                                 26,000
+ Depreciation                              2,000
- Increase in Accounts receivable          (4,000)
- Increase in Inventories                  (2,000)
- Decrease in Accounts payable             (2,000)
Net Cash Flow from Operating Activities   20,000

Purchase of Gross fixed assets             (15,000)
Net Cash Flow from Investing Activities   (15,000)

Change in Notes payable                      3,000
Change in LT Debt                            8,000
Change in Common Stock                      15,000
- Payment of dividends                     (18,000)
Net Cash Flow from Financing Activities    8,000

Change in Cash                             13,000
9. a. Total dividend paid = NI – change in R. E. = 3200 – (4000-2800) =\$2000
b. Change in GFA/purchase = change in NFA + dep = (14,900-13,300)+1800 = \$3400
GFA in 2006 = GFA of 2005 + purchase =20,000+ 3400 = \$23, 400

10.
Net income                                             3,200
+ Depreciation                                         1,800
+ Decrease in Accounts receivable                        500
- Increase in Inventories                               (600)
+ Increase in Accounts payable                         1,800
- Decrease in Accruals                                  (400)
Net Cash Flow from Operating Activities               6,300

Purchase of Gross fixed assets                        (3,400)
Net Cash Flow from Investing Activities              (3,400)

Change in Notes payable                                  400
Change in LT Debt                                     (1,300)
Change in Common Stock                                   600
- Payment of dividends                                (2,000)
Net Cash Flow from Financing Activities              (2,300)

Change in Cash                                             600

6,300 – 3,400 – 2,300 = 600 (check)
11. Net cash flow from Operating Activities = \$4,500
Net cash flow from Investing Activities = (\$12,200)
Net cash flow from Financing Activities = \$8,200

12. Net cash flow from Operating Activities = \$470,000
Net cash flow from Investing Activities = (\$350,000)*
Net cash flow from Financing Activities = (\$110,000)
*Note that Long-term investments are an investing activity. An increase in Long-term
investments represents an outflow of cash.

13. a. \$94,200                   b. \$113,500         c. \$19,300
14. NCF Operating Activities = \$22,900; NCF Investing Activities = (\$23,200); NCF Financing
Activities = \$100.
15. a. \$1.96 million (compute net income and then add back depreciation, since depreciation is
not a cash flow).
b. \$400,000 (note that when depreciation increases, taxes decrease. This is why depreciation,
although not a cash flow, can affect net cash flow from operations. Specifically, by
changing the amount of taxes a company owes.

16. a. (\$6,000) - note that change in cash and marketable securities = (\$4,000)
b. (\$2,000)                c. (\$28,000)          d. \$26,000
The sum of these three cash flows = -\$4000, which is the change in cash and marketable
securities. Marketable securities, as explained in chapter 2, are an alternative form of cash.
They are very short-term investments that generate a positive return; they can be converted
into cash very quickly. Essentially, cash that earns a return.
CHAPTER 4 – Solutions to Assignment Problems
Assignment 4.1:
1. a.
2005             2006
Net sales              100.0%           100.0%
Cost of goods sold      62.9%            64.1%
Gross profit           37.1%            35.9%
Operating expenses      27.1%            26.5%
Operating income       10.0%             9.5%
Income taxes             4.2%             4.1%
Net income              5.8%             5.4%

Note that the gross profit margin deteriorates by 1.2% and Operating profit margin deteriorates
by 0.5%. Company has been able to offset some of the gross margin deterioration by controlling
operating expenses – either real or manipulation of discretionary expenses.

2. (Note that some of the ratios you compute for this problem will look nonsensical. This is
done on purpose to stress computation of the ratios. Hopefully you will note that a company
with some of these ratios – in particular ACP and Inventory turnover, would probably be in
very poor shape).

2005           2006
Current ratio                        2.3            2.4
Average collection period           288.2          365
Inventory turnover ratio            .40            .39
Total asset turnover ratio          .28            .24
Payables ratio                      488.3          491.8
Debt ratio                          57%            35%
Cash conversion cycle               715.5          805.1
Net profit margin                   5.8%           5.4%
Return on equity                    3.8%           3.2%
Assignment 4.2:
a. Total dividends = Net income – Change in Retained earnings = 1,600,000 – 600,000 =
1,000,000.
b. Number of shares = Common stock/ Par value per share = 1,500,000/.25 = 6,000,000 shares.
c. Number of shares = Common stock/ Par value per share = 1,900,000/.25 = 7,600,000 shares.
d. Dividends per share = Total dividends / Number of shares = 1,000,000/7,600,000 = 13 cents.
e. ROE = Net income / Total Equity = 1,400,000/ (1,500,000 + 1,000,000 + 1,000,000) = 40%.
f. ROE = Net income / Total Equity = 1,600,000/ (1,600,000 + 2,400,000 + 1,900,000) = 27%.
g. ROE (Dupont) = Net income/Sales x Sales/Total assets x Total assets/Total equity.
ROE (2002-Dupont) = .200 x 1.167 x 1.714 = .40 = 40%
ROE (2003-Dupont) = .178 x 0.900 x 1.695 = .27 = 27%
Net profit margin declined in 2003 by 11% (from 20% to 17.8%), Total asset turnover ratio
declined by 23% (from 1.714 to 0.900) and the equity multiplier declined by 1.1%. The
major reason for the deterioration in ROE is a decrease in the efficiency of asset utilization.
Secondary reason is a decline in profitability.

Assignment 4.3:

The best approach to do these “fill in the balance sheet” type problems is to use any given values
(in this case, Total assets = \$1,000,000) to compute as many related values as possible.

For example, given that Assets (A) = 1,000,000, then from the fact that the Debt ratio (Total
liabilities/Total assets) = 60%, Total liabilities = 600,000. Since Total assets = Total liabilities +
Total equity (basic accounting relationship), Total equity must be 400,000.

On the given balance sheet, Total liabilities = Accounts payable + Long-term debt, and since
Long-term debt is given as 180,000, Accounts payable = 420,000. Also, on the given balance
sheet, since Total equity = Common stock + Retained earnings, and since Retained earnings is
given as 200,000, Common stock = 200,000.

Next use, Average collection period = 45 days = (Accounts receivable/Sales) x 360. From Total
asset turnover = Sales/Total assets = 2.0, Sales = 2,000,000. Thus,
45 = (Accounts receivable/2,000,000) x 360, so Accounts receivable = 250,000.

Then use, Inventory turnover ratio = 5 = COGS/Inventory. From Gross profit margin = 25% and
Sales = 2,000,000, COGS = 1,500,000. Thus,
5 = 1,500,000/Inventory, so Inventory = 300,000.

Then use Quick ratio = 1.0 = (Current assets - Inventory)/(Current liabilities). Note that Current
assets for this balance sheet = Cash + Accounts receivable + Inventory, so Current assets –
Inventory = Cash + Accounts receivable. Also note that for this balance sheet, Current liabilities
= Accounts payable. Thus,
1 = (Cash + 250,000)/(420,000), so Cash = 170,000.

Finally, Cash + Accounts receivable + Inventory + Fixed assets = Total assets. Thus, Fixed
assets = 280,000.

Summarizing:
Cash                             170,000              Accounts payable                 420,000
Accounts receivable              250,000               Current liabilities             420,000
Inventories                      300,000              Long-term debt                   180,000
Current assets                  720,000               Total liabilities               600,000
Fixed assets                     280,000              Common stock                     200,000
Total assets                  1,000,000              Retained earnings                200,000
Total claims                  1,000,000
2. Sales = 2,000,000; COGS = 1,500,000
3. CCC         = Inventory conversion period + Average collection period – Payables period
i. = 72 + 45 – 100.8 = 16.2 days.
4. ROE         = Net profit margin x Total asset turnover ratio x (Total assets/Equity)
= .10 x 2.0 x (1,000,000/400,000) = .50 = 50%

Problems:
1. A grocery store. Would you want to shop at a grocery store that had an inventory turnover
ratio of 2? That is, all items (fruit, meat, vegetables, etc.) turned over (i.e., sold) on average
only once every 6 months!
2. High inflation can distort the relationship between book values of assets and true economic
values. For example, if a firm has land on its balance sheet listed in value at \$1,000 and
inflation in land values in running at 40 percent annually, 5 years later the market value of
the land would be worth approximately \$5,400 but would only be listed on the balance sheet
as being worth \$1,000. A similar distortion would apply to plant and equipment.
For short-term assets, however, values would, in general, adjust with inflation. If inventory
turns over relatively rapidly, each turnover would adjust inventory values upward. The same
would be true of accounts receivable. Thus, the relationship between the book value of short-
term assets and long term assets will be distorted. Finally, since the income statement is a
flow measure, high inflation usually affects all revenues and costs in a similar manner.
Assume that a firm has revenue of \$1,000 and costs (total) of \$800 and thus profit of \$200. If
inflation is 50 percent and it impacts revenue and costs in a similar manner, then revenue will
grow to \$1,500 (due solely to inflation) and costs will increase to \$1,200 causing profit to
grow to \$300. Thus inflation can cause a dramatic increase in net income (even more
pronounced if some costs are fixed). Now consider the impact of this increase on a ratio such
as ROA (recall from above that assets do not necessarily grow in line with inflation).
3. The current ratio is CA/CL. A declining ratio can either be due to a relative decline in CA or
a relative increase in CL. Since the inventory turnover ratio and the ACP are constant
through time, inventory and accounts receivable appear to be relatively stable. The increase
in the Payables period would indicate a relatively rapidly increasing Accounts payable value,
which would cause a relative increase in CL and therefore a decline in the current ratio. The
analyst should investigate the causes of the increase in AP perhaps a new supplier to the firm
offers more lax credit terms than the previous supplier.
4. 72%; 14.4%; 45%
5. CA = 2(CL) = 200,000. (CA - Inv)/100,000 = 1.5; thus, Inv = 50,000.
6. HINT: For problems where you are only given ratios and NO actual dollar amounts, assume
that assets are \$100 and solve for all other numbers - then find the answer.
Thus, assume A = 100.
From ROA = NI/A; .20 = NI/100; thus, NI = 20.
Then, from ROE = NI/E; .50 = 20/E; thus, E = 40.
Then, from the definition, A = D + E; 100 = D + 40; thus, D = 60. (NOTE: this relationship
can be used for most of these types of problems).
Finally, compute the debt ratio = D/A = 60/100 = .60 = 60%.
7. Assume A = 100. Then from S/A = 4, S = 400. Then from D/A = .20, D = 20. Then from A =
D + E, E = 80. Then from NI/E = .10, NI = 8.
Finally, compute net profit margin = NI/S = 8/400 = 2%.
8. For this problem, you are given a dollar amount, so DO NOT assume that A = 100. Instead,
from ACP =(AR/S) x 360; 20 = (1,000/S) x 360; thus, S = 18,000. Then from NI/S = .05, NI
= 900. Then from S/A = 2, A = 9,000. Then from D/A = .75, D = 6,750. Then from A = D +
E, E = 2,250. Finally, ROE = NI/E = 900/2,250 = 40%.
9. Net profit margin = 8%; Debt ratio = 52%
10. ROA = 12.5%; ROE = 16.7%
11. Net profit margin = 8%; Debt ratio = 52%
We know that if we solve for x in (1950+x)/(800+x) = 2, we get the maximum amount by
which inventory = bank debt =x can increase without violating a current ratio of 2.Solving
for x we get, x = 350. In this case, Inv will be 1,050. Thus, (CA-Inv)/CL = (1950+350-
1050)/(800+350), and Quick ratio = 1.087.
12. Assume A = 100. Then D = 75 and E = 25 (recall A = D + E). Thus, Equity multiplier = A/E
= 100/25 = 4.
13. Answers assume a 360-day year.
a. \$100
b. \$450
c. \$150
d. 5.7%
e. \$400
f. \$500

14. ROE = 42% (since all equity financed, equity = total assets)
15. Max Increase in debt = 1.4
16. B
17. From ACP = (ARx360)/S, 60 = (150,000x360)/S, S = 900,000. From NI/S = .04, NI =
36,000. From D/A = .64 and A = 3,000,000, D = 1,920,000. From A = D + E, E = 1,080,000.
Then, ROE = NI/E = .033 = 3.3%.
18. Note that CA = Cash & Mkt. Sec. + AR + Inv. and Inventory turnover here is defined as
S/Inv. From CA/CL = 3 and CA = 810,000, CL = 270,000. From (CA-Inv)/CL = 1.4 and
note above and Cash & Mkt. Sec. = 120,000, AR = 258,000. From note above, now Inv =
810,000 - 120,000 - 258,000 = 432,000. From S/Inv = 6, S = 2,592,000. From ACP =
(ARx360)/S, ACP = 35.8 days.
19. From NI/S = .06, NI = 120,000. From tax rate = .40 and from NI = EBT - (.40)x(EBT), EBT
= 200,000. To check, note that 200,000 x .4 = taxes of 80,000 and EBT - taxes = 120,000.
From EBT = EBIT - Interest, EBIT = 220,000. Thus, TIE = EBIT/Interest = 11 times.
20. Assume that currently A = 100. Then, currently, from debt ratio = .5, D = 50 and E = 50.
From S/A = .25, S = 25. From NI/S = .10, NI = 2.5. Using these numbers note that ROE =
5% (they want to double the current ROE from 5% to 10%) checks out. For new, assume that
S and A remain the same such that S/A will remain the same. Thus, S = 25 and A = 100.
From NI/S = .14, NI = 3.5 For ROE = NI/E to be .10, E must be 35. From A = D + E, D = 65
and thus, debt ratio = D/A = 65%.
21. Assume A = 100. From D/A = .35, D = 35 and E = 65. From NI/E = .15, NI = 9.75. From
S/A = 2.8, S = 280 Thus, NI/S = .0348 = 3.48%.
22. For these conversion type problems, note that if D = D/E and E = 1, D/E will be the stated
amount. Thus, for the first one, if D = 2.5 and E = 1, then D/E = 2.5. From A = D + E, A =
2.5 + 1 = 3.5. Then, D/A = 2.5/3.5 = .714 = 71.5% and A/E (the equity multiplier) = 3.5/1 =
3.5 times. For the second one, let D = 1 and E = 1 (thus, D/E = 1). Then A = D + E and A =
2. Thus, D/A = .5 and A/E = 2. For the third one, let D = .6 and E = 1. Then, A = 1.6. Thus,
D/A = .375 = 37.5% and A/E = 1.6 times.
23. From NI/S = .075, NI = 150,000.
From NI/E = .24, E = 625,000
From NI/A = .15, A = 1,000,000
Thus, Total liabilities = NP + AP + LT Debt = 375,000.
From S = 2,000,000 and Gross profit = 400,000, COGS = 1,600,000.
From COGS/Inv = 4, Inv = 400,000.
From (APx360)/COGS = 20, AP = 88,889.
From ACP = (ARx360)/S = 40, AR = 222,222.
From CA/CL = 3.8 and CA = AR + Inv = 622,222, CL = 163,743.
From CL = Notes payable + AP, Notes payable = 74,854.
Thus, long-term debt = 375,000 - 74,854 - 88,889 = 211,257.
Finally, A = 1,000,000 = AR + Inv + Fixed Assets.
Thus, Fixed assets = 377,778.
Summarizing, AR = 222,222; Inv = 400,000; Fixed assets = 377,778;
Total assets = 1,000,000; Notes payable = 74,854; AP = 88,889;
Long-term debt = 211, 257; Equity = 625,000;
Total liab & eq. = 1,000,000.
24. See if you can derive the following answer on your own. Hint, compute Accounts receivable
first, and then use the Quick ratio and Current ratio to compute Current liabilities and
Inventories.
Accounts receivable          400           Current liabilities          400
Inventories                  800           Long-term debt              2000
Fixed assets                2800           Equity                      1600
Total assets               4000            Total claims               4000
CHAPTER 5 – Solutions to Assignment Problems
Assignment 5.1:
Balance Sheet
FreshFish, Inc.
Years ending December 31, 2006 and 2007
2006                    2007
Cash                                            \$ 20,000                 \$ 30,000
Accounts receivable                               10,000                   15,000
Inventory                                         80,000                  120,000
Total Current Assets                           \$110,000                  165,000
Net plant and equipment                         \$430,000                  645,000
Total assets                                   \$540,000                 \$810,000

Notes payable                                            15,000             15,000
Accounts payable to suppliers                            50,000             75,000
Accruals                                                  5,000              7,500
Total current liabilities                             \$ 70,000             97,500
Long-term debt                                          190,000            190,000
Common stock (\$2.00 par value)                           20,000             20,000
Capital surplus                                         150,000            150,000
Retained earnings                                       110,000            138,350
Total Liabilities and Equity                          \$540,000           \$595,850

2. OFN = \$810,000 – \$595,850 = \$214,150
3. 540,000(.50) – 55,000(.50) – 900,000(1.50)(.035)(.60) = 270,000 – 27,500 – 28,350
= \$214,150

Assignment 5.2:
You can answer this question for all parts using the OFN equation. Note that in that equation, the
last part is the change in retained earnings due to projected profit that is reinvested back into the
firm. This part of the equation is given as:
[(S0 + (g)(S0)](NPM) – Div0]
The first part of this equation is projected net income. With some minor mathematical
rearrangement, it can be written as (S0)(1+g)(NPM). The last term in the equation is the amount
of net income that is paid out in dividends. In the equation, it is given as a constant. For
Assignment 6.2, it is stated as a percent of net income (i.e., “Tabler pays out 40 percent of all its
annual profit in dividends”). If 40% of profit is paid out, then the remainder (i.e., 60%) must be
retained. Mathematically, this can be written as:
(S0)(1+g)(NPM)(.60)
Thus, the OFN equation becomes:
OFN = (TA0)(g) – [(L0)(g) + (S0)(1+g)(NPM)(.60)]
And filling in all other given values:
OFN = (1,220,000)(g) – [(500,000)(g) + (4,000,000)(1+g)(.05)(.60)]
= 1,220,000g – 500,000g – 120,000g – 120,000
= 600,000g – 120,000.
a.   For g = 0% = 0, OFN = -120,000
b.   For g = 10% = .10, OFN = -60,000
c.   For g = 20% = .10, OFN = 0
d.   For g = 30% = .10, OFN = 60,000
e.   For g = 40% = .10, OFN = 120,000
f.   For g = 50% = .10, OFN = 180,000

2. OFN = 0 when g = 20% (see c above).

Assignment 5.3:
a. Earnings per share = Net income divided by number of shares of common stock
outstanding. Net income = (.05)(90,000) = 4,500. Number of shares = Common stock
value of balance sheet divided by par value per share = 60,000/2 = 30,000. Thus,
Earnings per share = 4,500/30,000 = .15 = 15%

b. Dividends = Net income – Change in retained earnings = 4,500 – (30,000 – 28,200) =
2,700. Dividend payout ratio = Dividends divided by Net income (that is, the ratio
measures the percent of net income that is paid out in dividends).
Dividend payout ratio = 2,700/4,500 = .60 = 60%.

c. Use the equation: OFN = (TA0)(g) – [(L0)(g) + [(S0 + (g)(S0)](NPM) – Div0].
OFN = (200,000)(.40) – [(60,000)(.40) + [(90,000 + (.40)(90,000)](.05) – 4,000]
= 80,000 – 24,000 – 2,300
= 53,700.
2. Construct the proforma income statement:
Sales                               \$330,000
Operating Costs (70%)                 231,000
Fixed costs                            60,000
EBIT                                  39,000
Interest                               10,000
EBT                                   29,000
Taxes (40%)                            11,600
Net income                            17,400
Dividends                               9,000

Now, construct the proforma balance sheet:
Current assets       110,000                 Notes payable       20,000
Net fixed assets      55,000                 Accounts payable    22,000
Total assets        165,000                 Accruals            11,000
Long-term debt      50,000
Equity              58,400
Total claims      161,400
OFN = 165,000 – 161,400 = 3,600.

Problems:
1. Reduce the dividend payout rate or increase the net profit margin.
2. a. and b.
Apr          May           Jun           Jul         Aug           Sep
Cash Collections                 75,000       100,000      300,000       500,000      900,000      500,000
Cash Expenses                   350,000       350,000      350,000       350,000      350,000      350,000
Net Cash Flow (NCF)           (275,000)     (250,000)     (50,000)      150,000      550,000      150,000

Begin. Cash + NCF                75,000      (175,000)          -        150,000      600,000      625,000

Ending ST Loan Balance               -        225,000      275,000       125,000          -            -
Ending Cash Balance              75,000        50,000      50,000        50,000       475,000      625,000

NOTE: If ending cash balance is greater than 50,000, the ST loan is zero. If ending cash balance is less than
50,000, the ST loan will grow so as to make ending cash equal to 50,000.

c. Accounts receivable balance (Apr) = 100,000
Accounts receivable balance (May) = 300,000
Accounts receivable balance (Jun) = 500,000
Accounts receivable balance (Jul) = 900,000
Accounts receivable balance (Aug) = 500,000
Accounts receivable balance (Sep) = 200,000

3. Annual Inventory Related Interest Cost (current) = 25 x 500 x .10 = \$1,250
Annual Inventory Related Interest Cost (proposed) = 15 x 500 x .10 = \$750
So, reduction in annual inventory related interest cost = \$750.
Reduction in Rent = \$5,000 annual savings.
So, total benefit of proposed change = \$5,750

Number of Inventory orders per year (current) = 12
Number of Inventory orders per year (proposed) = 36
Increase in Inventory order cost = (36)(\$250) = \$6,000

Thus, benefit – cost = \$5,750 - \$6,000 = (\$250) – DO NOT CHANGE POLICY.
4.
COFFYS
Proforma Balance Sheet
For the Year Ending June 30, 2004

Cash                         \$14,000        Notes payable                \$10,000
Accounts receivable           11,200        Accounts payable              35,000
Inventories                  100,800        Accruals                       7,000
Current Assets              126,000         Current Liabilities          52,000

Gross fixed assets         1,148,000        Long term bank loan          400,000
Accumulated dep.              (84,000)      Common stock                 200,000
Net fixed assets           1,064,000        Retained earnings            226,000
Total assets                        1,190,000       Total Liab. & equity
878,000
All asset accounts grow by 40% and accounts payable and accruals (i.e., spontaneous liabilities)
grow by 40%. Financing variable (i.e., Notes payable, Long-term bank loan and Common stock)
values stay fixed. The change in Retained earnings is due to net income that is not paid in
dividends. Specifically,
Change in RE = (2003 Sales)(1 + Projected growth rate)(Net profit margin) – Dividends
= (800,000)(1.4)(.05) – 40,000
= 16,000
And thus proforma Retained earnings = 210,000 + 16,000 = 226,000.
Outside funds needed = 1,190,000 – 878,000 = 312,000.

Check:
OFN = (TA0)(g) – [(L0)(g) + [(S0 + (g)(S0)](NPM) – Div0]
= (850,000)(.40) – [(30,000)(.40) + [(800,000 + (.40)(800,000)](.05) – 40,000
= 340,000 – [12,000 + 16,000]
= 312,000.

5.
COFFYS
Proforma Balance Sheet
For the Year Ending June 30, 2004

Cash                         \$14,000        Notes payable                \$ 8,400
Accounts receivable           11,200        Accounts payable              35,000
Inventories                  100,800        Accruals                       7,000
Current Assets              126,000         Current Liabilities          50,400

Gross fixed assets         1,148,000        Long term bank loan          400,000
Accumulated dep.              (84,000)      Common stock                 200,000
Net fixed assets           1,064,000        Retained earnings            226,000
Total assets                 1,190,000         Total Liab. & equity        876,400
All asset accounts grow by 40% and accounts payable and accruals (i.e., spontaneous liabilities)
grow by 40%.

To solve for Notes payable, use the fact that the current ratio will be 2.5. Since you have
projected current assets = 126,000, this implies that projected current liabilities will be 50,400.
With Accounts payable = 35,000 and Accruals = 7,000 (due to spontaneous liabilities grow by
40%), Notes payable = 52,000 – 35,000 – 7,000 = 8,400.

The remaining financing variable (i.e., Long-term bank loan and Common stock) values stay
fixed. The change in Retained earnings is due to net income that is not paid in dividends.
Specifically,
Change in RE = (2003 Sales)(1 + Projected growth rate)(Net profit margin) – Dividends
= (800,000)(1.4)(.05) – 40,000
= 16,000
And thus proforma Retained earnings = 210,000 + 16,000 = 226,000.

Long term outside funds needed = 1,190,000 – 876,400 = 313,600. (This money will come from

6.
COFFYS
Proforma Balance Sheet
For the Year Ending June 30, 2004

Cash                            \$14,000        Notes payable                   \$21,000
Accounts receivable              11,200        Accounts payable                 35,000
Inventories                     100,800        Accruals                          7,000
Current Assets                 126,000         Current Liabilities             63,000

Gross fixed assets            1,148,000        Long term bank loan             413,000
Accumulated dep.                 (84,000)      Common stock                    200,000
Net fixed assets              1,064,000        Retained earnings               226,000
Total assets                          1,190,000        Total Liab. & equity
902,000
All asset accounts grow by 40% and accounts payable and accruals (i.e., spontaneous liabilities)
grow by 40%.

To solve for Notes payable, use the fact that the current ratio will be 2.0. Since you have
projected current assets = 126,000, this implies that projected current liabilities will be 63,000.
With Accounts payable = 35,000 and Accruals = 7,000 (due to spontaneous liabilities grow by
40%), Notes payable = 63,000 – 35,000 – 7,000 = 21,000.

To solve for Long-term bank loan, use the fact that the debt ratio will be 40 percent. The debt
ratio = total liabilities divided by total assets. With total assets projected to be 1,190,000, total
liabilities will be (.40)(1,190,000) = 476,000. Since Current liabilities = 63,000, Long-term bank
loan must be 476,000 – 63,000 = 413,000.
The remaining financing variable (i.e., Common stock) value stay fixed. The change in Retained
earnings is due to net income that is not paid in dividends. Specifically,
Change in RE = (2003 Sales)(1 + Projected growth rate)(Net profit margin) – Dividends
= (800,000)(1.4)(.05) – 40,000
= 16,000
And thus proforma Retained earnings = 210,000 + 16,000 = 226,000.

Money needed from selling additional common stock = 1,190,000 – 902,000 = 288,000.

7. a. \$101,000
b. - \$24,000
(TA = 1250000*1.15 =1437,500, 60% of which is debt, Total equity needed = 0.4 of
1437,500 = 575,000. Now addition to R. E = 49,000. Total R. E = 300,000+49,000 =
349,000. Total equity fund available = (50,000+200,000+349,000) = 599,000. Therefore,
common stock needed (575,000-599,000) = -24,000
8. \$130,400
9. \$112,500
10. a. \$150,000               b. \$137,400            c. \$124,800
11.
(a)                              2003 Actual    2004 Proforma
Cash                         400,000           500,000
Acc. receivable              900,000         1,125,000
Inventory                  1,200,000         1,500,000
Net Prop. & Plant          2,500,000         3,125,000
Total Assets              5,000,000         6,250,000

Acc. payable                 800,000          1,000,000
Long term debt             1,500,000          1,500,000
Common Stock               1,800,000          1,800,000
Retain earnings              900,000          1,140,000
Tot. Liab. & Equity       5,000,000          5,440,000

Total Outside Funds Needed = 810,000

(b)                                    2003 Actual   2004 Proforma
Cash                         400,000            500,000
Acc. receivable              900,000          1,125,000
Inventory                  1,200,000          1,500,000
Net Prop. & Plant          2,500,000          3,125,000
Total Assets              5,000,000          6,250,000

Acc. payable                 800,000          1,000,000
Long term debt             1,500,000          2,750,000
Common Stock               1,800,000          1,800,000
Retain. earnings             900,000          1,140,000
Tot. Liab. and Equity    5,000,000         6,690,000

12. a. Total Outside Funds Needed = 2,235,000
b. Total Outside Funds Needed = 885,000
CHAPTER 6 – Solutions to Assignment Problems
Assignment 6.1:
1. FV = PV (1+r). Let FV = 2 and PV =1. Thus, 2 = 1(1+r). When you solve for r, you get r=1.
Expressed as a percent, the interest rate is 100%.
2. FV = PV (1+r); 7397 = PV(1+.0439) or PV = 7297/1.0439; Solve PV = 7,085.93.
3. FV = PV (1+r); 13000 = PV(1.08) or PV = 13000/1.08; Solve for PV = 12,037.04.
4. Note that you will only need 25000 – 4500 = 20,500 one year from today. Thus, FV = PV
(1+r); 20500 = PV(1.075) or PV = 20500/1.075; Solve for PV = 19,069.77
5. FV = PV (1+r); 14739 = PV(1.12) or PV = 14739/1.12; Solve for PV = 13,159.82.

Assignment 6.2:
1. FVn = PV (1+r)n. Let FV = 2 and PV =1. Thus, 2 = 1(1+r)2 or 2½ = (1+r). When you solve
for r, you get r=.4142. Expressed as a percent, the interest rate is 41.42%.
2. PV = FV1(1/1+r)1 + FV2(1/1+r)2 ; PV = 3200(1/1.06)1 + 7300(1/1.06)2 ; PV = 3018.87 +
6496.97 = 9,515.84.
3. Note that the first deposit will grow for one year – that is, it will grow to become 7448 (1.07)
= 7969.36. When you add the extra 2476, you will have a total of 10,445.36 in your account.
4. Continuing from #3, the 10,445.36 will grow again by 7 percent to be 10445.367(1.07) =
11,176.54.
5. 15000 = X(1.12)2 + X(1.12)1 = X [(1.12)2 + (1.12)1] = X[2.3744]. Thus, X = 6,317.39.

Assignment 6.3:
1. FV2 = Deposit0 (1+r)2 + Deposit1 (1+r)1. (Note that the deposit made today (at t=0) will earn
interest for 2 years and the deposit made one year from today will earn interest for 1 year).
Thus, 4000 = 8000(1.04)2 + Deposit (1.04)1; 4000 = 8652 + Deposit (1.04). Solve for Deposit
and you get Deposit = -4,473.85. The negative sign implies that you will withdraw this
amount at the end of year one.
2. The question is what is the present value of the investment. That is, what is the present value
of 6500 one year from today + 5000 two years from today. We then compare the value of the
investment with the cost. If value > cost, you should buy. If value < cost, you should not buy.
PV = FV1(1/1+r)1 + FV2(1/1+r)2 ; PV = 6500(1/1.12)1 + 5000(1/1.12)2 ; PV = 5803.57 +
3958.97 = 9,789.54. Do not make investment.
3. 538 = 500 (1+r)1; 1.0760 = 1+r; r = .0760 = 7.6%
4. (1 + rnominal) = (1 + rreal) x (1 + i); (1 + rnominal) = (1.08) x (1.04) = 1.1232. rnominal = .1232 =
12.32%.
5. (1 + rnominal) = (1 + rreal) x (1 + i); (1.122) = (1 + rreal) x (1.036); (1 + rreal) = 1.083. rreal = .083
= 8.3%.
6. (1 + rnominal) = (1 + rreal) x (1 + i); (1.086) = (1.047)(1 + i); (1 + i) = 1.0372. i = .0372 = 3.72%
Problems:
1. 10.24%
2. 8.112%
3. 5.77%
4. 5.15%
5. 1.92%
6. 10.04%
7. 1294.80
8. 4108.90
9. 237.60
10. 4917.12
11. 969.31
12. 1696.25
13. 3752.35
14. 612.83
15. E(R) [i.e., Expected Return] on first = 11.5%;E(R) on second = 12.1%
Choose both since Expected Return > Required Return. NOTE: This problem implicitly
assumes that these two investments are of equal risk. Unless otherwise explicitly stated, for
all problems in this book, we will assume that all comparable investments are of equal risk.
16. E(R) on first = 10.2%; E(R) on second = 7.48%
Choose neither since for both E(R) < Required Return.
17. (d) is correct. For (a), PV must be less than 432 since interest rate is greater than 0.for (b), the
FV (t=1) must be greater than the PV (t=0) value since interest rate is greater than 0.for (c),
you would never pay more than the simple sum of all future cash flows (i.e., 2,300+2,300 =
4,600 < 6,600)
18. 70,661.16
19. 1,680.00; 1,915.20
20. In the following equation, solve for X (note that ^2 means raised to the second power, or int
this case, squared): 10,000 = 7,000 (1/1.13)^1 + X(1/1.13)^2 ==> X = 4,859
21. In the following equation, solve for r: 4,100 = 3,500 (1+r)^2 ==> r = 8.233%
22. Buy the two year subscription because the PV of buying a one year subscription today and
another one year subscription one year from today = 48 + 48(1/1.10) = 91.64 which is greater
than the two year subscription price of 70. This answer of course assumes that you actually
want to read this magazine for two years!
23. Assume that the two payments are due one month from today and 2 months from today.
Payoff = 791.09
24. Compare 20,000 - 2,850 = 17,150 to the PV of 20,000 two years from today.
20,000(1/1.08)^2 = 17,146.78. Since 17,150 > 17,146.78, choose (b) because it is "cheaper."
CHAPTER 7 – Solutions to Assignment Problems
Assignment 7.1:
1. PV = -30000, FV = 49000, n = 5, Compute I/Y = 10.31%.
PV = -73000, FV = 128000, n = 7, Compute I/Y = 8.35%.
2. Use cash flow register: CF0 = 0, C01 = 22000, F01 = 1, C02 = 27500, F02 = 1, C03 =
33000, F03 = 1, C04 = 35000, F04 = 1; Compute NPV (with I = 6%) = 100,660.33
3. Use cash flow register to find NPV. Then find FV of this amount. Thus, CF0 = 11000, C01 =
13000, F01 = 1, C02 = 17400, F02 = 1, C03 = 12800, F03 = 1, C04 = 9600, F04 = 1; C05 =
17200, F05 = 1; Compute NPV (with I = 8%) = 66878.10. Now find the future value of this
amount 10 years from today. PV = 66878.10, I = 8, n = 10, Compute FV = 144,384.81.

Assignment 7.2:
1. PV = -28000, fv = 30000, I = 6, n = 10, Compute PMT = 1,528.26.
2. First find F of deposits. PMT = 2500, I = 8, n = 20, Compute FV20 = 114404.91. Now find
withdrawals. PV = 114404.91, n = 25, I = 8, Compute PMT = 10,717.31
3. First find NPV of all cash flows with the unknown cash flow assumed to be 0. That is, CF0 =
5000, C01 = 0, F01 = 10, C02 = -60000, F02 = 1, C03 = 0, F03 = 2, C04 = 25000, F04 = 1,
C05 = 0, F05 = 11, C06 = -1500000, F06 = 25; Compute NPV (with I = 7%) = 335884.60.
Now find PMT. PV = 335884.60, I = 7, n = 25, Compute PMT = 28,822.43.
4. First find PV20 of perpetuity = 30000/.12 = 250000 (note this is value in year 20).
CF0 = 0, C01 = 12000, F01 = 3, C02 = 17000, F02 = 4, C03 = 21000, F03 = 8, C04 = 24000,

F04 = 4; C05 = 274000, F05 = 1; Compute NPV (with I = 12%) = 154,486.56.

Assignment 7.3:
1. PV = -1, FV = 2, I = 7/2 = 3.5, Compute n = 20.1488 semi-annual periods = 10.07 years.
2. Bank A: 10.00%; Bank B: 10.04%; Bank C: 9.95%; Bank D: 9.93%; Bank E: 9.86%.
3. PMT = 140000, n = 10, I = 9, Compute PV = 898472.08. This is value need at the end of
year 20. Since first deposit will be made today, set calculator in BEGIN mode. Now, FV =
898472.08, I = 9, n = 20, Compute PMT = 16,111.89.
4. Annual payment = \$8,652.62.

Beginning                              Ending
Year     Balance      Interest     Payment     Balance

1       40,000.00     3,200.00   \$8,652.62   34,547.38
2       34,547.38     2,763.79   \$8,652.62   28,658.56
3       28,658.56     2,292.68   \$8,652.62   22,298.63
4       22,298.63     1,783.89   \$8,652.62   15,429.90
5       15,429.90     1,234.39   \$8,652.62    8,011.68
6        8,011.68       640.93   \$8,652.62        0.00
Problems:
1. a – more compounding periods per year creates a larger effective interest rate.
2. e
3. 17 years
4. 4.45%
5. \$10,962.37
6. d
7. a
8. 19.56%
9. \$704
10. e
11. e

12. This question is misleading. This is not an annuity problem.
For example, n=10, PMT=0, r = 10, FV = 5,000, PV = ?1,927.72
n=10, PMT=0, r= 10, PV = 5,000, FV = ? 12, 968.71

Rate       PV         FV
0     5,000.00     5,000.00
5     3,069.57     8,144.47
10     1,927.72    12,968.71
15     1,235.92    20,227.79
20       807.53    30,958.68
25       536.87    46,566.13
30       362.69    68,929.25
35       248.68   100,532.78
40       172.86   144,627.33
45       121.70   205,423.45
50        86.71   288,325.20
Plot of Present Values

6,000.00

5,000.00
Present Value

4,000.00

3,000.00                                                Series1

2,000.00

1,000.00

-
0       5   10 15 20 25 30 35 40 45 50
Interest Rate

Plot of Future Values

350,000.00
300,000.00
250,000.00
Future Value

200,000.00
Series1
150,000.00
100,000.00
50,000.00
-
0       5 10 15 20 25 30 35 40 45 50
Interest Rate

13. \$15,129.38
14. \$45,349.14
15. \$26.97
16. \$889.23
17. 2.74%
18. 4.47%
19. \$96,969.53
20. 7.10%; 7.23%
21. \$31,265.66
22. 8.654%
23. \$7,669.12; \$18,419.93
24. \$76,175.84
25. \$6,714.27
Alternative 1:
I do not think solution manual gave right answer, I did in two different method and this is what I
get
CF1 = 20,000, CF1 = 0, F1= 10 (assume that t = 12 means ending of year 11)
CF2 = -25,000, F2 = 4, (ending at t = 14 or beginning at t = 15)
Cf3 = 0, f3 = 2 (assume that t = 18 means ending of year 17)
Cf4= -33,000, f4 = 4
I = 8%, NPV = - 50,257.52 (this is the spending at t =0)
You have to save for this for 10 yrs
Pv = - 70,257.52, FV = 0, N = 10, 1/Y = 8, PMT = ? 7,489.85
Alternative 2:
Pv1) PMT= 33,000; n=4; FV=0; PV=-118, 044.2006; 1/y= 8, (Solved as ANN Due) at the end of
t =17
Pv2) PMT=0; n=7; 1/y=8; FV= 118, 044.2006, PV=- 68,877.65 at the end of t = 10
PV3) PMT= 25000; n=4; i/y= 8; FV=0; Pv= -89,427.42468 (Solved as ANN Due) at the end of t
=11
PV4) Fv= 89,427.42468; n=1; 1/y= 8, PMT=0, PV= -82,803.171 at the end of t = 10
Pt 5) Pv= -20,000, n=10, FV= (68,877.65 +82,803.171), 1/y=8, PMT= -7,489.85

26. \$4,520,178.42 today; \$2,883,820.96 (5,082,277.89 is correct answer) in five years.
27. \$263.80
28. \$59,739.98
29. \$9.50
30. \$482.09
When PMT = 0, it does not matter if you use END or BGN mode. But I suggest you always keep
your calculator at end mode, just to avoid problems.
Cf0 = 0, cf1 = 0, f1 = 59 (beg of t = 60 implies end of t = 59)
Cf2 = -2500, f2=16, I = 1.25, NPV = - 17,322.37
PV = - 17,322.37, N = 48, 1/y = 1.25, FV = 0, PMT = ? 482.09

31. Amount of payment that goes to principal = 7757.16; Amount that goes to interest = 1,698.84
32. \$925,764
33. \$86,303.09
34. \$17,954.13
Correct method for the solution in END mode is as follows:
PV= -3000, PMT= -3000, n=4, I/y=9, FV= 17, 954. 13

35. \$276.21
36. \$167,790.24
37. \$5,468.21
38. \$61,534.10
39. \$165,918.32
40. \$71,474.07
41. \$871.47
As a first step, calculate the PV of the cash flows (at 10.5%): cf0 = 0, Cf1=1700, f1 = 1,
Cf2=1800, f2 = 1, cf3 = 0, f3 =1, cf4 = 2000, f4 = 1, NPV =4354. 1026
Therefore, you are 5000-4354. 1026=645.897 “short” of the 5000. This represents the PV of the
missing cash flow. To calculate the actual cash flow, calculate the FV of the 645.897:
PV=645.897, N=3; I=10.5; PMT = 0; FV=??=871.47
To verify your answer, enter the 871.47 as Cf3 and calculate the PV (it works out
to 5,000)
CHAPTER 9
ASSIGNMENT 9.1

1.
a. Treat as a perpetuity.      P = Coupon/Interest Rate = 82.50/0.08 = \$1,031.25

b. P = 1000/(1.0815) = \$315.24

c. N = 20; PMT = 70; I/Y = 8; FV = 1000; CPT PV.              P = \$901.82

2.
a. N = 60; FV = 1000; PMT = 35; I/Y = 4.5; CPT PV.            P = \$793.62

b. N = 80; FV = 1000; PMT = 25; I/Y = 2.25; CPT PV.           P = \$1,092.37

3. PV = -978; FV = 1000; PMT = 90; N = 14; CPT I/Y. Cost of Debt = YTM = 9.29%

4. N = 68; (i.e. 17x4 quarters) PV = -1020; FV = 1000; PMT = 20; CPT I/Y;
I/Y = 1.9467;        Thus, Cost of Debt = YTM = 1.9467 x 4 = 7.79%

ASSIGNMENT 9.2

1. Preferred should be treated as a perpetuity as it pays a perpetual stream of preferred dividends.
Price = 2.25/0.11 = \$20.45

QWE’s estimate of the required rate of return is higher than the actual required rate of return
investors are using to value the preferred stock.
The actual rate = 2.25/24 = 9.375%

2. Since the common stock pays constant dividends forever, the present value of the dividends is
obtained using the perpetuity formula, as in 1 above.

P = 1.50/0.09 = \$16.67

3. P0 = D1 / (k-g) = 2.50/(0.10-0.03) = \$35.71

4. First find P5 = D6 / (k-g) = \$1(1.05)/(0.12-0.05) = 1.05/0.07 = \$15.

Now P0 = 1/1.12 + 1/1.122 + 1/1.123 + 1/1.124 + (1+15)/1.125 = \$12.12.
Alternative Solution: After finding P5 note that the cash flow lends itself to the use of the third
row keys on your calculator. Thus we can use our usual setup to find the present value.
PMT = 1; FV = 15; N = 5; I/Y = 12; CPT PV.             P = \$12.12
ASSIGNMENT 9.3
1.
P0 = D1/(k-g) = D0(1+g)/(k-g). We can make k the subject of this equation.

k = g + D0(1+g)/P0 = 0.04 + 2(1.04)/38 = 0.04 + 0.0547 = 9.47%

2. First determine D4 = D3(1+g) = 3(1.06) = \$3.18

Then P3 = D4/(k-g) = 3.18/(0.14-0.06) = \$39.75

Now, P0 = 2/1.14 + 1/1.142 + (3+39.75)/1.143 = \$31.38

You can also use the CF (cash flow) procedure to do the calculations in the last step:

C01 = 2; F01 =1;    C02 = 1; F02 =1;       C03 = 42.75 (3+39.75); F03 = 1;          I=14.

3.

D1 = 1.75(1.5) = 2.625;        D2 = 1.7591.5)2 = 3.9375;     D3 =1.75(1.52)(1.3) = 5.11875

D4 = 1.75(1.52)(1.32) = 6.654375;      D5 = 1.75(1.52)(1.32)(1.2) = 7.98525;

D6 = 1.75(1.52)(1.32)(1.2)(1.07) = 8.5442175.

P5 = D6/(k-g) = 8.5442175/(0.15-0.07) = \$106.80

Then P0 = 2.625/1.15 + 3.9375/1.152 + 5.11875/1.153 + 6.654375/1.154 +
(7.98525+106.8027)/1.155 = \$69.50.

Again, you can use the CF procedure (probably easier) for the last step.

4. D1 = \$1(1.35) = 1.35; D2 = 1(1.352) = 1.8225; D3 = 1(1.353) = 2.460375;

D4 = 2.460375(1.2) = 2.95245; D5 = 2.95245(1.2) = 3.54294;

D6 = 3.54294(1.2) = 4.251528; D7 = D8 = D9 = …… = D∞ = 4.251528.

After this, it is probably best to use the cash flow procedure for the last step:

C01 = 1.35; F01 = 1;      C02 = 1.8225; F02 = 1;     C03 = 2.460375; F03 = 1;

C04 = 2.95245; F04 =1;      C05 = 3.54294; F05 = 1; C06 = 4.251528; F06 = 999.

Use I = 15. Then the (NPV) Price = \$21.71
Alternatively, the last step can be done using the analytical method:

First find P6 = D7/k = 4.251528/0.15 = \$28.34.

P0 = 1.35/1.15 + 1.8225/1.152 + 2.460375/1.153 + 2.95245/1.154 + 3.54294/1.155 +
(4.251528+28.34)/1.156 = \$21.71

1. PV = -1100; N = 25; PMT = 90; FV =1000; CPT I/Y.

Market interest rate = YTM = 8.06%

2. To be indifferent between calling the bond and not calling the bond, the call price of \$1,075
must be equal to the present value of the remaining payments. Thus:

PV = -1075; PMT = 80; N = 25; FV = 1000; CPT 1/Y.            7.34%

3. Use the usual procedure for finding the price of a bond. Just be careful to use the appropriate
YTM for I/Y for the various times.

a. \$1,000        b. \$1,087.45; c. \$873.08;    d. \$974.69;    e. \$972.97

4. FV = 1000; PV = -1092; PMT = 50; N=40; CPT I/Y. I/Y = 4.5%. Thus YTM = 9%

5. FV=1000; N=8; PMT = 0; I/Y = 4. CPT PV.            Price = \$730.69

6. FV=1000; N=34; PMT = 40; I/Y = 3.625; CPT PV.             P = \$1,072.62

7. FV = 1000; N = 30; PMT = 35; PV = -825; CPT I/Y. I/Y = 4.585. YTM = 9.17%

8. YTM = 9.09%

9. P = \$859.16

10. First find the yield to maturity of the zero coupon bonds.
N = 30; FV =1000; PV = -99.38; PMT = 0; CPT I/Y .          YTM = 8%.
Now, the yield to maturity of the coupon bond is also 8%. Thus for the coupon bond:

N = 60; FV = 1000; PV = -886.88; I/Y = 4; CPT PMT. PMT = 35. Coupon Rate = 7%.

11. Price per share = 20000000/1000000 = \$2. D = P x k = 2x0.11 = \$2.20 per share.

12. P0 = D0(1+g)/(k-g) = 1.50(1.04)/(0.12-0.04) = 1.56/0.08 = \$19.50

13. P0 = D0(1+g)/(k-g) = 4(1-0.05)/(0.20--0.05) = 4(0.95)/0.25 = \$15.20
14. P0 = D0(1+g)/(k-g);     15 = 1(1+g)/(0.12-g); 1.80 -15g = 1+g; g = 0.8/16 = 5%

15. P0 = D0(1+g)/(k-g); 72.25 = 5.12(1.06)/(k-0.06); k = 13.51%

16. The first dividend that begins the constant growth forever is D5. Thus, we can find P4 using:

P4 = D4 (1+g)/(k-g) = 3.5(1.08)/(0.14-0.08) = \$63.

Now, either use he cash flow procedure or the analytical method to solve for P0.

P0 = 2/1.14 + 1.50/1.142 + 2.50/1.143 + (3.50+63)/1.144 = \$43.97

17. First let’s find the discount rate, k.     24 = 3/k. Thus k = 12.5%.

Now, with the 3 percent expected growth, the dividend one year from now, D1 = 3(1.03) = \$3.09.
Therefore, P0 = 3.09/(0.125-0.03) = \$32.53.

18. g = 2.14/2 – 1 = 7%.         P0 = 2.14/(0.26-0.07) = \$11.26

Take note of the fact that the question gave some pieces of information that were irrelevant to
solving the problem.

19. First determine k, the investors required rate of return. k = 2.10/15 = 14%.

Then P0 = 2.10(1.04)/(0.14-0.04) = \$21.84.

20.     D1 = 4(0.75) = 3; D2 3(0.86) = 2.58; D3 = 2.58(0.94) = 2.4252.

P3 = 2.4252(1.044)/(0.184-0.044) = 18.09. P0 = 3/1.184 + 2.58/1.1842 +
(2.4252+18.09)/1.1843 = 2.534 +1.8404 + 12.36 =16.73
CHAPTER 10
ASSIGNMENT 10.1
1.

Payback         Discounted
NPV            IRR             PI              Period          Payback Per.

A          \$3,456.40      22.58%          1.38            2.8 years       3.22 years

B          \$3,885.38      20.66           1.35            3.09            3.59

C          \$5,583.82      19.48           1.24            3.11            3.44
Never Pays
D          -\$2,536.31     2.62            0.80            4.84            Back (∞)

2.
PMT = \$26,000,000; FV = 20,000,000; N = 10; I/Y = 12; CPT PV.
PV (Benefits) = \$153,345,263.50.
Thus, NPV = PV (Benefits) – PV (Costs) = 153,345,263.50 – 200,000,000 = - \$ 46,654,736.50
IRR = 6.25%
PI = PV (Benefits)/PV (Costs) = 153,345,263.5/200,000,000 = 0.77

3. P0 = 10,000,000/(0.14-0.05) = \$111,111,111.11

NPV = 111,111,111.11 – 100,000,000 = \$11,111,111.11

The IRR is the discount rate that will make the present value of the benefits equal to the initial
cost (that is the discount rate that will make the NPV equal to zero).       100,000,000 =
10,000,000/(k-0.05);
k = IRR = 15%

PI = 111,111,111.11/100,000,000 = 1.11
ASSIGNMENT 10.2
1.
R                     NPV
0                    -300
10                   86.78
20                     250
30                  275.15
40                  214.29
50                     100
60                   -46.86
70                  -212.80
80                  -388.89
2.

NPV Profile for Project A
400
300
200
100
0
NPV

-100 0      10      20     30     40      50     60     70    80     90
-200
-300
-400
-500
Discount Rate

The IRRs estimated from the graph are 7% and 57%

ASSIGNMENT 10.3

1. The net cash flow per month is 12x600 – 1800 = \$5400.
Thus, PMT = \$5400; FV = \$500,000; N =120; I/Y = 1; CPT PV.
PV = \$527,880.21

2. The net cash flow per year = 20x6000 – 33000 = \$87,000.
Thus, PMT = 87000; N = 12; FV = 400000; I/Y = 12; CPT PV.
PV = \$641,580.59. The offer of \$675,000 exceeds the present value of cash flows from
the property. Therefore SELL.

3. YTM = 8.5% = Pretax cost of debt. After tax cost of debt = (1-0.3)x(8.5%) = 5.95%.
For common stock: 20=1.5(1.05)/(k-0.05). Solve this equation for k, the
investors required rate of return.

k = 0.05 + 0.07875 = 12.875%

Cost of capital = 0.25(5.95) + 0.75(12.875) = 11.14%
4. Bond. FV = 1000; N =50; PMT = 27.5; PV = -695; CPT I/Y. I/Y = 4.2249%. Since
coupons are paid semiannually, the YTM = 2x4.2249 = 8.45%
After tax cost of debt = (1-0.3)(8.45) = 5.915%

Stock. 26.5 = 2.1(1.055)/(k-0.055). Solving for k, we have: k= 13.86%

Cost of capital = 0.6(5.915) + 0.4(13.86) = 9.09%

1.

PROJECT NPV               IRR         PI         Payback Period     Disc. Payback Period

A            \$603.58      31.79%      1.60       2.5 yrs            3.07 yrs

B            -\$456.15     7.93%       0.92       4 yrs              Infinity

C            -\$3974.15 6.54%          0.86       3.67 yrs           Infinity

D            \$3807.59     16.43%      1.22       3.70 yrs           4.22 yrs

2. The project has 2 IRRs because the cash flows change signs two times. The IRRs are 48.18%
and -50.55%. To solve for the IRR, you need to solve the following equation for r.
1996/(1+r) – 740/(1+r)2 -1010 = 0. You can use trial and error or you can solve using the
quadratic formula. For the quadratic, first multiply the equation through by (1+r)2 and simplify to

If the cost of capital is 20%, the project should be accepted because it has a positive NPV. NPV
= \$139.44.

3.      a. \$100,000
b. \$65,738.04
c. 18%

4. NPV = PV(Benefits) – PV (costs).           6,900 = PV(Benefits) – 15000. Therefore PV
(Benefits) = \$21,900.

Use cash flow keys to find IRR = 24.95%.

PI = PV (benefits)/ PV(costs) = 21900/15000 = 1.46

Cost of capital (or discount rate). Since we know that the present value of the benefits equals
\$21,900, we can solve for the discount rate.
PMT = 4500; N = 8; PV = -21,900; FV = 0; CPT I/Y. I/Y = cost of capital = 12.59%.

5. PI = PV (Benefits)/ PV (Costs). Thus we have 0.96 = PV (Benefits)/1000000. So,
PV(Benefits) = \$960,000.
NPV = PV(Benefits) – PV(Costs) = 960000 – 1000000 = -\$40,000.

6. b.

7. e

8. a

9. NPV = \$9,298.81;       IRR = 19.63%;          PI = 1.116. Accept Project as NPV is
positive.

10. B. It has the highest NPV.

11. A,B,C,D (ALL). They all have positive NPV.

12. NPV = \$54.85

13. Bonds: PV = -1095; FV = 1000; PMT = 116; N =24; CPT I/Y. I/Y = Pretax cost of
debt = 10.50%. After-tax cost of debt = (1-0.3) (10.5) = 7.35%

Stock. k = 0.07+5.25(1.07)/68.25 = 15.23%

Cost of capital = 0.5(7.35) + 0.5(15.23) = 11.29%

14. Bonds: PV = -8785; N = 60; FV = 10000; PMT = 390; CPT I/Y. I/Y = 4.487%. Thus
the YTM = Pre-tax cost of debt = 2(4.487) = 8.97%.
After-tax cost of debt = (1-0.30)(8.97%) = 6.28%.

Stocks: 33.75 = 2.90(1.0375)/(k-0.0375). Solving for k we get k = 12.66%, the cost of
equity.

Thus, cost of capital = 0.8(6.28) + 0.2 (12.66) = 7.56%.
CHAPTER 11
Assignment 11.1:
1.   Determine Net Cash Flow: NCF = (2,000,000 – Depreciation)(1 – T) + Depreciation
NCF = (2,000,000 – 1,000,000)(.7) + 1,000,000 = 1,700,000.
CF0 = -10000000; C01= 1700000; F01=10; Compute NPV (with I = 13) = -775,386.09.

2.     Project A: CF0 = -80000; C01=18000; F01=8; Compute NPV (with I = 10) = 16,028.67. With same
figures in CF register, compute IRR = 15.29%

Project B: CF0 = -40000; C01=10000; F01=8; Compute NPV (with I = 10) = 13,349.26. With same
figures in CF register, compute IRR = 18.62%

Note that NPV indicates that we should accept Project A and IRR indicates that we should accept
Project B. ALWAYS CHOOSE THE PROJECT WITH THE HIGHEST NPV, so choose Project A.

3.    Enter all values in cash flow register and compute:

NPV (A) = 4497.54; IRR(A) = 19.31%
NPV (B) = 7937.38; IRR(B) = 28.97%
 Choose Project B because higher NPV.

4.    If you construct graph correctly, you should find that the two lines cross at a discount rate of
approximately 16.25%. Note that with I = 16.25, NPV (P) = 1249.76 and NPV (Q) = 1249.77.
 At rates above 16.25%, NPV(P) > NPV(Q)
 At rates above 16.25%, NPV(P) < NPV(Q).

Assignment 11.2:
1.   (Assume tax rate = 0). First compute the NPV of cost of each machine.
X100: CF0=-45000; C01=-5000; F01=4; C02=-5000+6000=1000; F02=1; Compute NPV (I=12) = -
59619.32. Note that this is NPV of costs.

X1300: CF0=-65000; C01=-2000; F01=6; C02=-2000+10000=8000; F02=1; Compute NPV (I=12) =
-69604.02. Note that this is NPV of costs.

Because these two projects have different lives, to compare we must now compute EAC.
EAC(X100): PV = -59619.32; N=5 (i.e., project life); I/Y=12, CPT PMT = 16,538.98.
EAC(X1300): PV = -69604.02; N=7 (i.e., project life); I/Y=12, CPT PMT = 15,251.48.

Thus EAC (X100) = 16,538.98. EAC (X1300) = 15,251.48. Choose X1300 because it has a lower
equivalent annual cost.
2.    Initial Cash Outflow:
Decrease in NWC               + 2M
CF0                          -29M

Note that annual depreciation = (31-3)/20 = 1.4M

Annual Operating NCF = (Rev – Costs – Dep)(1-T) + Dep
= [(5)(.9) – (.6)(5)(.9) - .6 – 1.4](.7) + 1.4 = 1.26M per year for 20 years

Final Year Non-Operating Cash Flow:
Sell Machine for Scrap Value                   3M
Replace NWC                                    -2M
Total                                      1M

To Compute NPV: CF0 = -29, C01 = 1.26; F01 = 19; C02 = 2.26; F02 = 1;
CPT NPV (with I = 11) = -18.842M

Assignment 11.3:
Q36: CF0 = -3M; C01 = .6M; F01 = 8; CPT NPV = 200,955.72.
Z96: CF0 = -4M; C01 = .7M; F01 = 10; CPT NPV = 301,196.97.

Since these projects have different lives, to compare, must compute Equivalent Annual Annuity.

EAA(Q36):        PV = 200955.72; I = 10; N = 8; CPT PMT = EAA = 37,667.95.
EAA(Z96):        PV = 301196.97; I = 10; N = 10; CPT PMT = EAA = 49018.42.

Choose Z96, since it has higher EAA.

Problems:
1.   Must compute EAA of each project. Rank of EAA: D, C, A, B.
2.
 Relevant – Opportunity cost
 Not relevant – Sunk cost
 Relevant – Initial cost
 Not relevant – Sunk cost
 Relevant – Incremental expense
 Not relevant – Sunk cost
 The incremental revenue of 93% of \$2 million is relevant.
 The tax savings associated with depreciation is relevant. Specifically, 36% of incremental
depreciation.
 Relevant – Incremental expense
 Not relevant – No incremental cost
 Relevant – Incremental
 Not relevant – must be paid regardless of whether project is accepted or rejected. Therefore, not
incremental.
3. The easiest way to do this problem is to assume the company can sell radiators for \$150 per radiator.
Then:
NPV (Buy from Supplier) = 13,477,081. NPV (Manufacture) = 9,439,730. ???
Project Buy: CF0=0, CF1=(150-120)*100,00*(1-0.3)=2.1 million, F1=10, NPV=13,477,081

Project Manufacture:

(150-80)*100,000=7 mil , 7 mil – 0.5m (depreciation)=6.5 million, 6.5*(1-0.3)=4.55 mil
4.55 mil + 0.5 mil (depreciation)=5.05 mil

CF0=-5 million, CF1=5.05 mil, F1=10, NPV= 27,409,171

4.     EAC(A) = 1160.76; EAC(B) = 1813.90 – Choose project with lower equivalent annual cost.
5.     NPV(Superior) = 17,802.68; NPV (Peerless) = 16,816.12 – Choose project with highest NPV.
6.     IRR(A) = 34.90%; NPV(A) = 5,849.33
IRR(B) = 31.61%; NPV(B) = 10,490.40
7.     Crossover rate = 7.167%; NPV(X) = NPV(Y) = 6720.60.
8.     a. Yes – incremental; b. No – Sunk; c. No – financing cost (captured in NPV analysis);
d. Yes – incremental; e. Yes – incremental.
9.     Note that annual NCF = Net income + Depreciation = 700,000 per year. NPV = 227,462.17.
10.   3,690.93
11.   Note that annual NCF = Net income + Depreciation = 6.55M per year. NPV = -5.879M.
12.   CF0 = (12,000,000); CF1 through CF10 = 2,880,000; No final year non-operating cash flow. NPV =
1,919,695.
13.   CF0 = (26,800,000); Operating net cash flow = 26,800,000; Final year non-operating cash flow =
2,200,000. NPV = 97,762,829.
14.   (56,004.33)
15.   For this problem, assume that the cost of capital is 14%. Then, NPV = (320,096). Reject.
16.
Step 1: Initial Investment in the Project

Opportunity cost of the land     -8M
New Building construction         -70M
Increase in Net Working capital -10M
Total Year 0 Cash Flow        -93.7M

Step 2: Annual Operating Cash Flow
Note that Incremental revenue = (3000)(300)(30) = 27M
and Depreciation = (5.7-.7)/25 + 70/25 = 3.0M

NCF = (27M - 3.2M - 4.5M - 2.3M - 3.0M)(.6) + 3.0M = 11.4M for 25 years.

Step 3: Final Year non-operating Cash Flow
Sell land              8M
Sell equipment         .7M
Recover NWC           10M
Total              18.7M

To compute NPV:
CF0=-93.7; C01 = 11.4; F01=24; C02=11.4+18.7=30.1; F02 = 1; CPT NPV = -14.642M.

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