calculate return on equity by harvey1

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									FIN101 – Fall 2008                     Exam #1 Review Problems

Chapter One – Critical Thinking

1-6. In the corporate form of ownership, the shareholders are the owners of the firm. The shareholders
elect the directors of the corporation, who in turn appoint the firm’s management. This separation of
ownership from control in the corporate form of organization is what causes agency problems to exist.
Management may act in its own or someone else’s best interests, rather than those of the shareholders. If
such events occur, they may contradict the goal of maximizing the share price of the equity of the firm.

1-7. A primary market transaction.

Chapter Two – Critical Thinking

2-2. The recognition and matching principles in financial accounting call for revenues, and the costs
associated with producing those revenues, to be “booked” when the revenue process is essentially
complete, not necessarily when the cash is collected or bills are paid. Note that this way is not necessarily
correct; it’s the way accountants have chosen to do it.

2-3. Historical costs can be objectively and precisely measured, whereas market values can be difficult to
estimate, and different analysts would come up with different numbers. Thus, there is a tradeoff between
relevance (market values) and objectivity (book values).

2-7. It’s probably not a good sign for an established company, but it would be fairly ordinary for a start-
up, so it depends.

2-8. For example, if a company were to become more efficient in inventory management, the amount
of inventory needed would decline. The same might be true if it becomes better at collecting its
receivables. In general, anything that leads to a decline in ending NWC relative to beginning NWC would
have this effect. Negative net capital spending would mean more long-lived assets were liquidated than
purchased.

Chapter Two Problems

2-2. The income statement starts with revenues and subtracts costs to arrive at EBIT. We then subtract
out interest to get taxable income, and then subtract taxes to arrive at net income. Doing so, we get:

                   Income Statement
       Sales         $625,000
       Costs         260,000
       Depreciation    79,000
       EBIT          $286,000
       Interest        43,000
       Taxable income       $243,000
       Taxes           85,050
       Net income $157,950

2-3.   The dividends paid plus addition to retained earnings must equal net income, so:

Net income = Dividends + Addition to retained earnings
Addition to retained earnings = $157,950 – 60,000
Addition to retained earnings = $97,950

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FIN101 – Fall 2008                     Exam #1 Review Problems

2-8. To calculate the OCF, we first need to construct an income statement. The income statement starts
with revenues and subtracts costs to arrive at EBIT. We then subtract out interest to get taxable income,
and then subtract taxes to arrive at net income. Doing so, we get:

                     Income Statement
        Sales        $16,550
        Costs        5,930
        Depreciation 1,940
        EBIT         $8,680
        Interest      1,460
        Taxable income      $7,220
        Taxes (35%)     2,527
        Net income $4,693

        Now we can calculate the OCF, which is:

        OCF = EBIT + Depreciation – Taxes
        OCF = $8,680 + 1,940 – 2,527
        OCF = $8,093

2-9.    Net capital spending is the increase in fixed assets, plus depreciation. Using this relationship, we
find:

Net capital spending = NFAend – NFAbeg + Depreciation
Net capital spending = $2,120,000 – 1,875,000 + 220,000
Net capital spending = $465,000

2-19. a.        The income statement starts with revenues and subtracts costs to arrive at EBIT. We then
subtract interest to get taxable income, and then subtract taxes to arrive at net income. Doing so, we get:

               Income Statement
                       Sales $2,700,000
               Cost of goods sold    1,690,000
               Other expenses       465,000
               Depreciation 530,000
               EBIT $ 15,000
               Interest 210,000
               Taxable income       –$195,000
               Taxes (35%)         0
               Net income –$195,000

        The taxes are zero since we are ignoring any carryback or carryforward provisions.

        b.     The operating cash flow for the year was:

               OCF = EBIT + Depreciation – Taxes
               OCF = $15,000 + 530,000 – 0
               OCF = $545,000



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FIN101 – Fall 2008                     Exam #1 Review Problems

       c.     Net income was negative because of the tax deductibility of depreciation and interest
expense. However, the actual cash flow from operations was positive because depreciation is a non-cash
expense and interest is a financing, not an operating, expense.

Chapter Three Critical Thinking

3-3. A current ratio of 0.50 means that the firm has twice as much in current liabilities as it does in
current assets; the firm potentially has poor liquidity. If pressed by its short-term creditors and suppliers
for immediate payment, the firm might have a difficult time meeting its obligations. A current ratio of
1.50 means the firm has 50% more current assets than it does current liabilities. This probably represents
an improvement in liquidity; short-term obligations can generally be met com-pletely with a safety factor
built in. A current ratio of 15.0, however, might be excessive. Any excess funds sitting in current assets
generally earn little or no return. These excess funds might be put to better use by investing in productive
long-term assets or distributing the funds to shareholders.

3-7. Return on equity is probably the most important accounting ratio that measures the bottom-line
performance of the firm with respect to the equity shareholders. The Du Pont identity emphasizes the role
of a firm’s profitability, asset utilization efficiency, and financial leverage in achieving a ROE figure. For
example, a firm with ROE of 20% would seem to be doing well, but this figure may be misleading if it
were a marginally profitable (low profit margin) and highly levered (high equity multiplier). If the firm’s
margins were to erode slightly, the ROE would be heavily impacted.

Chapter Three Problems

3-3.   The receivables turnover for the company was:

Receivables turnover = Credit sales / Receivables
Receivables turnover = $5,871,650 / $645,382
Receivables turnover = 9.10 times

Using the receivables turnover, we can calculate the day’s sales in receivables as:

       Days’ sales in receivables = 365 days / Receivables turnover
Days’ sales in receivables = 365 days / 9.10
Days’ sales in receivables = 40.12 days

       The average collection period, which is the same as the day’s sales in receivables, was 40.12 days.

3-4.   The inventory turnover for the company was:

Inventory turnover = COGS / Inventory
Inventory turnover = $8,493,825 / $743,186
Inventory turnover = 11.43 times

       Using the inventory turnover, we can calculate the days’ sales in inventory as:
Days’ sales in inventory = 365 days / Inventory turnover
Days’ sales in inventory = 365 days / 11.43
Days’ sales in inventory = 31.94 days

       On average, a unit of inventory sat on the shelf 31.94 days before it was sold.

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FIN101 – Fall 2008                     Exam #1 Review Problems

3-5. To find the debt-equity ratio using the total debt ratio, we need to rearrange the total debt ratio
equation. We must realize that the total assets are equal to total debt plus total equity. Doing so, we find:

Total debt ratio = Total debt / Total assets
0.70 = Total debt / (Total debt + Total equity)
0.30(Total debt) = 0.70(Total equity)
Total debt / Total equity = 0.70 / 0.30
       Debt-equity ratio = 2.33

       And the equity multiplier is one plus the debt-equity ratio, so:

       Equity multiplier = 1 + D/E
Equity multiplier = 1 + 2.33
Equity multiplier = 3.33


3-7. With the information given, we must use the Du Pont identity to calculate return on equity. Doing
so, we find:

ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
ROE = (.08)(1.32)(1.60)
ROE = 0.1690 or 16.90%

3-8. We can use the Du Pont identity and solve for the equity multiplier. With the equity multiplier we
can find the debt-equity ratio. Doing so we find:

ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
0.1570 = (0.10)(1.35)(Equity multiplier)
Equity multiplier = 1.16

Now, using the equation for the equity multiplier, we get:

Equity multiplier = 1 + Debt-equity ratio
1.16 = 1 + Debt-equity ratio
Debt-equity ratio = 0.16

3-10. With the information provided, we need to calculate the return on equity using an extended return
on equity equation. We first need to find the equity multiplier which is:

Equity multiplier = 1 + Debt-equity ratio (or Assets/Equity)
Equity multiplier = 1 + 0.80
Equity multiplier = 1.80

Now we can calculate the return on equity as:

      ROE = (ROA)(Equity multiplier)
ROE = 0.089(1.80)
ROE = 0.1602 or 16.02%



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FIN101 – Fall 2008                     Exam #1 Review Problems

The return on equity equation we used was an abbreviated version of the Du Pont identity. If we multiply
the profit margin and total asset turnover ratios from the Du Pont identity, we get:

(Net income / Sales)(Sales / Total assets) = Net income / Total assets = ROA

With the return on equity, we can calculate the net income as:

       ROE = Net income / Total equity
0.1602 = Net income / $590,000
Net income = $94,518

3-17. Using the Du Pont identity to calculate ROE, we get:

       ROE = (Profit margin)(Total asset turnover)(Equity multiplier)
       ROE = (Net income / Sales)(Sales / Total assets)(Total asset / Total equity)
       ROE = ($132,186 / $2,678,461)($2,678,461 / $784,596)($784,596 / $407,490)
       ROE = 0.3244 or 32.44%

3-29. To calculate the profit margin, we first need to calculate the sales. Using the days’ sales in
receivables, we find the receivables turnover is:

       Days’ sales in receivables = 365 days / Receivables turnover
       29.70 days = 365 days / Receivables turnover
       Receivables turnover = 12.29 times

       Now, we can use the receivables turnover to calculate the sales as:

       Receivables turnover = Sales / Receivables
       12.29 = Sales / $138,600
       Sales = $1,703,333

       So, the profit margin is:

       Profit margin = Net income / Sales
       Profit margin = $132,500 / $1,703,333
       Profit margin = 0.0778 or 7.78%

       The total asset turnover is:

       Total asset turnover = Sales / Total assets
       Total asset turnover = $1,703,333 / $820,000
       Total asset turnover = 2.08 times

We need to use the Du Pont identity to calculate the return on equity. Using this relationship, we get:

       ROE = (Profit margin)(Total asset turnover)(1 + Debt-equity ratio)
       ROE = (0.778)(2.08)(1 + 0.60)
       ROE = 0.2585 or 25.85%



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FIN101 – Fall 2008                     Exam #1 Review Problems

Chapter Four Critical Thinking

4-4. It depends. The large deposit will have a larger future value for some period, but after time, the
smaller deposit with the larger interest rate will eventually become larger. The length of time for the
smaller deposit to overtake the larger deposit depends on the amount deposited in each account and the
interest rates.

4-8. The key considerations would be: (1) Is the rate of return implicit in the offer attractive relative to
other, similar risk investments? and (2) How risky is the investment; i.e., how certain are we that we will
actually get the $10,000? Thus, our answer does depend on who is making the promise to repay.

Chapter Four Problems

4-2.   To find the FV of a lump sum, we use:

       FV = PV(1 + r)t

       FV = $3,150(1.18)5 = $ 7,206.44
       FV = $8,453(1.06)10 =    $ 15,138.04
       FV = $89,305(1.11)17 =   $526,461.25
                           20
       FV = $227,382(1.05)      =      $603,312.14

4-3.   To find the PV of a lump sum, we use:

       PV = FV / (1 + r)t

       PV = $15,451 / (1.04)12        = $ 9,650.65
       PV = $51,557 / (1.09)4         = $36,524.28
       PV = $886,073 / (1.17)16       = $71,861.41
       PV = $901,450 / (1.20)21       = $19,594.56

4-10. To find the PV of a lump sum, we use:

       PV = FV / (1 + r)t
       PV = $800,000,000 / (1.08)20
       PV = $171,638,566

4-19. Even though we need to calculate the value in eight years, we will only have the money for six
years, so we need to use six years as the number of periods. To find the FV of a lump sum, we use:

       FV = PV(1 + r)t
       FV = $15,000(1.08)6
       FV = $23,803.11




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