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**Homework 5 Review & Chapter 7**

Lecture 4 Homework 5 Review & Chapter 7

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Homework 5 Review

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Question 1 Sustainable Growth Based on the following information, the sustainable growth rate for Hendrix Guitars, Inc., is 13.02%. The ROA is 11.52%. Profit margin=6.4 % Total asset turnover=1.80 Total debt ratio=0.60 Payout ratio=60 %

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Question 1 We should begin by calculating the D/E ratio. We calculate the D/E ratio as follows: Total debt ratio = .60 = TD / TA Inverting both sides we get: 1 / .60 = TA / TD Next, we need to recognize that TA / TD = 1 + TE / TD Substituting this into the previous equation, we get: 1 / .60 = 1 + TE /TD Subtract 1 (one) from both sides and inverting again, we get: D/E = 1 / [(1 / .60) – 1] D/E = 1.5 With the D/E ratio, we can calculate the EM and solve for ROE using the DuPont identity:

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**Question 1 ROE = (PM)(TAT)(EM) ROE = (.064)(1.80)(1 + 1.5)**

ROE = or 28.80% Now, we use the ROE equation: ROE = ROA(EM) .2880 = ROA(2.5) ROA = or 11.52% Now we can calculate the retention ratio as: b = 1 – .60 b = .40 Finally, putting all the numbers we have calculated into the sustainable growth rate equation, we get: Sustainable growth rate = (ROE × b) / [1 – (ROE × b)] Sustainable growth rate = [.2880(.40)] / [1 – .2880(.40)] Sustainable growth rate = or 13.02%

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**Question 2 Sustainable Growth Rate**

No Return, Inc., had equity of $165,000 at the beginning of the year. At the end of the year, the company had total assets of $250,000. During the year the company sold no new equity. Net income for the year was $80,000 and dividends were $49,000. (Input answers as a percent rounded to 2 decimal places, without the percent sign.) The sustainable growth rate for the company is ___ percent. The sustainable growth rate is ____ percent if you use the formula and beginning of period equity. If you use end of period equity in this formula, the sustainable growth rate is ____ percent. Is this number too high or too low? Why?

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Question 2 Since the company issued no new equity, shareholders’ equity increased by retained earnings. Retained earnings for the year were: Retained earnings = NI – Dividends Retained earnings = $80,000 – 49,000 Retained earnings = $31,000 So, the equity at the end of the year was: Ending equity = $165, ,000 Ending equity = $196,000

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**Question 2 The ROE based on the end of period equity is:**

The plowback ratio is: Plowback ratio = Addition to retained earnings/NI Plowback ratio = $31,000 / $80,000 Plowback ratio = or = 38.75% Using the equation presented in the text for the sustainable growth rate, we get: Sustainable growth rate = (ROE × b) / [1 – (ROE × b)] Sustainable growth rate = [.4082(.3875)] / [1 – .4082(.3875)] Sustainable growth rate = or 18.79% The ROE based on the beginning of period equity is ROE = $80,000 / $165,000 ROE = or 48.48%

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Question 2 Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we get: Sustainable growth rate = ROE × b Sustainable growth rate = × .3875 Sustainable growth rate = or 18.79% Using the shortened equation for the sustainable growth rate and the end of period ROE, we get: Sustainable growth rate = × .3875 Sustainable growth rate = or 15.82% Using the end of period ROE in the shortened sustainable growth rate results in a growth rate that is too low. This will always occur whenever the equity increases. If equity increases, the ROE based on end of period equity is lower than the ROE based on the beginning of period equity. The ROE (and sustainable growth rate) in the abbreviated equation is based on equity that did not exist when the net income was earned.

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**Question 2 Sustainable Growth Rate**

No Return, Inc., had equity of $165,000 at the beginning of the year. At the end of the year, the company had total assets of $250,000. During the year the company sold no new equity. Net income for the year was $80,000 and dividends were $49,000. (Input answers as a percent rounded to 2 decimal places, without the percent sign.) The sustainable growth rate for the company is percent. The sustainable growth rate is 18.79% percent if you use the (ROE x b) formula and beginning of period equity. If you use end of period equity in this formula, the sustainable growth rate is 15.82% percent. Is this number too high or too low? This is too low because equity has increased (see previous slide) Why?

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Question 3 Assets and costs are proportional to sales. Debt and equity are not. A dividend of $ was paid, and McGillicudy wishes to maintain a constant payout ratio. Next year's sales are projected to be $23,040. The external financing needed is $ _____

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Income Statement Balance Sheet Sales $ 19,200 Assets $ 93,000 Debt $ 20,400 Costs 15,550 Equity 72,600 ======== Taxable income $ 3,650 Total Taxes (34 %) 1,241 Net income $ 2,409

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**Question 3 An increase of sales to $23,040 is an increase of:**

Sales increase = ($23,040 – 19,200) / $19,200 Sales increase = .20 or 20% Assuming costs and assets increase proportionally, the pro forma financial statements will look like this: Pro forma income statement Pro forma balance sheet Sales $23, Assets $ ,600 Debt $20,400.00 Costs 18, Equity 74,334.48 EBIT 4, Total $ ,600 Total $ 94,734.48 Taxes(34%)1,489.20 Net income $2,890.80

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Question 3 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($ / $2,409)($2,890.80) Dividends = $1,156.32 The addition to retained earnings is: Addition to retained earnings = $2, – 1,156.32 Addition to retained earnings = $1,734.48 And the new equity balance is: Equity = $72, ,734.48 Equity = $74,334.48 So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $111,600 – 94,734.48 EFN = $16,865.52

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Question 4 A 20 percent growth rate in sales is projected. Prepare a pro forma income statement assuming costs vary with sales and the dividend payout ratio is constant.

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**HEIR JORDAN CORPORATION**

Income Statement Sales $ 29,000 Costs 11,200 ======== Taxable Income $ 17,800 Taxes (34%) 6,052 Net income $ 11,748 Dividends $ 4,935 Addition to retained earnings 6,813

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**HEIR JORDAN CORPORATION Pro Forma Income Statement**

Sales =$29,000*1.2=$34,800 Costs =$11,200*1.2=$13,440 ======== Taxable Income $21,360 Taxes (34%) $7,262.40 Net income $14,097.60 Dividends (Ratio = 4,935/11,748 = .42) $ Addition to retained earnings $

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**HEIR JORDAN CORPORATION Liabilities and Owners' Equity**

Balance Sheet Assets Liabilities and Owners' Equity Percentage $ of Sales Current assets Current liabilities Cash $ 3,525 % Accounts payable $ 3,000 Accounts receivable 7,500 Notes payable Inventory 6,000 ======== Total $ 10,500 $ 17,025 Long-term debt $ 19,500 Fixed assets Net plant and equipment $ 30,000 Owners' equity Common stock and paid-in surplus $ 15,000 Retained earnings 2,025 Total liabilities and Total assets $ 47,025 owners' equity

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Question 5: Supply the missing information using the percentage of sales approach. Assume that accounts payable vary with sales, whereas notes payable do not. (Input answers as a percent rounded to 2 decimal places, without the percent sign.)(Enter "n/a" where needed.) HEIR JORDAN CORPORATION Balance Sheet ($) (%) ($) (%) Assets Liabilities and Owners’ Equity Current assets Current liabilities Cash $3, A/P $3, A/R 7, Notes payable 7,500 n/a Inventory 6, Total $10,500 n/a Total $17, Long-term debt 19,500 n/a Fixed assets Owners’ equity Net P&E 30, CS & Paid surplus $15,000 n/a Retained earnings 2,025 n/a Total $17,025 n/a Total assets $47, Total liabilities and owners’ equity $47,025 n/a

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Question 6: Prepare a pro forma balance sheet showing EFN, assuming a 15 percent increase in sales, no new external debt or equity financing, and a constant payout ratio. Assuming costs vary with sales and a 15 percent increase in sales, the pro forma income statement will look like this: HEIR JORDAN CORPORATION Pro Forma Income Statement Sales $33,350.00 Costs 12,880.00 Taxable income $20,470.00 Taxes (34%) 6,959.80 Net income $ 13,510.20 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($4,935/$11,748)($13,510.20) Dividends = $5,674.94 And the addition to retained earnings will be: Addition to retained earnings = $13, – 5,674.94 Addition to retained earnings = $7,835.26 The new total addition to retained earnings on the pro forma balance sheet will be: New total addition to retained earnings = $2, ,835.26 New total addition to retained earnings = $9,860.26

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**EFN = Total assets – Total liabilities and equity **

The pro forma balance sheet will look like this: HEIR JORDAN CORPORATION Pro Forma Balance Sheet Assets Liabilities and Owners’ Equity Current assets Current liabilities Cash $ 4, Accounts payable $ 3,450.00 Accounts receivable 8, Notes payable 7,500.00 Inventory 6, Total $ 10,950.00 Total $ 19,578.75 Long-term debt 19,500.00 Fixed assets Net plant and Owners’ equity equipment 34, Common stock and paid-in surplus $15,000.00 Retained earnings 9,860.26 Total $ 24,860.26 Total liabilities and owners’ equity $ 55,310.26 Total assets $ 54,078.75 So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $54, – 55,310.26 EFN = –$1,231.51

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Question 7 Find the following financial ratios for Smolira Golf Corp. (use year-end figures rather than average values where appropriate): For solvency and utilization ratios: (Round answers to 2 decimal places.) For profitability ratios: (Input answers as a percent rounded to 2 decimal places, without a percent sign.)

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** Liabilities and Owners' Equity **

SMOLIRA GOLF CORP. 2004 and 2005 Balance Sheets Assets Liabilities and Owners' Equity 2004 2005 Current assets Current liabilities Cash $ 815 $ 906 Accounts payable $ 983 $ 1,292 Accounts receivable 2,405 2,510 Notes payable 720 840 Inventory 4,608 4,906 Other 105 188 Total $ 7,828 $ 8,322 Total $ 1,808 $ 2,320 Fixed assets Long-term debt $ 4,817 $ 4,960 Net plant and equipment $ 15,164 $ 19,167 Owners' equity ======== Common stock and paid-in surplus $ 10,000 Total assets $ 22,992 $ 27,489 Retained earnings 6,367 10,209 $ 16,367 $ 20,209 Total liabilities and owners' equity

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SMOLIRA GOLF CORP. 2005 Income Statement Sales $ 33,500 Costs of goods sold 18,970 Depreciation 1,980 ======== Earnings before interest and taxes $ 12,550 Interest paid 486 Taxable Income $ 12,064 Taxes (35%) 4,222 Net income $ 7,842 Dividends $ 4,000 Addition to retained earnings 3,842

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**Current ratio = Current assets / Current liabilities **

Short-term solvency ratios: Current ratio = Current assets / Current liabilities Current ratio 2004 = $7,828 / $1,808 = 4.33 times Current ratio 2005 = $8,322 / $2,320 = 3.59 times Quick ratio = (Current assets – Inventory) / Current liabilities Quick ratio 2004 = ($7,828 – 4,608) / $1,808 = 1.78 times Quick ratio 2005 = ($8,322 – 4,906) / $2,320 = 1.47 times Cash ratio = Cash / Current liabilities Cash ratio = $815 / $1,808 = 0.45 times Cash ratio 2005 = $906 / $2,320 = 0.39 times

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**Asset utilization ratios:**

Total asset turnover = Sales / Total assets Total asset turnover = $33,500 / $27,489 = 1.22 times Inventory turnover = Cost of goods sold / Inventory Inventory turnover = $18,970 / $4,906 = 3.87 times Receivables turnover = Sales / Accounts receivable Receivables turnover = $33,500 / $2,510 = times Long-term solvency ratios: Total debt ratio = (Total assets – Total equity) / Total assets Total debt ratio 2004 = ($22,992 – 16,367) / $22,992 = 0.29 Total debt ratio 2005 = ($27,489 – 20,209) / $27,489 = 0.26 Debt-equity ratio = Total debt / Total equity Debt-equity ratio 2004 = ($1, ,817) / $16,367 = 0.40 Debt-equity ratio 2005 = ($2, ,960) / $20,209 = 0.36 Equity multiplier = 1 + D/E Equity multiplier = = 1.40 Equity multiplier = = 1.36 Times interest earned = EBIT / Interest Times interest earned = $12,550 / $486 = times Cash coverage ratio = (EBIT + Depreciation) / Interest Cash coverage ratio = ($12, ,980) / $486 = times

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**Profitability ratios:**

Profit margin = Net income / Sales Profit margin = $7,842 / $33,500 = 23.41% Return on assets = Net income / Total assets Return on assets = $7,842 / $27,489 = 28.53% Return on equity = Net income / Total equity Return on equity = $7,842 / $20,209 = 38.80%

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Question 8 The most recent financial statements for Moose Tours, Inc., follow. Sales for 2005 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity and no new debt or equity is issued, external financing in the amount of $_____ is needed to support the 20 percent growth rate in sales.

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MOOSE TOURS, INC. 2004 Income Statement Sales $ 905,000 Costs 710,000 Other expenses 12,000 ======== Earnings before interest and taxes $ 183,000 Interest paid 19,700 Taxable Income $ 163,300 Taxes (35%) 57,155 Net income $ 106,145 Dividends $ 42,458 Addition to retained earnings 63,687

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**Balance Sheet as of December 31, 2004 Liabilities and Owners' Equity**

MOOSE TOURS, INC. Balance Sheet as of December 31, 2004 Assets Liabilities and Owners' Equity Current assets Current liabilities Cash $ 25,000 Accounts payable $ 65,000 Accounts receivable 43,000 Notes payable 9,000 Inventory 76,000 Total $ 74,000 $ 144,000 Long-term debt $ 156,000 Owners' equity Fixed assets Common stock and Net plant and equipment $ 364,000 paid-in surplus $ 21,000 Total assets $ 508,000 Retained earnings 257,000 $ 278,000 Total liabilities and owners' equity

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Assuming costs vary with sales and a 20 percent increase in sales, the pro forma income statement will look like this: MOOSE TOURS INC. Pro Forma Income Statement Sales $ 1,086,000 Costs 852,000 Other expenses 14,400 EBIT $ 219,600 Interest 19,700 Taxable income $199,900 Taxes(35%) 69,965 Net income $129,935 The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times net income, or: Dividends = ($42,458/$106,145)($129,935) Dividends = $51,974 And the addition to retained earnings will be: Addition to retained earnings = $129,935 – 51,974 Addition to retained earnings = $77,961

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**New addition to retained earnings = $257,000 + 77,961 **

The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257, ,961 New addition to retained earnings = $334,961 The pro forma balance sheet will look like this: MOOSE TOURS INC. Pro Forma Balance Sheet Assets Liabilities and Owners’ Equity Current assets Current liabilities Cash $30,000 Accounts payable $78,000 Accounts receivable 51,600 Notes payable 9,000 Inventory 91,200 Total $87,000 Total $ 172,800 Long-term debt 156,000 Fixed assets Net plant and equipment 436,800 Owners’ equity Common stock and paid-in surplus $21,000 Retained earnings 334,961 Total $355,961 Total liabilities and owners’ Total assets $609,600 equity $598,961

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Question 8 The most recent financial statements for Moose Tours, Inc., follow. Sales for 2005 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity and no new debt or equity is issued, external financing in the amount of $_____ is needed to support the 20 percent growth rate in sales.

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Question 8 So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $609,600 – 598,961 EFN = $10,639

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Question 9 The most recent financial statements for Moose Tours, Inc., follow. Sales for 2005 are projected to grow by 20 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity and wishes to keep its debt-equity ratio constant, external financing in the amount of $ is needed to support the 20 percent growth rate in sales.

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**Question 9 The D/E ratio of the company is:**

So the new total debt amount will be: New total debt = ($355,961) New total debt = $294,500.11 So the EFN is: EFN = $609,600 – ($294, ,961) = –$40,861.11 An interpretation of the answer is not that the company has a negative EFN. Looking back at Question 8, we see that for the same sales growth, the EFN is $10,639. The negative number in this case means the company has too much capital. There are two possible solutions. First, the company can put the excess funds in cash, which has the effect of changing the current asset growth rate. Second, the company can use the excess funds to repurchase debt and equity. To maintain the current capital structure, the repurchase must be in the same proportion as the current capital structure.

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**At a 20 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:**

And the addition to retained earnings will be: Addition to retained earnings = $129,935 – 51,974 Addition to retained earnings = $77,961 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257, ,961 New addition to retained earnings = $334,961 The new total debt will be: New total debt = ($334,961) New total debt = $294,500 So, the new long-term debt will be the new total debt minus the new short-term debt, or: New long-term debt = $294,500 – 87,000 New long-term debt = $207,500

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**EFN = Total assets – Total liabilities and equity **

So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $609,600 – 650,461 EFN = –$40,861

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**Question 10 EFN and Sustainable Growth**

The most recent financial statements for Moose Tours, Inc., follow. Sales for 2005 are projected to grow by 30 percent. Interest expense will remain constant; the tax rate and the dividend payout rate will also remain constant. Costs, other expenses, current assets, and accounts payable increase spontaneously with sales. If the firm is operating at full capacity and wishes to keep its debt-equity ratio constant, external financing in the amount of $_____ is needed to support the 30 percent growth rate in sales. (Round answers to nearest whole dollar.) If the projected sales growth rate for 2005 is 35 percent instead of 30 percent, the amount of external financing needed is $_____. At a sales growth rate of _____% percent, the EFN is equal to zero. Note: This last question cannot be answered if you do not allow debt to change to meet the debt-equity ratio at the beginning of the question.

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MOOSE TOURS, INC. 2004 Income Statement Sales $ 905,000 Costs 710,000 Other expenses 12,000 ======== Earnings before interest and taxes $ 183,000 Interest paid 19,700 Taxable Income $ 163,300 Taxes (35%) 57,155 Net income $ 106,145 Dividends $ 42,458 Addition to retained earnings 63,687

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**Balance Sheet as of December 31, 2004 Liabilities and Owners' Equity**

MOOSE TOURS, INC. Balance Sheet as of December 31, 2004 Assets Liabilities and Owners' Equity Current assets Current liabilities Cash $ 25,000 Accounts payable $ 65,000 Accounts receivable 43,000 Notes payable 9,000 Inventory 76,000 Total $ 74,000 $ 144,000 Long-term debt $ 156,000 Owners' equity Fixed assets Common stock and Net plant and equipment $ 364,000 paid-in surplus $ 21,000 Total assets $ 508,000 Retained earnings 257,000 $ 278,000 Total liabilities and owners' equity

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20% Sales Growth 30% Sales 35% Sales Sales $1,086,000 $1,176,500 $1,221,750 Costs 852,000 923,000 958,500 Other expenses 14,400 15,600 16,200 EBIT $ 219,600 $ 237,900 $ 247,050 Interest 19,700 Taxable income $ 199,900 $ 218,200 $ 227,350 Taxes (35%) 69,965 76,370 79,573 Net income $ 129,935 $ 141,830 $ 147,778 Dividends $ ,974 $ 56,732 $ 59,111 Add to RE 77,961 85,098 88,667

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Under the sustainable growth rate assumption, the company maintains a constant debt-equity ratio. The D/E ratio of the company is: D/E = ($156, ,000) / $278,000 D/E = At a 30 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be: Dividends = ($42,458/$106,145)($141,830) = $56,732 And the addition to retained earnings will be: Addition to retained earnings = $141,830 – 56,732 = $85,098 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257, ,098 = $342,098 The new total debt will be: New total debt = ($342,098) = $300,405 So, the new long-term debt will be the new total debt minus the new short-term debt, or: New long-term debt = $300,405 – 93,500 = $206,905

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So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $660,400 – 663,503 EFN = –$3,103

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**At a 35 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:**

And the addition to retained earnings will be: Addition to retained earnings = $147,778 – 59,111 = $88,667 The new addition to retained earnings on the pro forma balance sheet will be: New addition to retained earnings = $257, ,667 = $345,667 The new total debt will be: New total debt = ($366,667) = $303,357 So, the new long-term debt will be the new total debt minus the new short-term debt, or: New long-term debt = $303,357 – 96,750 = $206,607

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**EFN = Total assets – Total liabilities and equity **

So the EFN is: EFN = Total assets – Total liabilities and equity EFN = $685,800 – 670,024 EFN = $15,776

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**Question 10 EFN and Sustainable Growth**

Note: At 30% growth, there is a paydown in external financing, while at 35% growth there is a positive need for external financing At a sales growth rate of 30.82%, the EFN is equal to zero. Why is this internal growth rate different from that found by using the equation in the text?

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**Interest Rates and Bond Valuation**

Chapter 7 Interest Rates and Bond Valuation

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**Key Concepts and Skills**

Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields

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**Bond Definitions Bond Par value (face value) Coupon rate**

Coupon payment Maturity date Yield or Yield to maturity

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**Present Value of Cash Flows as Rates Change**

Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lump sum Remember, as interest rates increase present values decrease So, as interest rates increase, bond prices decrease and vice versa

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**Coupon Bond—Yield to Maturity**

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**When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate**

The price of a coupon bond and the yield to maturity are negatively related The yield to maturity is greater than the coupon rate when the bond price is below its face value

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**Valuing a Discount Bond with Annual Coupons**

Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.11)5] / / (1.11)5 B = = Using the calculator: N = 5; I/Y = 11; PMT = 100; FV = 1000 CPT PV = Remember the sign convention on the calculator. The easy way to remember it with bonds is we pay the PV (-) so that we can receive the PMT (+) and the FV(+). Slide 7.8 discusses why this bond sells at less than par

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**Valuing a Premium Bond with Annual Coupons**

Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? Using the formula: B = PV of annuity + PV of lump sum B = 100[1 – 1/(1.08)20] / / (1.08)20 B = = Using the calculator: N = 20; I/Y = 8; PMT = 100; FV = 1000 CPT PV =

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**Graphical Relationship Between Price and Yield-to-maturity**

Bond Price Bond characteristics: Coupon rate = 8% with annual coupons; Par value = $1000; Maturity = 10 years Yield-to-maturity

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**Bond Prices: Relationship Between Coupon and Yield**

If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price Why? Selling at a discount, called a discount bond If YTM < coupon rate, then par value < bond price Selling at a premium, called a premium bond There are the purely mechanical reasons for these results. We know that present values decrease as rates increase. Therefore, if we increase our yield above the coupon, the present value (price) must decrease below par. On the other hand, if we decrease our yield below the coupon, the present value (price) must increase above par. There are more intuitive ways to explain this relationship. Explain that the yield-to-maturity is the interest rate on newly issued debt of the same risk and that debt would be issued so that the coupon = yield. Then, suppose that the coupon rate is 8% and the yield is 9%. Ask the students which bond they would be willing to pay more for. Most will say that they would pay more for the new bond. Since it is priced to sell at $1000, the 8% bond must sell for less than $ The same logic works if the new bond has a yield and coupon less than 8%. Another way to look at it is that return = “dividend yield” + capital gains yield. The “dividend yield” in this case is just the coupon rate. The capital gains yield has to make up the difference to reach the yield to maturity. Therefore, if the coupon rate is 8% and the YTM is 9%, the capital gains yield must equal approximately 1%. The only way to have a capital gains yield of 1% is if the bond is selling for less than par value. (If price = par, there is no capital gain.) Technically, it is the current yield, not the coupon rate + capital gains yield, but from an intuitive standpoint, this helps some students remember the relationship and current yields and coupon rates are normally reasonably close.

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**The Bond-Pricing Equation**

This formalizes the calculations we have been doing.

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**Example 7.1 Find present values based on the payment period**

How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? B = 70[1 – 1/(1.08)14] / / (1.08)14 = Or PMT = 70; N = 14; I/Y = 8; FV = 1000; CPT PV = The students can read the example in the book. The basic information is as follows: Coupon rate = 14%, semiannual coupons YTM = 16% Maturity = 7 years Par value = $1000

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**Interest Rate Risk Price Risk Reinvestment Rate Risk**

Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds

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Interest-Rate Risk Prices and returns for long-term bonds are more volatile than those for shorter-term bonds There is no interest-rate risk for any bond whose time to maturity matches the holding period

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Figure 7.2

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**Computing Yield-to-maturity**

Yield-to-maturity is the rate implied by the current bond price Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign)

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**YTM with Annual Coupons**

Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $ Will the yield be more or less than 10%? N = 15; PV = ; FV = 1000; PMT = 100 CPT I/Y = 11% The students should be able to recognize that the YTM is more than the coupon since the price is less than par.

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**YTM with Semiannual Coupons**

Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1000, 20 years to maturity and is selling for $ Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there? N = 40; PV = ; PMT = 50; FV = 1000; CPT I/Y = 4% (Is this the YTM?) YTM = 4%*2 = 8%

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Table 7.1

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**Current Yield vs. Yield to Maturity**

Current Yield = annual coupon / price Yield to maturity = current yield + capital gains yield Example: 10% coupon bond, with semiannual coupons, face value of 1000, 20 years to maturity, $ price Current yield = 100 / = = 8.35% Price in one year, assuming no change in YTM = Capital gain yield = ( – ) / = = -.35% YTM = = 8%, which the same YTM computed earlier This is the same information as the YTM calculation on slide The YTM computed on that slide was 8%

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Bond Pricing Theorems Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond This is a useful concept that can be transferred to valuing assets other than bonds

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**Bond Prices with a Spreadsheet**

There is a specific formula for finding bond prices on a spreadsheet PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis) Settlement and maturity need to be actual dates The redemption and Pr need to given as % of par value Click on the Excel icon for an example Please note that you have to have the analysis tool pack add-ins installed to access the PRICE and YIELD functions. If you do not have these installed on your computer, you can use the PV and the RATE functions to compute price and yield as well. Click on the TVM tab to find these calculations.

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**Differences Between Debt and Equity**

Not an ownership interest Creditors do not have voting rights Interest is considered a cost of doing business and is tax deductible Creditors have legal recourse if interest or principal payments are missed Excess debt can lead to financial distress and bankruptcy Equity Ownership interest Common stockholders vote for the board of directors and other issues Dividends are not considered a cost of doing business and are not tax deductible Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid An all equity firm can not go bankrupt

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The Bond Indenture Contract between the company and the bondholders and includes The basic terms of the bonds The total amount of bonds issued A description of property used as security, if applicable Sinking fund provisions Call provisions Details of protective covenants

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**Bond Classifications Registered vs. Bearer Forms Security Seniority**

Collateral – secured by financial securities Mortgage – secured by real property, normally land or buildings Debentures – unsecured Notes – unsecured debt with original maturity less than 10 years Seniority This is standard terminology in the US – but it may not transfer to other countries. For example, debentures are secured debt in the United Kingdom

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**Bond Characteristics and Required Returns**

The coupon rate depends on the risk characteristics of the bond when issued Which bonds will have the higher coupon, all else equal? Secured debt versus a debenture Subordinated debenture versus senior debt A bond with a sinking fund versus one without A callable bond versus a non-callable bond Debenture: secured debt is less risky because the income from the security is used to pay it off first Subordinated debenture: will be paid after the senior debt Bond without sinking fund: company has to come up with substantial cash at maturity to retire debt and this is riskier than systematic retirement of debt through time Callable – bondholders bear the risk of the bond being called early, usually when rates are lower. They don’t receive all of the expected coupons and they have to reinvest at lower rates.

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**Bond Ratings – Investment Quality**

High Grade Moody’s Aaa and S&P AAA – capacity to pay is extremely strong Moody’s Aa and S&P AA – capacity to pay is very strong Medium Grade Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay

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**Bond Ratings - Speculative**

Low Grade Moody’s Ba, B, Caa and Ca S&P BB, B, CCC, CC Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation. Very Low Grade Moody’s C and S&P C – income bonds with no interest being paid Moody’s D and S&P D – in default with principal and interest in arrears It is a good exercise to ask students which bonds will have the highest yield-to-maturity (lowest price) all else equal.

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**Government Bonds Treasury Securities Municipal Securities**

Federal government debt T-bills – pure discount bonds with original maturity of one year or less T-notes – coupon debt with original maturity between one and ten years T-bonds coupon debt with original maturity greater than ten years Municipal Securities Debt of state and local governments Varying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal level

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Example 7.4 A taxable bond has a yield of 8% and a municipal bond has a yield of 6% If you are in a 40% tax bracket, which bond do you prefer? 8%(1 - .4) = 4.8% The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal At what tax rate would you be indifferent between the two bonds? 8%(1 – T) = 6% T = 25% You should be willing to accept a lower stated yield on municipals because you do not have to pay taxes on the interest received. You will want to make sure the students understand why you are willing to accept a lower rate of interest. It may be helpful to take the example and illustrate the indifference point using dollars instead of just percentages. The discount you are willing to accept depends on your tax bracket. Consider a taxable bond with a yield of 8% and a tax-exempt municipal bond with a yield of 6% Suppose you own one $1000 bond in each and both bonds are selling at par. You receive $80 per year from the corporate and $60 per year from the municipal. How much do you have after taxes if you are in the 40% tax bracket? Corporate: 80 – 80(.4) = 48; Municipal = 60

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Zero-Coupon Bonds Make no periodic interest payments (coupon rate = 0%) The entire yield-to-maturity comes from the difference between the purchase price and the par value Cannot sell for more than par value Sometimes called zeroes, deep discount bonds, or original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips are good examples of zeroes

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**Floating Rate Bonds Coupon rate floats depending on some index value**

Examples – adjustable rate mortgages and inflation-linked Treasuries There is less price risk with floating rate bonds The coupon floats, so it is less likely to differ substantially from the yield-to-maturity Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”

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**Other Bond Types Disaster bonds Income bonds Convertible bonds**

Put bonds There are many other types of provisions that can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns It is a useful exercise to ask the students if these bonds will tend to have higher or lower required returns compared to bonds without these specific provisions. Disaster bonds – issued by property and casualty companies. Pay interest and principal as usual unless claims reach a certain threshold for a single disaster. At that point, bondholders may lose all remaining payments Higher required return Income bonds – coupon payments depend on level of corporate income. If earnings are not enough to cover the interest payment, it is not owed. Higher required return Convertible bonds – bonds can be converted into shares of common stock at the bondholders discretion Lower required return Put bond – bondholder can force the company to buy the bond back prior to maturity Lower required return

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Bond Markets Primarily over-the-counter transactions with dealers connected electronically Extremely large number of bond issues, but generally low daily volume in single issues Makes getting up-to-date prices difficult, particularly on small company or municipal issues Treasury securities are an exception

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**Work the Web Example Bond quotes are available online**

One good site is Bonds Online Click on the web surfer to go to the site Follow the bond search, corporate links Choose a company, enter it under Express Search Issue and see what you can find!

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**Treasury Quotations Highlighted quote in Figure 7.4**

8 Nov :23 132: What is the coupon rate on the bond? When does the bond mature? What is the bid price? What does this mean? What is the ask price? What does this mean? How much did the price change from the previous day? What is the yield based on the ask price? Coupon rate = 8% Matures in November 2021 Bid price is 132 and 23/32 percent of par value. If you want to sell $100,000 par value T-bonds, the dealer is willing to pay (100,000) = $132,718.75 Ask price is 132 and 24/32 percent of par value. If you want to buy $100,000 par value T-bonds, the dealer is willing to sell them for (100,000) = $132,750.00 The difference between the bid and ask prices is called the bid-ask spread and it is how the dealer makes money. The price changed by -12/32 percent or $375 for a $100,000 worth of T-bonds The yield is 5.14%

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**Clean vs. Dirty Prices Clean price: quoted price**

Dirty price: price actually paid = quoted price plus accrued interest Example: Consider T-bond in previous slide, assume today is July 15, 2005 Number of days since last coupon = 61 Number of days in the coupon period = 184 Accrued interest = (61/184)(.04*100,000) = Prices (based on ask): Clean price = 132,750 Dirty price = 132, , = 134,076.09 So, you would actually pay $134, for the bond Assuming that the November maturity is November 15, then the coupon dates would be November 15 and May 15. Therefore, July 15 would be = 61 days since the last coupon The number of days in the coupon period would be = 184

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**Inflation and Interest Rates**

Real rate of interest – change in purchasing power Nominal rate of interest – quoted rate of interest, change in purchasing power and inflation The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation Be sure to ask the students to define inflation to make sure they understand what it is.

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The Fisher Effect The Fisher Effect defines the relationship between real rates, nominal rates and inflation (1 + R) = (1 + r)(1 + h), where R = nominal rate r = real rate h = expected inflation rate Approximation R = r + h The approximation works pretty well with “normal” real rates of interest and expected inflation. If the expected inflation rate is high, then there can be a substantial difference.

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Fisher Equation

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Example 7.6 If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? R = (1.1)(1.08) – 1 = .188 = 18.8% Approximation: R = 10% + 8% = 18% Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

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**Term Structure of Interest Rates**

Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different Yield curve—a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations Upward-sloping long-term rates are above short-term rates Flat short- and long-term rates are the same Inverted long-term rates are below short-term rates

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**Interpreting the Yield Curve**

(Figure 7.7) Models of term structure, such as the preferred habitat theory, help analysts use data from the The Wall Street Journal as a forecasting tool. Understanding the shape of the yield curve makes reading The Wall Street Journal data more meaningful.

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Figure 7.7 www: Click on the web surfer to go to Bloomberg to get the current Treasury yield curve

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**Figure 7.6 – Upward-Sloping Yield Curve**

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**Figure 7.6 – Downward-Sloping Yield Curve**

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**Factors Affecting Required Return**

Default risk premium – remember bond ratings Taxability premium – remember municipal versus taxable Liquidity premium – bonds that have more frequent trading will generally have lower required returns Anything else that affects the risk of the cash flows to the bondholders will affect the required returns

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Quick Quiz How do you find the value of a bond and why do bond prices change? What is a bond indenture and what are some of the important features? What are bond ratings and why are they important? How does inflation affect interest rates? What is the term structure of interest rates? What factors determine the required return on bonds?

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7 0 Interest Rates and Bond Valuation. 1 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they.

7 0 Interest Rates and Bond Valuation. 1 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they.

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