April 3, 2019

CHAPTER 4 B-39

Now we can use the DuPont identity to find the equity multiplier as:

ROE = PM(TAT)(EM)

.1473 = (.062)(1 / .60)EM

EM = (.1473)(.60) / .062

EM = 1.43

So, the D/E ratio is:

D/E = EM – 1

D/E = 1.43 – 1

D/E = 0.43

20. We are given the profit margin. Remember that:

ROA = PM(TAT)

We can calculate the ROA from the internal growth rate formula, and then use the ROA in this

equation to find the total asset turnover. The retention ratio is:

b = 1 – .25

b = .75

Using the internal growth rate equation to find the ROA, we get:

21. We should begin by calculating the D/E ratio. We calculate the D/E ratio as follows:

Total debt ratio = .65 = TD / TA

Inverting both sides we get:

Next, we need to recognize that

Substituting this into the previous equation, we get:

B-40 SOLUTIONS

Subtract 1 (one) from both sides and inverting again, we get:

With the D/E ratio, we can calculate the EM and solve for ROE using the DuPont identity:

ROE = (PM)(TAT)(EM)

Now we can calculate the retention ratio as:

b = 1 – .30

b = .70

Finally, putting all the numbers we have calculated into the sustainable growth rate equation, we get:

22. To calculate the sustainable growth rate, we first must calculate the retention ratio and ROE. The

retention ratio is:

And the ROE is:

So, the sustainable growth rate is:

If the company grows at the sustainable growth rate, the new level of total assets is:

To find the new level of debt in the company’s balance sheet, we take the percentage of debt in the

capital structure times the new level of total assets. The additional borrowing will be the new level of

debt minus the current level of debt. So:

New TD = [D / (D + E)](TA)

CHAPTER 4 B-41

And the additional borrowing will be:

The growth rate that can be supported with no outside financing is the internal growth rate. To

calculate the internal growth rate, we first need the ROA, which is:

This means the internal growth rate is:

Internal growth rate = (ROA × b) / [1 – (ROA × b)]

23. Since the company issued no new equity, shareholders’ equity increased by retained earnings.

Retained earnings for the year were:

Retained earnings = NI – Dividends

So, the equity at the end of the year was:

The ROE based on the end of period equity is:

The plowback ratio is:

Plowback ratio = Addition to retained earnings/NI

Using the equation presented in the text for the sustainable growth rate, we get:

Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]

The ROE based on the beginning of period equity is

B-42 SOLUTIONS

Using the shortened equation for the sustainable growth rate and the beginning of period ROE, we

get:

Sustainable growth rate = ROE × b

Using the shortened equation for the sustainable growth rate and the end of period ROE, we get:

Sustainable growth rate = ROE × b

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.

24. The ROA using end of period assets is:

The beginning of period assets had to have been the ending assets minus the addition to retained

earnings, so:

Beginning assets = Ending assets – Addition to retained earnings

And the ROA using beginning of period assets is:

Using the internal growth rate equation presented in the text, we get:

Internal growth rate = (ROA × b) / [1 – (ROA × b)]

Using the formula ROA × b, and end of period assets:

Using the formula ROA × b, and beginning of period assets:

CHAPTER 4 B-43

25. 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 $ 1,114,800

Costs 867,600

Other expenses 22,800

EBIT $ 224,400

Interest 14,000

Taxable income $ 210,400

Taxes(35%) 73,640

Net income $ 136,760

The payout ratio is constant, so the dividends paid this year is the payout ratio from last year times

net income, or:

And the addition to retained earnings will be:

The new retained earnings on the pro forma balance sheet will be:

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 $ 30,360 Accounts payable $ 81,600

Accounts receivable 48,840 Notes payable 17,000

Inventory 104,280 Total $ 98,600

Total $ 183,480 Long-term debt 158,000

Fixed assets

Net plant and Owners’ equity

equipment 495,600 Common stock and

paid-in surplus $ 140,000

Retained earnings 278,632

Total $ 418,632

Total liabilities and owners’

Total assets $ 679,080 equity $ 675,232

B-44 SOLUTIONS

So the EFN is:

26. First, we need to calculate full capacity sales, which is:

The capital intensity ratio at full capacity sales is:

Capital intensity ratio = Fixed assets / Full capacity sales

The fixed assets required at full capacity sales is the capital intensity ratio times the projected sales

level:

Note that this solution assumes that fixed assets are decreased (sold) so the company has a 100

percent fixed asset utilization. If we assume fixed assets are not sold, the answer becomes:

27. The D/E ratio of the company is:

So the new total debt amount will be:

This is the new total debt for the company. Given that our calculation for EFN is the amount that

must be raised externally and does not increase spontaneously with sales, we need to subtract the

spontaneous increase in accounts payable. The new level of accounts payable will be, which is the

current accounts payable times the sales growth, or:

CHAPTER 4 B-45

This means that $13,600 of the new total debt is not raised externally. So, the debt raised externally,

which will be the EFN is:

The pro forma balance sheet with the new long-term debt will be:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 30,360 Accounts payable $ 81,600

Accounts receivable 44,400 Notes payable 17,000

Inventory 104,280 Total $ 98,600

Total $ 183,480 Long-term debt 216,444

Fixed assets

Net plant and Owners’ equity

equipment 495,600 Common stock and

paid-in surplus $ 140,000

Retained earnings 278,632

Total $ 418,632

Total liabilities and owners’

To make the balance sheet balance, the company will have to increase its assets. We will put this

amount in an account called excess cash, which will give us the following balance sheet:

B-46 SOLUTIONS

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 30,360 Accounts payable $ 81,600

Excess cash 54,596

Accounts receivable 44,400 Notes payable 17,000

Inventory 104,280 Total $ 98,600

Total $ 238,076 Long-term debt 216,444

Fixed assets

Net plant and Owners’ equity

equipment 495,600 Common stock and

paid-in surplus $ 140,000

Retained earnings 278,632

Total $ 418,632

Total liabilities and owners’

So, the amount of debt and equity needed will be:

So, the repurchases of debt and equity will be:

Assuming all of the debt repurchase is from long-term debt, and the equity repurchase is entirely

from the retained earnings, the final pro forma balance sheet will be:

CHAPTER 4 B-47

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 30,360 Accounts payable $ 81,600

Accounts receivable 44,400 Notes payable 17,000

Inventory 104,280 Total $ 98,600

Total $ 183,480 Long-term debt 193,000

Fixed assets

Net plant and Owners’ equity

equipment 495,600 Common stock and

paid-in surplus $ 140,000

Retained earnings 247,480

Total $ 387,480

Total liabilities and owners’

Total assets $ 697,080 equity $ 697,080

Challenge

28. The pro forma income statements for all three growth rates will be:

MOOSE TOURS INC.

Pro Forma Income Statement

15 % Sales

Growth 20% Sales

Growth 25% Sales

Growth

Sales $1,068,350 $1,114,800 $1,161,250

Costs 831,450 867,600 903,750

Other expenses 21,850 22,800 23,750

EBIT $215,050 $224,400 $233,750

Interest 14,000 14,000 14,000

Taxable income $201,050 $210,400 $219,750

Taxes (35%) 70,368 73,640 76,913

N

et income $130,683 $136,760 $142,838

Dividends $39,205 $41,028 $42,851

Add to RE 91,478 95,732 99,986

And the addition to retained earnings will be:

B-48 SOLUTIONS

Addition to retained earnings = $91,478

The new retained earnings on the pro forma balance sheet will be:

The pro forma balance sheet will look like this:

15% Sales Growth:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 29,095 Accounts payable $ 78,200

Accounts receivable 46,805 Notes payable 17,000

Inventory 99,935 Total $ 95,200

Total $ 175,835 Long-term debt $ 158,000

Fixed assets

Net plant and Owners’ equity

equipment 474,950 Common stock and

paid-in surplus $ 140,000

Retained earnings 274,378

Total $ 414,378

Total liabilities and owners’

Total assets $ 650,785 equity $ 667,578

So the EFN is:

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:

The new retained earnings on the pro forma balance sheet will be:

CHAPTER 4 B-49

The pro forma balance sheet will look like this:

20% Sales Growth:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 30,360 Accounts payable $ 81,600

Accounts receivable 48,840 Notes payable 17,000

Inventory 104,280 Total $ 98,600

Total $ 183,480 Long-term debt $ 158,000

Fixed assets

Net plant and Owners’ equity

equipment 495,600 Common stock and

paid-in surplus $ 140,000

Retained earnings 278,632

Total $ 418,632

Total liabilities and owners’

Total assets $ 679,080 equity $ 675,232

So the EFN is:

EFN = Total assets – Total liabilities and equity

At a 25 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:

And the addition to retained earnings will be:

The new retained earnings on the pro forma balance sheet will be:

The pro forma balance sheet will look like this:

B-50 SOLUTIONS

25% Sales Growth:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 31,625 Accounts payable $ 85,000

Accounts receivable 50,875 Notes payable 17,000

Inventory 108,625 Total $ 102,000

Total $ 191,125 Long-term debt $ 158,000

Fixed assets

Net plant and Owners’ equity

equipment 516,250 Common stock and

paid-in surplus $ 140,000

Retained earnings 282,886

Total $ 422,886

Total liabilities and owners’

Total assets $ 707,375 equity $ 682,886

So the EFN is:

EFN = Total assets – Total liabilities and equity

29. The pro forma income statements for all three growth rates will be:

MOOSE TOURS INC.

Pro Forma Income Statement

20% Sales

Growth 30% Sales

Growth 35% Sales

Growth

Sales $1,114,800 $1,207,700 $1,254,150

Costs 867,600 939,900 976,050

Other expenses 22,800 24,700 25,650

EBIT $224,400 $243,100 $252,450

Interest 14,000 14,000 14,000

Taxable income $210,400 $229,100 $238,450

Taxes (35%) 73,640 80,185 83,458

N

et income $136,760 $148,915 $154,993

Dividends $41,028 $44,675 $46,498

Add to RE 95,732 104,241 108,495

At a 30 percent growth rate, and assuming the payout ratio is constant, the dividends paid will be:

And the addition to retained earnings will be:

CHAPTER 4 B-51

Addition to retained earnings = $135,948 – 40,784

Addition to retained earnings = $104,241

The new addition to retained earnings on the pro forma balance sheet will be:

The new total debt will be:

So, the new long-term debt will be the new total debt minus the new short-term debt, or:

The pro forma balance sheet will look like this:

Sales growth rate = 30% and debt/equity ratio = .7526:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 32,890 Accounts payable $ 88,400

Accounts receivable 52,910 Notes payable 17,000

Inventory 112,970 Total $ 105,400

Total $ 198,770 Long-term debt 216,047

Fixed assets

Net plant and Owners’ equity

equipment 536,900 Common stock and

paid-in surplus $ 140,000

Retained earnings 287,141

Total $ 427,141

Total liabilities and owners’

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

B-52 SOLUTIONS

And the addition to retained earnings will be:

The new retained earnings on the pro forma balance sheet will be:

The new total debt will be:

So, the new long-term debt will be the new total debt minus the new short-term debt, or:

CHAPTER 4 B-53

Sales growth rate = 35% and debt/equity ratio = .75255:

MOOSE TOURS INC.

Pro Forma Balance Sheet

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 34,155 Accounts payable $ 91,800

Accounts receivable 54,945 Notes payable 17,000

Inventory 117,315 Total $ 108,800

Total $ 206,415 Long-term debt $ 215,848

Fixed assets

Net plant and Owners’ equity

equipment 557,550 Common stock and

paid-in surplus $ 140,000

Retained earnings 291,395

Total $ 431,395

Total liabilities and owners’

Total assets $ 763,965 equity $ 756,043

So the excess debt raised is:

At a 35 percent growth rate, the firm will need funds in the amount of $7,922 in addition to the

external debt already raised. So, the EFN will be:

30. We must need the ROE to calculate the sustainable growth rate. The ROE is:

ROE = (PM)(TAT)(EM)

Now we can use the sustainable growth rate equation to find the retention ratio as:

This implies the payout ratio is:

B-54 SOLUTIONS

This is a negative dividend payout ratio of 66 percent, which is impossible. The growth rate is not

consistent with the other constraints. The lowest possible payout rate is 0, which corresponds to

retention ratio of 1, or total earnings retention.

The maximum sustainable growth rate for this company is:

Maximum sustainable growth rate = (ROE × b) / [1 – (ROE × b)]

31. We know that EFN is:

EFN = Increase in assets – Addition to retained earnings

The increase in assets is the beginning assets times the growth rate, so:

Increase in assets = A g

The addition to retained earnings next year is the current net income times the retention ratio, times

one plus the growth rate, so:

And rearranging the profit margin to solve for net income, we get:

NI = PM(S)

Substituting the last three equations into the EFN equation we started with and rearranging, we get:

EFN = A(g) – PM(S)b(1 + g)

32. We start with the EFN equation we derived in Problem 31 and set it equal to zero:

Since:

ROA = NI / A

ROA = PM(S) / A

We can substitute this into the internal growth rate equation and divide both the numerator and

denominator by A. This gives: