April 3, 2019

CHAPTER 4 B-35

10. Below is the balance sheet with the percentage of sales for each account on the balance sheet. Notes

payable, total current liabilities, long-term debt, and all equity accounts do not vary directly with

sales.

HEIR JORDAN CORPORATION

Balance Sheet

($) (%) ($) (%)

Assets Liabilities and Owners’ Equity

Current assets Current liabilities

Cash $ 3,050 8.03 Accounts payable $ 1,300 3.42

11. 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 $43,700.00

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 accumulated retained earnings on the pro forma balance sheet will be:

B-36 SOLUTIONS

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 $ 3,507.50 Accounts payable $ 1,495.00

Accounts receivable 7,935.00 Notes payable 6,800.00

Inventory 8,740.00 Total $ 8,295.00

Total $20,182.50 Long-term debt 25,000.00

Fixed assets

Net plant and Owners’ equity

12. We need to calculate the retention ratio to calculate the internal growth rate. The retention ratio is:

b = 1 – .20

b = .80

Now we can use the internal growth rate equation to get:

13. We need to calculate the retention ratio to calculate the sustainable growth rate. The retention ratio

is:

b = 1 – .25

b = .75

Now we can use the sustainable growth rate equation to get:

CHAPTER 4 B-37

14. We first must calculate the ROE to calculate the sustainable growth rate. To do this we must realize

two other relationships. The total asset turnover is the inverse of the capital intensity ratio, and the

equity multiplier is 1 + D/E. Using these relationships, we get:

ROE = (PM)(TAT)(EM)

The plowback ratio is one minus the dividend payout ratio, so:

15. We must first calculate the ROE using the DuPont ratio to calculate the sustainable growth rate. The

ROE is:

ROE = (PM)(TAT)(EM)

The plowback ratio is one minus the dividend payout ratio, so:

b = 1 – .60

b = .40

Now we can use the sustainable growth rate equation to get:

Intermediate

16. To determine full capacity sales, we divide the current sales by the capacity the company is currently

using, so:

The maximum sales growth is the full capacity sales divided by the current sales, so:

B-38 SOLUTIONS

17. To find the new level of fixed assets, we need to find the current percentage of fixed assets to full

capacity sales. Doing so, we find:

Next, we calculate the total dollar amount of fixed assets needed at the new sales figure.

The new fixed assets necessary is the total fixed assets at the new sales figure minus the current level

of fixed assts.

18. We have all the variables to calculate ROE using the DuPont identity except the profit margin. If we

find ROE, we can solve the DuPont identity for profit margin. We can calculate ROE from the

sustainable growth rate equation. For this equation we need the retention ratio, so:

b = 1 – .30

b = .70

Using the sustainable growth rate equation and solving for ROE, we get:

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

Now we can use the DuPont identity to find the profit margin as:

ROE = PM(TAT)(EM)

19. We have all the variables to calculate ROE using the DuPont identity except the equity multiplier.

Remember that the equity multiplier is one plus the debt-equity ratio. If we find ROE, we can solve

the DuPont identity for equity multiplier, then the debt-equity ratio. We can calculate ROE from the

sustainable growth rate equation. For this equation we need the retention ratio, so:

b = 1 – .30

b = .70

Using the sustainable growth rate equation and solving for ROE, we get:

CHAPTER 4 B-39

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

ROE = PM(TAT)(EM)

So, the D/E ratio is:

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:

Plugging ROA and PM into the equation we began with and solving for TAT, we get:

ROA = (PM)(TAT)

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: