Question

Rentz Corporation is investigating the optimal level of current assets for the coming year. Management expects sales to increase to approximately $3 million as a result of an asset expansion presently being undertaken. Fixed assets total $2 million, and the firm plans to maintain a 45% debt-to-assets ratio. Rentz's interest rate is currently 8% on both short-term and long-term debt (which the firm uses in its permanent structure). Three alternatives regarding the projected current assets level are under consideration: (1) a restricted policy where current assets would be only 45% of projected sales, (2) a moderate policy where current assets would be 50% of sales, and (3) a relaxed policy where current assets would be 60% of sales. Earnings before interest and taxes should be 10% of total sales, and the federal-plus-state tax rate is 40%.

1. What is the expected return on equity under each current assets level? Round your answers to two decimal places.
   

   Restricted policy		%
   Moderate policy		%
   Relaxed policy		%

2. 
   
3. In this problem, we assume that expected sales are independent of the current assets investment policy. Is this a valid assumption?
   1. Yes, this assumption would probably be valid in a real world situation. A firm's current asset policies have no significant effect on sales.
   2. Yes, sales are controlled only by the degree of marketing effort the firm uses, irrespective of the current asset policies it employs.
   3. Yes, the current asset policies followed by the firm mainly influence the level of long-term debt used by the firm.
   4. Yes, the current asset policies followed by the firm mainly influence the level of fixed assets.
   5. No, this assumption would probably not be valid in a real world situation. A firm's current asset policies may have a significant effect on sales.
   
   -Select-IIIIIIIVVItem 4
4. 
   
5. How would the firm's risk be affected by the different policies?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer 1

In the given question the following data are given :

1. Expected sales is $3,000,000
2. Fixed Assets is $2,000,000
3. Debt-to-asset ratio is 45% in any situation
4. Interest rate on Debt is 8%
5. Restricted policy where current assets is 45% of expected sales
6. Moderate policy where current assets is 50% of expected sales
7. Relaxed policy where current assets is 60% of expected sales
8. Earnings before interest and taxes (EBIT) is 10% of expected sales
9. Tax rate is 40%

Answer – a

To calculate the expected return on equity under each current asset level the following formula shall be used –

Return on equity = Earnings after tax (EAT) / Total Equity

Where-

Total Equity = Total Asset – Total Debt;

EAT = Earnings after interest and taxes

Now we have to calculate Total Asset, Total Debt and EAT for computing Return on Equity.

Let us first calculate Total Asset

Particulars	Policies
	Restricted Policy	Moderate Policy	Relaxed Policy
Sales (A)	$               3,000,000	$               3,000,000	$               3,000,000
Current Asset (B)	$               1,350,000	$               1,500,000	$               1,800,000
	($3,000,000 * 45%)	($3,000,000 * 50%)	($3,000,000 * 60%)
Fixed Asset ( C )	$               2,000,000	$               2,000,000	$               2,000,000
Total Asset (B + C)	$               3,350,000	$               3,500,000	$               3,800,000

Now we have to calculate Total Debt using Debt-to-asset ratio of 45%

Particulars	Policies
	Restricted Policy	Moderate Policy	Relaxed Policy
Total Asset	$               3,350,000	$               3,500,000	$               3,800,000
Debt-to-asset = 45%
Total Debt	$               1,507,500	$               1,575,000	$               1,710,000
	($3,350,000 * 45%)	($3,500,000 * 45%)	($3,800,000 * 45%)

Hence Total Equity is as follows :

Particulars	Policies
	Restricted Policy	Moderate Policy	Relaxed Policy
Total Asset (A)	$               3,350,000	$               3,500,000	$               3,800,000
Total Debt (B)	$               1,507,500	$               1,575,000	$               1,710,000
Total Equity (A - B)	$               1,842,500	$               1,925,000	$               2,090,000

Computation of Earnings after tax

Particulars	Policies
	Restricted Policy	Moderate Policy	Relaxed Policy
Sales (A)	$               3,000,000	$               3,000,000	$               3,000,000
EBIT (10% of Sales) (B)	$                   300,000	$                   300,000	$                   300,000
Interest (8% of Debt) ( C)	$                   120,600	$                   126,000	$                   136,800
EBT (B - C)   (D)	$                   179,400	$                   174,000	$                   163,200
Tax (40% of EBT)    ( E)	$                     71,760	$                     69,600	$                     65,280
EAT (D - E)	$                   107,640	$                   104,400	$                     97,920

Now calculate Return on Equity using the below mentioned formula :

Return on equity = Earnings after tax (EAT) / Total Equity

Particulars	Policies
	Restricted Policy	Moderate Policy	Relaxed Policy
EAT (A)	$                         107,640	$                         104,400	$                            97,920
Total Equity (B)	$                      1,842,500	$                      1,925,000	$                      2,090,000
ROE (A/B)	5.84%	5.42%	4.69%

Answer – c

Q- In this problem, we assume that expected sales are independent of the current assets investment policy. Is this a valid assumption?

A- III. Yes, the current asset policies followed by the firm mainly influence the level of long-term debt used by the firm.

Since it is clearly evident that in the given policies when the current assets increases it eventually increases total assets and therefore the total debt shall also increase because Rentz corporation follows a rigid policy of maintaining a debt-to-asset ratio of 45%

Answer – e

It is evident from return on equity calculated in (a) above that as the current assets investment policy changes the return changes significantly although all other constraints remaining the same like sales, interest and tax rates, it proves that when the component of current asset increases in the given scenario the return on investment shall decrease and therefore risk would also be affected.