Question

Mr. Gold is in the widget business. He currently sells 1.2 million widgets a year at $5 each. His variable cost to produce the widgets is $3 per unit, and he has $1,740,000 in fixed costs. His sales-to-assets ratio is five times, and 20 percent of his assets are financed with 10 percent debt, with the balance financed by common stock at $10 par value per share. The tax rate is 40 percent.
  
His brother-in-law, Mr. Silverman, says Mr. Gold is doing it all wrong. By reducing his price to $4.50 a widget, he could increase his volume of units sold by 40 percent. Fixed costs would remain constant, and variable costs would remain $3 per unit. His sales-to-assets ratio would be 6.3 times. Furthermore, he could increase his debt-to-assets ratio to 50 percent, with the balance in common stock. It is assumed that the interest rate would go up by 1 percent and the price of stock would remain constant.

a. Compute earnings per share under the Gold plan. (Round your answer to 2 decimal places.)
  

b. Compute earnings per share under the Silverman plan. (Round your answer to 2 decimal places.)
  

c. Mr. Gold’s wife, the chief financial officer, does not think that fixed costs would remain constant under the Silverman plan but that they would go up by 20 percent. If this is the case, should Mr. Gold shift to the Silverman plan, based on earnings per share?

Answer 1

a) Given sales = 1.2 Million units

Sale price =$5

Hence total sales= 1.2 Million units *$5 =$6 Million or $6,000,000

Given sales to asset ratio = 5 times

Hence Sales/ Total Asset= 5

$6000000/ Total assets = 5

Total assets = $6000000/5 = $1200000

Give 20% of assets is financed by Debt hence Debt - 20% of 1200000= 240000

Assets financed by equity = 80% of 1200000=960000

Given face value of equity = $10

Hence number of shares = Total Equity capital/ Face value of equity

=960000/10

=96000 Shares

Income statement is given by-

	Sales	6000000	(1.2 Million *$5)
Less	Variable cost	3600000	(1.2 Million *$3)
	Gross margin	2400000
Less	Fixed cost	1740000
	EBIT	660000
Less	Interest	24000	(Debt capital * interest rate)
	EBT	636000
Less	Tax	254400	(40% of EBT)
	PAT	381600
	Number of shares	96000
	Earning per share	3.98	(PAT/ Number of shares)

b) Given sales = 1.2 Million units*(1+40%)= 1,680,000 units

Sale price =$4.5

Hence total sales= 1.68 Million units *$4.5 =$7.56 Million or $7,560,000

Given sales to asset ratio = 6.3 times

Hence Sales/ Total Asset= 6.3

$7560000/ Total assets = 6.3

Total assets = $7560000/6.3 = $1200000

Given 50% of assets is financed by Debt hence Debt - 50% of 1200000= 600000 at 11% interest rate(10+1)%

Assets financed by equity = 50% of 1200000=600000

Given face value of equity = $10

Hence number of shares = Total Equity capital/ Face value of equity

=600000/10= 60000 equity shares

Income statement is given by-

	Sales	7560000	(1.68 Million *$4.5)
Less	Variable cost	5040000	(1.68 Million *$3)
	Gross margin	2520000
Less	Fixed cost	1740000
	EBIT	780000
Less	Interest	66000	(Debt capital * interest rate)
	EBT	714000
Less	Tax	285600	(40% of EBT)
	PAT	428400
	Number of shares	60000
	Earning per share	7.14	(PAT/ Number of shares)

c)

Fixed cost = 1740000*(1+20%)= 2088000

Income statement is given by

	Sales	7560000	(1.68 Million *$4.5)
Less	Variable cost	5040000	(1.68 Million *$3)
	Gross margin	2520000
Less	Fixed cost	2088000
	EBIT	432000
Less	Interest	66000	(Debt capital * interest rate)
	EBT	366000
Less	Tax	146400	(40% of EBT)
	PAT	219600
	Number of shares	60000
	Earning per share	3.66	(PAT/ Number of shares)

Since the earning per share goes down from 3.98/ Share to 3.66/ share hence the plan of Gold is more profitable from earning per share point of view as compared to Silverman's Plan after considering CFO assumption

Hence Mr gold should not shift to Silverman's plan