BWP projects sales of 100,000 units next year at an average price of $50 per uni

Question

BWP projects sales of 100,000 units next year at an average price of $50 per unit. Variable costs are estimated at 40% of revenue, and fixed costs will be $2.4 million. BWP has $1 million in bonds outstanding on which it pays 7.5%, and its marginal tax rate is 39%. There are 100,000 shares of stock outstanding which trade at their book value of $30.

BWP intends to purchase a machine that will result in a major improvement in product quality along with a small increase in manufacturing efficiency. The machine will cost $1 million, which will be borrowed at 9%. The quality improvement is expected to have a significant impact on BWP's competitive position. Indeed, management expects sales to increase by 5% in spite of a planned 10% price increase. The efficiency improvement combined with the price increase will result in variable costs of 36% of revenue. Fixed cost, however, will rise by 19%. Calculate BWP's DFL and DTL before and after the acquisition of the new machine. Round your answers to two decimal places.

Explanation / Answer

DFL, which means Degree of Financial Leverage, indicates the benefit on Return on Equity % and EPS caused due to increase in Debt-Equity ratio of a business. The concept is also known as Trading on Equity...

DFL formula= [% Change in EPS / % Change in EBIT] .............................................. [A]

Also, DFL= EBIT / [(EBIT) - Interest expenses] .......................................... [B]

EBIT of business without new machine purchase= Total Yearly Revenue - Total Variable Costs - Total Fixed Costs= [1,00,000 units* $50 per unit] - 40% of [1,00,000 units* $50 per unit] -$24,00,000= $50,00,000 - 40% of $50,00,000 - $24,00,000 = $50,00,000 - $20,00,000 - $24,00,000 = $6,00,000 ........................... [I]

EPS of business without new machine purchase= (EBIT - Interest Expense - Corporate Taxation) / Total number of outstanding equity shares = ($6,00,000 - (0.075 * $10,00,000) - 39% of Taxable Corporate Income) / 1,00,000 equity shares= ($6,00,000 - $75,000 - 0.39 of Taxable Corporate Income) / 1,00,000 equity shares= ($5,25,000 - 0.39 of $5,25,000) / 1,00,000 equity shares= $3,20,250 / 1,00,000 equity shares= $3.20 per equity share

DFL of business without new machine purchase as per formula [B]= $6,00,000/ ($6,00,000- $75,000)= 1.143

EBIT of business with new machine purchase = New projected total yearly revenue - New projected total variable costs - New projected total fixed costs= (1,00,000 units*1.05* $50 per unit *1.10) - 36% of New projected total yearly revenue - New projected total fixed costs = (1,05,000 units * $55 per unit) - 36% of New projected total yearly revenue - New projected total fixed costs= $57,75,000 - 36% of $57,75,000 - ($24,00,000 + ($24,00,000*19%)) = $57,75,000 - $20,79,000 - ($24,00,000 + $4,56,000)= $8,40,000 ..................... [II]

EPS of business with new machine purchase=($8,40,000 - Interest Expenses - Corporate Taxatio)/ 1,00,000 equity shares= ($8,40,000 - (0.075*$10,00,000) - (0.09*$10,00,000)- 39% of Taxable Corporate Income) / 1,00,000 equity shares = ($8,40,000 - $75,000 - $90,000 - 0.39 of taxable corporate income) / 1,00,000 equity shares = ($6,75,000 - (0.39*$6,75,000)) / 1,00,000 equity shares= ($6,75,000- $2,63,250) / 1,00,000 equity shares= $4,11,750 / 1,00,000 equity shares= $4.12 per equity share

As per formula [B], DFL after new machine purchase= $8,40,000 / ($8,40,000 - $75,000 - $90,000) = 1.244

Applying the above results of EBIT and EPS in formula [A], We get:

DFL= [($4.12 - $3.20) / $3.20] / [($8,40,000-$6,00,000) / $6,00,000] = [0.92/3.20] / [2,40,000/6,00,000] =

28.75% / 40.00% = 28.75 / 40.00 = 0.71875 ........................... [This is the ANSWER for effect of increase in DFL after new machine purchase on EPS of business; the answer of 0.71875 indicates that the EPS has increased less than proportionately as compared to increase in EBIT after additional borrowing @ 9% p.a. for purchase of new machinery]

RoCE= $8,40,000 / ($30,00,000 + $10,00,000 + $10,00,000)= $8,40,000 / ($50,00,000)= 0.168= 16.80%

The company stands to benefit in the said case of increase in DFL because its average Debt Cost rate of 8.25% p.a. [i.e. average of 7.50% p.a. + 9.00% p.a.] is lesser than its RoCE [Return on Capital Employed] of 16.80%

Note: In the given problem, the Depreciation rates on existing machineries of business and on new machinery are not given; hence Net Profit and EBIT figures are worked out without deducting Depreciation expenses.

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