Question

Wired Communications Corporation (WCC) supplies headphones to airlines for use with movie and stereo programs. The headphones sell for $288 per set, and this year’s sales are expected to be 45,000 units. Variable production costs for the expected sales under current production methods are estimated at $10,200,000, and fixed (operating) costs are currently $1,560,000. WCC has $4,800,000 of debt outstanding at an interest rate of 8%. There are 240,000 shares of common stock outstanding, and there is no preferred stock. WCC pays out 70% of earnings and is in the 40% marginal tax bracket. The company is considering investing $7,200,000 in new equipment. Sales would not increase, but variable costs per unit decline by 20%. Also fixed operating costs would increase to $1,800,000. WCC could raise the required capital by borrowing $7,200,000 at 10% or by selling 240,000 additional shares at $30 per share.

a. What would be WCC’s EPS (1) under the old production process (2) under the new process if it uses debt, and (3) under the new process if it uses common stock financing?

b. Calculate the DOL, DFL and DTL under the existing setup and under the new setup with each type of financing. Assume that the expected sales level 45,000 units or $12,960,000.

c. At what unit sales level would WCC have the same EPS, assuming it undertakes the investment and finances with debt or with stock?

d. At what unit sales level would EPS=0 under the three production/financing setupsthat is under the old plan, the new plan with debt financing and the new plan with stock financing? )

e. On the basis of the analysis in parts a through c, which plan is the riskiest, which has the highest expected EPS, and which would you recommend? Assume here that there is fairly high probability of sales falling as low as 25,000 units, and determine EPS under debt and stock financing options at 25,000 units of sales level to help assess the riskiness of the two financing plans.

Answer 1

a) The EPS calculation under all the three scenarios is as shown below

	Old Process	New with Debt	New With Equity
Debt	4800000 at 8%	4800000 at 8%+ 7200000 at 10%	4800000 at 8%
No. of shares	240000	240000	240000+240000=480000
No of Units	45000	45000	45000
Sales	12960000	12960000	12960000
Variable Cost	10200000	8160000	8160000
Fixed Cost	1560000	1560000	1560000
EBIT	1200000	3240000	3240000
Interest	384000	1104000	384000
EBT	816000	2136000	2856000
Tax	326400	854400	1142400
PAT	489600	1281600	1713600
EPS	2.04	5.34	3.57

The EPS under old process, new process with Debt and new process with stock will be $2.04/ share. $5.34/share and $3.57/share respectively

b) The formulas are

Degree of operating Leverage (DOL) = (Sales – Variable Cost) / (Sales – Variable Cost – Fixed Cost)

Degree of Financial leverage (DFL) =EBIT/EBT

and  Degree of Total Leverage (DTL) =DOL*DFL

So, DOL, DFL and DTL for all three cases are as shown in table below :

	Old Process	New with Debt	New With Equity
DOL	2.30	1.48	1.48
DFL	1.47	1.52	1.13
DTL	3.38	2.25	1.68

c) For same EPS, the EBIT level is given by

(EBIT-I1)*(1-tax rate)/N1 = (EBIT-I2)*(1-tax rate)/N2

where I1 and I2 are the interest amounts paid in the two cases and N1 and N2 are the no of shares outstanding in the two cases.

So, (EBIT -1104000) /240000 = (EBIT -384000)/480000

(1-tax rate) factor is common and hence removed

=> EBIT = 2*1104000 - 384000 = $1824000

So, unit sales = (1824000+1560000+8160000)/288 = 40083.33

So, when no of units sold is 40083 apx, the EPS would be same

d) For EPS =0, PAT should be 0 and hence EBT should also be 0

This happens when EBIT =I

or (Sales - VC-FC) = I or Sales =VC+FC+I

For Old process, Sales = 10200000+1560000+384000 = $12144000

No of units = 12144000/288 = 42166.67 or 42167 units

For New process with Debt, Sales = 8160000+1560000+11044000 = $10824000

No of units = 10824000/288 = 37583.33 or 37583 units

For New process with Common stock, Sales = 8160000+1560000+384000 = $10104000

No of units = 10104000/288 = 35083.33 or 35083 units

e) The old process has the highest DTL and is the most riskiest.

The new process with Debt has the highest possible EPS

If no of units fall to 25000 , EPS calculation is as shown

	Old Process	New with Debt	New With Equity
Debt	4800000 at 8%	4800000 at 8%+ 7200000 at 10%	4800000 at 8%
No. of shares	240000	240000	240000+240000=480000
No of Units	25000	25000	25000
Revenue	7200000	7200000	7200000
Variable Cost	10200000	8160000	8160000
Fixed Cost	1560000	1560000	1560000
EBIT	-4560000	-2520000	-2520000
Interest	384000	1104000	384000
EBT	-4944000	-3624000	-2904000
Tax	-1977600	-1449600	-1161600
PAT	-2966400	-2174400	-1742400
EPS	-12.36	-9.06	-3.63

New process with Common stock has the best EPS (least negative) and is recommended.