I. Background.

Western Chipsets, Inc. is a medium$-$sized supplier of sophisticated electronic components $($chipsets$)$ used in telecom and Internet switching hardware. The firm$$s largest customers are Cisco Systems $($CSCO$),$ Lucent Technologies $($LU$),3$ComCorp $($COMS$),$ Nortel Networks $($NT$),$ and Tellabs, Inc. $($TLAB$).$

Western Chipsets$$ primary product is a chipset designed to combine voice and data signals in a highly efficient way and feed the resulting data stream into fiber optic cable networks.

While the market for this chipset is highly competitive, Western Chipsets has been able to experience higher$-$than$-$average operating margins primarily because of its sophisticated order$-$processing systems and extremely lean operations; the lag between customer orders and product shipments has been cut to an industry$-$leading $30$ days $($compared to the industry average of $65$ days$).$ As the result of this low lead time, Western Chipsets has been able to operate without any inventories.

Western Chipsets recently completed a move of its manufacturing operations to a new, state$-$of$-$the$-$art facility. The facility allows Western Chipsets to produce a maximum of $1,000,000$ of its chipsets per month.

II$.$ Results of $2002$ operations.

Western Chipsets

Audited Income Statement for Year Ended Dec$-31-2002$

Revenues $ $271,000,000$

CGS $143,000,000$

Gross margin $ $128,000,000$

G&A $($incl$.$ taxes$)23,000,000$

Net income $ $105,000,000$

$2002$ CGS Detail

Direct materials $-$ actual $ $32,000,000$

Direct labor $-$ actual $9,000,000$

Overhead $102,000,000$

Total CGS $ $143,000,000$

Chipsets manufactured and shipped $7,000,000$

Average unit cost $20\mathrm{.}43$

III. $2003$ Budgets $$ prepared in December $2002.$

$2003$ Revenue Budget

Estimated $2003$ production and sales $7,700,000$

Estimated $2003$ average selling price $ $36\mathrm{.}30$

Budgeted revenues $ $279,510,000$

$2003$ CGS Budget

Unit direct materials cost estimate $ $4\mathrm{.}50$

Unit direct labor cost estimate $1\mathrm{.}30$

Unit direct cost estimate $ $5\mathrm{.}80$

Estimate $2003$ production and sales $7,700,000$

Total direct cost estimate $ $44,660,000$

Budgeted $2003$ overhead $110,000,000$

$2003$ CGS Budget $ $154,660,000$

$2003$ Budgeted I$/$S

Revenues $ $279,510,000$

CGS $154,660,000$

Gross margin $ $124,850,000$

G&A $($incl$.$ taxes$)24,000,000$

Net income $ $100,850,000$

IV$.$ Management stock option compensation plan.

The management team of Western Chipsets has been historically well compensated. An important component of compensation, designed to retain talent and to force managers to behave as owners, has been a significant stock$-$option grant to managers. The grant of options has been tied to certain annual firmwide performance targets. These triggers were generally set to be achievable $$ the firm had met them every year through $2002.$

Based on the $2003$ budgets, the compensation committee of the Western Chipsets$$ board of directors set a stock option compensation plan for managers of the firm. The plan guaranteed substantial grants of in$-$the$-$money stock options to all levels of the management team as long as the firm$$s net income for $2003$ exceeds the $$100,000,000$ level.

V$.2003$ Preliminary results $$ prepared on December $3,2003.$

The top management team of Western Chipsets examined the firm$$s operations through the first $11$ months of $2003$ on December $3.$ The actual results and the estimates for December $2003$ are below.

The December estimates were prepared based on the number of firm orders received by the firm for delivery in the month of December. No further orders were anticipated.

The direct materials and direct labor costs were prepared based on the actual average unit DM and DL usage through November $($$$4\mathrm{.}47$ and $$1\mathrm{.}21,$ respectively$).$ These were expected to be essentially the same in December.

Finally, overhead and G&A amounts for December were prepared using all of the payments scheduled to be made for equipment leases, facility leases, taxes, and other G&A amounts. Western Chipsets could not postpone paying for any of these items. All overhead and G&A costs are fixed $$ they do not go up or down with the number of units, at least not in the short run.

$2003$

Results

Through Nov$-03$ Dec$-03$ Estimates

Total

Production and sales $7,290,000312,0007,602,000$

Average selling price $ $36\mathrm{.}00$ $ $36\mathrm{.}00$ $ $36\mathrm{.}00$

Revenues $ $262,440,000$ $ $11,232,000$ $ $273,672,000$

Direct materials usage $32,586,3001,394,64033,980,940$

Direct labor usage $8,820,900377,5209,198,420$

Direct costs $41,407,2001,772,16043,179,360$

Overhead $90,000,00019,000,000109,000,000$

CGS $131,407,20020,772,160152,179,360$

$2003$

Results

Through Dec$-03$

Nov$-03$ Estimates Total

Revenues $ $262,440,000$ $ $11,232,000$ $ $273,672,000$

CGS $131,407,20020,772,160152,179,360$

Gross margin $ $131,032,800$ $ $(9,540,160)$ $ $121,492,640$

G&A $($incl$.$ taxes$)19,000,0004,300,00023,300,000$

Net income $ $112,032,800$ $ $(13,840,160)$ $ $98,192,640$

$2.$ How many units must be produced and inventoried for Western Chipsets to exactly meet the $$100,000,000$ option trigger?