Question $2-$ CVP analysis and decision making

$(25$ marks$)$

K&L$,$ a newly established company, manufactures and sells two products called Kappa and Lambda. The following data is obtained for tackling various decision contexts:

Per unit selling price

Per unit costs and expenses:

Direct materials

Direct labor

Variable manufacturing overhead

Variable selling expenses

Kappa

Lambda

$$120$

$$100$

$$36$

$$28$

$14$

$18$

$12$

$14$

$7$

$10$

Common fixed costs total $$1,000,000$ per quarter.

$($ii$)$ Sales for the quarter is budgeted at $$3,000,000.$

$($iii$)$ The units produced and sold of Kappa and Lambda are budgeted at $20,000$ units and $6,000$ units per quarter respectively. Required:

$($a$)$ Compute the following for K&L:

$(1)$ the overall contribution margin

$(2)$ the overall break$-$even point in dollar sales.

$(3)$ the margin of safety in percentage.

$($b$)$ The material requirements of Kappa and Lambda are provided as below:

Kappa

Lambda

Materials per unit

$6$ grams

$5$ grams

$(3$ marks$)$

$(3$ marks$)$

$(3$ marks$)$

Due to shortage of materials, the raw materials available for production is limited to $130,000$ grams in the next quarter. The material cost is $$6$ per gram.

$(1)$ Which products would you advise K&L to produce first?

$(5$ marks$)$

$(2)$ How would you allocate the constrained materials to Kappa and Lambda? $(3)$ What is the maximum price that K&L is willing to pay for each gram of additional materials?

$(4$ marks$)$

$(3$ marks$)$

$($c$)$ Refer to the original data. K&L is thinking about discontinuing the product line of Lambda. The common fixed processing costs of $$1,000,000$ will be reallocated to Kappa. The idle facilities can be used to produce $2,000$ units of Kappa to meet the increased demand.

$(1)$ Should the product line of Lambda be discontinued? Show all necessary calculations.

$(4$ marks$)$