Question

Grumpy Trucking manufactures trucks and currently produces all of the required parts for its trucks internally. Grumpy has received an offer from an external vendor to supply all of the axles for Grumpy’s trucks at a cost of $5,000 per axle. The following information relates to Grumpy’s axle production:

Production                                    2,000 axles

Variable costs                              4,000 per axle produced

Machine costs                             $1,000,000

Other fixed costs                         $500,000

(a) Machine costs represent rental payments for equipment used in axle production. If Grumpy accepts the external vendor’s offer, it could choose not to rent the machine. What is the maximum production volume at which Grumpy should accept the external vendor’s offer?

(b) Suppose that if Grumpy accepts the external vendor’s offer, it could retool its axle-producing factory to instead improve its trucks’ transmissions. Doing so would increase the selling price of each truck by $10,000 and the variable production cost of each truck by $6,000. Retooling costs would total $1,000,000. What is the maximum cost per axle that Grumpy should be willing to pay the external vendor if this retooling option is available? Assume there are two axles for each truck (i.e. axle production of 2,000 units corresponds to 1,000 units of truck production).

Answer 1

(a) 1000 Units of axles is the Maximum production volume at which grumpy should accept the external vendor's offer.

Explanation:

1000 units x $5000 per axle by vendor = $ 5,000,000 for external vendor

1000 units x$ 4000 variable cost own production = $ 4,000,000

+ Machinery cost for rental payment for equipment = $ 1,000,000

Total = $ 5,000,000 for own production.

other fixed cost of $500,000 is a sunk cost not relevant for decision making

(b) $6000 is the Maximum cost per axle that Grumpy should be willing to pay the external vendor if retooling option is available

Explanation:

Additional contribution per truck (Sales - variable cost )$10,000 - $6,000 = $4,000

Retooling costs = $ 1,000,000

Break even number of Trucks = Retooling costs / additional contribution $1,000,000 / $ 4,000 = 250 trucks

250 trucks x 2 axles for each truck = 500 axles

another 500 axles (1000 axles - 500 axles) will produce 250 trucks which yied contribution of $4000 extra per truck = $1,000,000

So, $1,000,000/ 1000 axles = $1,000 per axle extra can be offered

$5,000 + $1,000 = $6000 per axle