Question

A) Let us suppose your company has the option to produce a component in-house for $20 per units, but they would have to invest in the machineries which costs $100000. Alternatively, they could buy it from a third party, which is charging $38 per unit. What is the minimum quantity of components to make the investment in the machinery worthwhile?

B) Let us suppose you could either produce tablets or phone the next quarter. Given a shortage in suppliers due to a natural disaster at a third world country where you normally source your components, you are unable to produce both. If the economy is good, you expect to sell 2000 units of the phone, which profits you $400 per unit, if the economy is bad, you expect to sell 500 units.

Alternatively, regardless of the economy, you expect to sell 1200 units of the tablet, profiting you $250 each unit.

At what probability of the economy being good, would you be indifferent between producing the two products.

Answer 1

(A) Suppose N is the units at which the two propositions are equal

Thus

20N+100000 =38N

18N = 100000 which gives N = 5555

Hence the company must produce at least 5555 units to break even and justify the investment.

(B) Suppose the probability is p ( the economy is good)

Then the payoff in two cases will be equal.

px 2000x400+ (1-p) x 500x400 = 1200x250

800000p -200000p + 200000 = 300000

600000p =100000

which gives p = 1/6 =0.1666

For any probability being more than 1/6, it will be better to produce phones.