Smyth Industries operated as a monopolist for the past several years,earning annual profits amounting to $50 million,which it could have maintained if Jones Incorporated did not enter the market.The result of this increased competition is lower prices and lower profits; Smyth Industries now earns $10 million annually.The managers of Smyth Industries are trying to devise a plan to drive Jones Incorporated out of the market so Smyth can regain its monopoly position (and profit).One of Smyth's managers suggests pricing its product 50 percent below marginal cost for exactly one year.The estimated impact of such a move is a loss of $1 billion.Ignoring antitrust concerns,compute the present value of Smyth Industries' profits if it remains a duopolist in this market when the interest rate is 5 percent.
A) $100 million
B) $200 million
C) $210 million
D) $1.05 billion

Question

Quizplus · Accepted Answer

If Smyth Industries decides to price its product 50% below marginal cost for one year, it will incur a loss of $1 billion. However, this strategy can potentially drive Jones Incorporated out of the market, allowing Smyth to regain its monopoly position and earn profits of $50 million annually.

To calculate the present value of Smyth's profits as a duopolist, we can use the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. In this case, n is assumed to be perpetual, since there is no specified end date.

Using this formula, we can calculate the present value of Smyth's profits as follows:

PV = $50 million / (1 + 0.05)^0 + $10 million / (1 + 0.05)^1 + $10 million / (1 + 0.05)^2 + $10 million / (1 + 0.05)^3 + ...

PV = $50 million + $9.52 million + $9.07 million + $8.63 million + ...

PV = $210 million (rounded to the nearest million)

Therefore, the present value of Smyth Industries' profits as a duopolist is $210 million, which is greater than the potential loss of $1 billion from the aggressive pricing strategy. Therefore, the best choice is C) $210 million.

Smyth Industries Operated as a Monopolist for the Past Several