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, answer the following question: If Smyth Industries engages in predatory pricing by slashing its price 50 percent below marginal cost, the present value of current and future profits is:

First of all we need a discount rate, so I looked for similar questions and the discount rates went from 4% to 8%, so i decided to use 6%.

the company has 2 alternatives, keep operating in a competitive market or slash its prices to try to erase the competition.

the present value of the first alternative using the perpetuity formula = \$10,000,000 / 0.06 = \$166,666,667

the present value of the second alternative is:

PV of slashing costs = \$1,000,000,000 / 1.06 = \$943,396,226 + the present value of future net incomes

the present value of future net incomes = \$50,000,000 / 0.06 = \$833,333,333, but we must discount this number this terminal value applies to end of the current, not now: \$833,333,333 / 1.06 = \$786,163,552

the NPV of slashing prices = \$786,163,552 - \$943,396,226 = -\$157,232,674, so it is definitely a very bad idea.