A corporation is trying to decide whether to buy the patent for a product design

Question

A corporation is trying to decide whether to buy the patent for a product designed by another company. The decision to buy will require an investment of $8 million, and the demand for the product is not known. If demand is light, the company expects a return of $1.3 million each year for three years. If the demand is moderate, the return will be $2.5 million each year for four years, and a high demand will mean a return of $4 million each year for four years. It is estimated that the probability of a high demand is 0.4 and the probability of a light demand is 0.2. The firm's interest rate (risk free) is 12%. Calculate the expected present worth of the investment. On this basis, should the company make the investment? (All figures represent after-tax values.)

Explanation / Answer

NPV for light demand:
=> -$8,000,000 + {[$1,300,000] x [1-(1+0.12)-3]/0.12} = -$4,877,619.35

NPV for moderate demand:
=> -$8,000,000 + {[$2,500,000] x [1-(1+0.12)-4]/0.12} = -$406,626.63

NPV for high demand:
=> -$8,000,000 + {[$4,000,000] x [1-(1+0.12)-4]/0.12} = $4,149,397.38

Present worth of project:
=> (-$4,877,619.35 x 0.2) + (-$406,626.63 x 0.4) + ($4,149,397.38 x 0.4) = $521,584.43

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