Question

"A corporation is trying to decide whether to buy the patent for a product designed by another company. The decision to buy will mean an investment of $7 million, and the demand for the product is not known. If demand is light, the company expects a return of $1.65 million each year for the first three years and no return in the fourth year. If demand is moderate, the return will be $3.27 million each year for four years, and high demand means a return of $4.42 million each year for four years. It is estimated the probability of a high demand is 0.54, and the probability of a light demand is 0.19. The firm's interest rate is 14.5%.
Calculate the expected present worth of the patent. Express your answer in millions of dollars. For example, if the answer is $12.3 million, enter 12.3. (All figures represent after-tax values.)"

Answer 1

Let L, M, H be the events of light, moderate and high demand

pL = 0.19, pH = 0.54, pM = 1 - 0.19 - 0.54 = 0.27.

interest rate is ,r =14.5

return if demand is light: R = 1.65(1+ r)^4 + 1.65(1+r)^3 + 1.65(1+r)^2 = 2.84+2.48+2.16 = 6.48

return if demand is moderate: R = 3.27(1+ r)^4 + 3.27(1+r)^3 + 3.27(1+r)^2 + 3.27(1+r)= 5.62+4.91+4.29+3.74=18.56

return if demand is high: R = 4.42(1+ r)^4 + 4.42(1+r)^3 + 4.42(1+r)^2 + 4.42(1+r)= 7.6+6.63+5.79+5.06=25.08

Expected returns = 0.19*6.48+0.27*18.56+0.54*25.08 = 19.7856

Expected net worth = 19.7856-7 = 12.7856