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 $9.9 million, and the demand for the product is not known. If demand is light, the company expects a return of $2.35 million each year for the first three years and no return in the fourth year. If demand is moderate, the return will be $3.73 million each year for four years, and high demand means a return of $4.55 million each year for four years. It is estimated the probability of a high demand is 0.51, and the probability of a light demand is 0.17. The firm's interest rate is 15.7%.
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

Answer is $10.79 million.

• It has been given that the probability for light demand is 17% while for High demand is 51%. Rest of the probability is for Moderate demand. Probability for Moderate demand will be 100%- 17%- 51%= 32%
• Since there is probability for every scenario of demand, we will have to multiply the savings expected per year with the probability and add all the scenarios to reach on the best estimate of cash inflows.

		Inflows as per question					Inflows multiplied with Probability
Demand	Probability	Yr 1	Yr 2	Yr 3	Yr 4		Yr 1	Yr 2	Yr 3	Yr 4
Light	17%	2.35	2.35	2.35			0.40	0.40	0.40	0.00
Moderate	32%	3.73	3.73	3.73	3.73		1.19	1.19	1.19	1.19
High	51%	4.55	4.55	4.55	4.55		2.32	2.32	2.32	2.32
Total							3.91	3.91	3.91	3.51

Demand in Millions for year 1 to year 4 will be calculated as above

• Since Interest rate is 15.7%, we will have to compute present value of $1 at 15.7% interest rate being compounded annually for Year 1-4.

Present value factor

0.8643

0.7470

0.6457

0.5580

Let’s multiply PVF with the inflows we computed above

Yr 1	Yr 2	Yr 3	Yr 4
3.3825	2.9235	2.5268	1.9610

Present Worth for patent is equal to present value for future cash flows. If we total the present values for Year 1 to Year 4, we reach at the total present value for $10.79 million.