Question

Nike has developed a prototype for a Nike-branded baseball that the firm plans to market to Major League baseball, college baseball, and high school baseball. They hope that the baseball is accepted as the new standard for most leagues, but the ball’s rate of market adoption is uncertain. In order to have the ball ready in 1 year, Nike would have to invest $50 million to set up contractual relationships with third-party contract manufacturers in China. The ball’s average total cost would be $0.50 and the selling price would be $1.50. Based on market surveys, Nike believes that there is a 25% chance of a high rate of adoption, in which 100 million balls will be sold annually forever, and a 75% chance of a low rate of adoption, in which 10 million balls will be sold annually forever. The adoption rate will be determined in one year when the first orders for the balls come in. The annual fixed costs associated with the project would be $30 million per year. Ignore tax effects and assume that Nike’s cost of capital is at 10% and the risk-free rate is 5%.

a) What is the NPV of the project based on the project’s expected future cash flows? Based on this measure, should Nike accept the project?
b) What is the embedded option in this project? Is the project worthwhile when considering the option?

Answer 1

a)

	Selling Price	1.50
	Cost Price	0.50
	Profit per unit	1.00
	Number of units	32.50	25%	100
	(in million)		75%	10
	Contribution	32.50	million
Less:	Fixed Cost	30.00	million
	Annual expected cash flow	2.50	million
	Cost of Capital	10%
	Therefore, Present Value of Cash Inflow (PVCI)	25.00
	Present Value of Cash Outflow (PVCO)	50.00
	Therefore, Net Present Value (NPV)		-25.00
	Since the NPV is highly negative, the project should not be accepted.

b)

	Risk neutral probability would be as follows:
p =	(1 + rf) * S - Sp
	So - Sp
Where,
	rf = Risk-free rate = 5%
	S = Overall PVCI = $25 mn
	Sp = Pessimistic PVCI = ($200) mn
	So = Optimistic PVCI = $700 mn
p =	(1+0.05) * 25 - (-200)	i.e.	25.14%
	700 - (-200)
1-p =			74.86%

	Therefore, the option value using the binomial model
C =	p * Co + (1-p) * Cp
	1 + r
Where,
	Cp = Pessimistic NPV = ($0) mn
	Co = Optimistic NPV = $650 mn
C =	0.2514 * 650 + 0.7486 * 0	i.e.	155.62
	1 + 0.05

Hence, considering the embedded option, the project is worthwhile.