Question

Nadine Chelesvig has patented her invention. She is offering a patent manufacturer two contracts for the exclusive right to manufacture and market her product. Plan A calls for an immediate single lump payment to her of $32,000. Plan B calls for an annual payment of $1,200 plus a royalty of $0.50 per unit sold. The remaining life of the patent is 10 years. Nadine uses a MARR of 9 %/year.

Required:
a. What must be the uniform annual sales volume of the product for Nadine to be indifferent between the contracts, based on a present worth analysis?
b. If the sales volume is below the volume determined in (a), which contract would the manufacturer prefer?

Answer 1

Nadine Chelesvig

a. The uniform annual sales volume of the product for Nadine to be indifferent between the contracts, based on a present worth analysis is:

= 7,572 units

b. If the sales volume is below the volume determined in (a), the manufacturer would prefer Contract A to B.

Step-by-step explanation:

a) Data and Calculations:

Plan A present value = $32,000 (because it is an immediate single lump payment)

Plan B annual payment = $1,200 plus a royalty of $0.50 per unit sold

The useful life of the patent = 10 years

MARR = 9%

Present value annuity factor for 10 years at 9% = 6.418

Therefore, Plan A's equivalent annual payment = $32,000/6.418 = $4,986

For Nadine to be indifferent between Plan A and Plan B, the present value of Plan B annual payment = Plan A equivalent annual payment

That is, $1,200 + $0.50x = $4,986, where x = units sold

Solving the above equation, $0.50x = $4,986 -$1,200

= $0.50x = $3,786

x = $3,786/$0.50

x = 7,572 units