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 $35,000. Plan B calls for an annual payment of $1,200 plus a royalty of $0.40 per unit sold. The remaining life of the patent is 10 years. Nadine uses a MARR of 7 %/year.
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

Answer:

A) 9458 units

B) She would prefer the one with the single lump payment of $35,000 because the present value of the other one would increase with an increase in the units sold.

Explanation:

A) To calculate the uniform annual sales volume based on a present worth analysis, we will make use of the formula for present value of annuity.

Thus;

P = PMT × (1 - ((1/(1 - rⁿ))/r

From the question, we are given;

P = $35,000

PMT = (1200 + 0.4x)

r = 7% = 0.07

n = 10

Thus, Plugging in the relevant values, we have;

(1200 + 0.4x)((1 - (1/(1 + 0.07)^10))/0.07 = 35000

This gives;

(1200 + 0.4x) × 7.0236 = 35000

(1200 + 0.4x) = 35000/7.0236

(1200 + 0.4x) = 4983.2

0.4x = 4983.2 - 1200

0.4x = 3783.2

x = 3783.2/0.4

x = 9458 units

B) She would prefer the one with the single lump payment of $35,000 because the present value of the other one would increase with an increase in the units sold.