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?

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.

the answer is a. $209,000

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