Question

Nadine Chelesvig has patented her invention. She is offering a potential manufacturer two contracts for the exclusive right to manufacture and market her product. Plan A calls for an immediate single lump sum payment to her of $30,000. Plan B calls for an annual payment of $1,000 plus a royalty of $0.50 per unit sold. The remaining life of the patent is 10 years. Nadine uses a MARR of 10 percent/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

Answer 1

Answer:

The uniform annual sales volume of the product for Nadine to be indifferent between the contracts is 7,772 units per year.

Explanation:

We have to compare the present-value of both plans to answer this question.

The Plan A has a present value of $30,000 as is an inmediate payment.

The Plan B has both an annual payment and a royalty, for a span of ten years.

The present value for Plan B is:

$PV_b=\sum_{i=1}^{10}(1000+0.50q)/(1+i)^i$

This can be simplified with a annuity factor for 10 years, with i=10%.

$A_{10}=\frac{1-(1+i)^{-10}}{i}= \frac{1-1.1^{-10}}{0.10}\\\\A_{10}=\frac{1-0.386}{0.10}=\frac{0.614}{0.10}=6.14$

Then, the PV can be calculated as:

$PV_b=6.14(1,000+0.50q)\\\\PV_b=6,140+3.07q$

To be indifferent, both present values have to be equal:

$PV_b=PV_a\\\\6,140+3.07q=30,000\\\\q=(30,000-6,140)/3.07=23,860/3.07=7,772$

The uniform annual sales volume of the product for Nadine to be indifferent between the contracts is 7,772 units per year.