Question

Book: Fundamentals of Economic Engineering Analysis. Chapter: 11 Question: 6

A manufacturer offers an inventor the choice of two contracts for the exclusive right to manufacture and market the investor's patented design. Plan 1 calls for an immediate single payment of $50,000. Plan 2 calls for an annual payment of $2,000 plus royalty of $1.00 for each unit sold. The remaining life of the patent is 10 years. MARR is 10% per year.

a. What must be the uniform annual sales to make Plan 1 and Plan 2 equally attractive?

b. If fewer than the number of (Part a) are scheduled for production and sales, which plan is more attractive?

*Please use Excel & not factor notion to provide the answer*

(Answer for Part A is: 6,137 but I cannot figure out how to get the answer).

Answer 1

We have the following information

Plan 1: An immediate single payment of $50,000

Annual worth of Plan 1 = 50,000(A/P, i, n)

Annual worth of Plan 1 = 50,000(A/P, 10%, 10)

(A/P, 10%, 10) = [0.1 (1 + 0.1)¹⁰/((1 + 0.1)¹⁰ – 1)] (This formula can be inserted in Excel to get the result)

Annual worth of Plan 1 = 50,000[0.1 (1 + 0.1)¹⁰/((1 + 0.1)¹⁰ – 1)]

Annual worth of Plan 1 = 50,000 × 0.163

Annual worth of Plan 1 = $8,137.

Plan 2: An annual payment of $2,000 plus royalty of $1.00 for each unit sold.

Annual worth of Plan 2 = $2,000 + ($1.00 × Q)

Where Q is annual sales

Now, we have to find out the uniform annual sales to make Plan 1 and Plan 2 equally attractive.

Annual worth of Plan 1 = Annual worth of Plan 2

8,137 = 2,000 + Q

Q = 6,137.

If the fewer than 6,137 annual quantities are scheduled for production and sales, then Plan 1 is more attractive as its annual worth is higher.