3. Ashley has patented her senior design project. She is offering a potential ma

Question

3. Ashley has patented her senior design project. She is offering a potential manufacturer two options for the exclusive rights to manufacture and market her product. Plan A calls for a 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 life of the patent is 10 years. What will be the uniform annual sales volume of the product for Ashley to be indifferent to the two plans based on future worth analysis for a MARR of 10% per year? (7,765 units) 3. Ashley has patented her senior design project. She is offering a potential manufacturer two options for the exclusive rights to manufacture and market her product. Plan A calls for a 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 life of the patent is 10 years. What will be the uniform annual sales volume of the product for Ashley to be indifferent to the two plans based on future worth analysis for a MARR of 10% per year? (7,765 units) 3. Ashley has patented her senior design project. She is offering a potential manufacturer two options for the exclusive rights to manufacture and market her product. Plan A calls for a 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 life of the patent is 10 years. What will be the uniform annual sales volume of the product for Ashley to be indifferent to the two plans based on future worth analysis for a MARR of 10% per year? (7,765 units)

Explanation / Answer

Future value of first option:

Here, Principal (P)= $30,000

Time(T)= 10 years

Number of time interest received in a year(n)= 1

Rate of interest(r)= 10%= 0.1

Now,

Amount(A)= P(1+r/n)nT

A= 30,000(1+0.1/1)1×10

A= 30,000(1.1)10

A= 30,000×2.5937424601

A=72812.273803

Future value of second option:

Let the annual sale volume be = X units

Here annual payment(P)= $1000+X0.5

Number of years(T)= 10

Rate of interest(r)= 10%=0.1

Therefore future value(FV)= P[ { (1+r)T-1}/r ]

FV = (1,000+ X0.5) [ { (1+0.1)10-1}/0.1 ]

FV= (1,000 + X0.5) [ { (1.1)10-1}/0.1 ]

FV= (1,000 +X0.5) { ( 2.5937424601-1)/0.1}

FV=(1,000+ X0.5)(1.5937424601/0.1)

FV= (1,000 + X0.5)(15.937424601)

Since Ashley is indifference between both options

Therefore the future worth of both options will be equal

Now, FV of second option = FV of first option

(1,000+X0.5)(15.937424601) = 72812.2738

(1,000+X0.5) = 72812.273803/15.937424601

X0.5 = 3882.3618464753

X = 3882.3618464753/0.5

X = 7,764.723 = 7,765 units

therefore the annual sale volume is 7,765 units

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