Respuesta :
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:
[tex]PV_b=\sum_{i=1}^{10}(1000+0.50q)/(1+i)^i[/tex]
This can be simplified with a annuity factor for 10 years, with i=10%.
[tex]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[/tex]
Then, the PV can be calculated as:
[tex]PV_b=6.14(1,000+0.50q)\\\\PV_b=6,140+3.07q[/tex]
To be indifferent, both present values have to be equal:
[tex]PV_b=PV_a\\\\6,140+3.07q=30,000\\\\q=(30,000-6,140)/3.07=23,860/3.07=7,772[/tex]
The uniform annual sales volume of the product for Nadine to be indifferent between the contracts is 7,772 units per year.
It is assumed that the individual proposes these two contracts to a potential manufacturer. Each patent is valid for 10 years.
MARR= [tex]\frac{10\%}{year}.[/tex]
For Plan A:
The instant lump-sum payment= [tex]\$30,000[/tex]
calculating the annual worth for plan A:
[tex]\to AW = payment(\frac{A}{P},i,n)[/tex]
[tex]= 30,000(\frac{A}{P}, 10\%,10) \\\\= 30,000(0.1627)\\\\ =\$ 4881\\\\[/tex]
For plan B:
When the annual payment= [tex]\$1000[/tex] with the royalty of [tex]\$0.50[/tex] /sold unit.
Q= sold quantity number
[tex]\text{AW = annual payment} + \text{royalty} \times Q \=1000+0.50 Q\\\\[/tex]
Calculating the annual worth of 2.
[tex]\to AW (Plan\ A) = AW (Plan\ B)\\\\ \to 4881 = 1000+0.50 Q\\\\ \to 4881 - 1000=0.50 Q\\\\ \to 3881 = 0.50 Q\\\\\to Q=\frac{3881}{0.50}\\\\\to Q=7762\\[/tex]
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