You are considering in investing one of the two options: Investment A requires a $255,000 upfront payment from you and generates $21,000 revenue annually. Investment B requires an $175,000 upfront payment from you with annual gains of $29,000. After how many years would the total return from Investment A and B be equal?

a. 6
b. 8
c. 10
d. 12
e. Never

Option (E) Never

Explanation:

NPV from Investment Project 1 = ($255,000) + $21,000 / (r)

NPV from Investment Project 2 = ($175,000) + $29,000 / (r)

The question says that find the number of years that equals the total return which means the NPV from both investments is equal:

($255,000) + $21,000 / (r) = ($175,000) + $29,000 / (r)

$21,000 / (r) - $29,000 / (r) = $255,000 - $175,000

-$8000 / r = $80,000

r = - 8000 / 80000 = -0.01 = - 10%

The negative sign shows that project A can not make a positive NPV that will be equal to that of project B and vice versa. It can also be illustrated by putting the value of r in "NPV from Investment Project 1"

NPV from Investment Project 1 = ($255,000) + 21000 / -0.01

= ($255,000) - $210,000 = ($465,000)

This shows that the company will have to make losses of $465,000 which is not possible because company will not select projects with negative NPVs.

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