Question

Consider the following two investment alternatives, in which Alternative II is more economically attractive than Alternative I:

                                                        Alternative I                Alternative II

            Initial Investment                    $10,000                       $40,000

            Useful life                               5 years                         10 years

            Terminal market value            $1,000                         $5,000

            Annual expenses                     $20,000                             $7,000

            EUAC (12%), approx.            $22,617                         $13,800

Determine the percent change in the annual expenses for Alternative I that would make the two investments equally attractive. (Enter your answer as a positive or negative number without the percent % sign.)

Answer 1

ANSWER:

Let the annual expenses of alternative 1 be x.

i = 12% and n = 5 years

aw of alternative 1 = initial investment(a/p,i,n) + annual expenses + market value(a/f,i,n)

aw of alternative 1 = -10,000(a/p,12%,5) + x + 1,000(a/f,12%,5)

aw of alternative 1 = -10,000 * 0.2774 + x + 1,000 * 0.1574

aw of alternative 1 = - 2,774 + x + 157.4

aw of alternative 1 = - 2,616.6 + x

i = 12% and n = 10 years

aw of alternative 2 = initial investment(a/p,i,n) + annual expenses + market value(a/f,i,n)

aw of alternative 2 = -40,000(a/p,12%,10) - 7,000 + 5,000(a/f,12%,10)

aw of alternative 2 = -40,000 * 0.177 - 7,000 + 5,000 * 0.057

aw of alternative 2 = - 7,080 - 7,000 + 285

aw of alternative 2 = - 13,795

aw of alternative 1 = aw of alternative 2

-2,616 + x = -13,795

x = -13,795 + 2,616.6

x = - 11,178.4

change in percent in annual expense = ( ( annual expenses earlier - annual expenses now) / annual expenses earlier) * 100

change in percent in annual expense = ( ( 20,000 - 11,178.4 ) / 20000) * 100

change in percent in annual expense = ( 8,821.6 / 20,000) * 100

change in percent in annual expense = 0.44108 * 100

change in percent in annual expense = 44.108%

so the change in percent in annual expenses for alternative 1 is 44.1% to make the two alternatives equally attractive.