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 $12,250 $7,000 EUAC (12%), approx. $14,867 $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

Let the annual expenses in alternative I be 'X' for both investment to be equally attractive.
For both investment to be equally attractive, EUAC for I must be equal to EUAC for II.

Thus, EUAC I = EUAC II
EUAC I = 10000 * (A/P, 12%, 5) + X - 1000 * (A/F, 12%, 5)
where

(A/P, 12%, 5)   = 0.2774

(A/F, 12%, 5) = 0.1574

Putting values and equating with EUAC II ,

10000 * (0.2774) + X - 1000 * (0.1574) = 13800

2774 + X - 157.4 = 13800
Solving,

X = $ 11183.4

% change in annual expenses = ((Final expense - initial expense ) * 100 )/ ( initial expense) = (( 11183.4 -12250) *100) / (12250) = - 8.788 %


Answer : - 8.788