Question

Consider these two alternatives.

Alternative 1 Alternative 2

Capital investment ? $4400 ? $6400

Annual revenues ?$1450 ?$1950

Annual expenses ?$370 ?$510

Estimated market value ?$850 ? $1250

Useful life 9 years 12 years

a. Suppose that the capital investment of Alternative 1 is known with certainty. By how much would the estimate of capital investment for Alternative 2 have to vary so that the initial decision based on these data would be? reversed? The annual MARR is 18?% per year. b. Determine the life of Alternative 1 for which the AWs are equal.

Answer 1

Solution

Initial decision regarding the choice between two alternatives would depend upon the annual worth (AW) of the alternative 1 and 2.

AW =-Capital Investment( A/P,1%,N) - Annual Expenses

                                   + Annual Revenue Estimated MV ( A/P,1%,N)

If MARR = 18%, the annual worth of alternative 1(AW1 ) is:

AW1 =- 4,400(A/ P.,18%, 9) -$370+$1,450 + $850(A/F, 18%, 9)

           =-$4,400(0.2324) + $1080+ $850(0.0524)

           =-$1026+$1080+$45

           = $99

Similarly, the annual worth of alternative 2(AW2) is:

AW, = -$6,400 (ATP,18%, 10) – $510+$1,950+$1,250(ALF,18%, 10)

           =-$6,400 (O.2225) + $1,440 +$1,250 (0.0425)

           =-$1424 +$1440+ $53

          = $69

The annual worth of alternative 1(AW1) is greater than the annual worth of alternative 2(AW2) Thus, the initial decision is to choose Alternative 1

However, to determine such capital investment of Alternative 2 that the initial decision would be reversed. equate the annual worth of two alternatives. Assume the capital investment of alternative as I2,

AH1(18%) = AW2(18%)

$99 = -I1 (A/P, 18%, 10)- $510+ $1,950 +$1,250(A/F, 18%, 10)

I1 (0.2225) = -$510+ $1,950+$53-$99

I1 = $6,265

Hence, to reverse the initial decision the capital investment of Alternative 2 would have to be less than or equal to $6,265