Question

The cash flows for two alternatives are shown. Determine which should be selected on the basis of an annual worth analysis at 10% per year interest. First Cost, $ Annual cost, $ per year Şalvage Value, $ Life, years 25,000 3000 1100 3 17000 3200 2100 Both A and B

Answer 1

AW of alternative A=AW1=-25000*(A/P,0.10,3)-3000+1100*(A/F,0.10,3)

Let us calculate the interest factors

(A/P,1,n) = 1 -

$(A/P,0.10,3)=\frac{0.10}{1-\frac{1}{(1+0.10)^{3}}}=0.402115$

$(A/F,i,n)=\frac{i}{(1+i)^{n}-1}$

0.10 (A/F, 0.10,3) = (1 +0.103 - 1 = 0.302115 (1 + 0.10) 3

So,

AW of alternative A=AW1=-25000*0.402115-3000+1100*0.302115=-$12720.55

Now take the case of alternative B

AW of alternative B=AW2=-17000*(A/P,0.10,5)-3200+2100*(A/F,0.10,5)

Let us calculate the interest factors

$(A/P,0.10,5)=\frac{0.10}{1-\frac{1}{(1+0.10)^{5}}}=0.263797$

$(A/F,0.10,5)=\frac{0.10}{(1+0.10)^{5}-1}=0.163797$

So,

AW of alternative B=AW2=-17000*0.263797-3200+2100*0.163797=-$7340.58

AW of costs is lower in case of alternative B. Alternative B should be selected.

So, correct option is

B