Question

The PW-based relation for the incremental cash flow series to find Δi* between the lower first-cost alternative X and alternative Y has been developed.

0 = -36,000 + 9000(P/A,Δi*,10) + ( -3000(P/F,Δi*,10))0 = -36,000 + 9000(P/A,Δi*,10) +  -3000(P/F,Δi*,10)

Determine the highest MARR value for which Y is preferred over X.

Any MARR value greater than  % favors Y.

Answer 1

Interest Rate will be 21.03%

Above which Y will be preffered over X

we have to see when the equation given becomes zero

step1

0=-36000+ 9000(1+i)^10 -1 / i(1+i)^10 +   -3000(1/1+i)^10)

Step2

Use Two 2 interest rate for interpolation i.e 22% and 21%

21%	22%
-36000+ 9000(1.21)^10 -1/0.21(1.21)^10+ (-3000(1/1.21)^10)	-36000+ 9000(1.22)^10-1/0.22(1.22)^10+ (-3000(1/1.22)^10)
=-36000 + 9000*(5.7275/1.4127) + (-3000*0.1486)	=-36000+9000*(6.3046/1.6070) + (-3000*0.1368)
=40.7691	-1102.04

Lets interpolate

Value is above 21% but below 22%

Difference of 22%-21% =1%

40.7691-(-1102.04)= =1142.809

40/1142.802

=0.035

Hence I= 21+0.035

=21.03%

I hope the answer and steps are clear any query you may ask I will reply. Kindly upvote it helps me.Good Luck