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 = -30,000 + 9000(P/A,Δi*,10) + ( -5000(P/F,Δi*,10))0 = -30,000 + 9000(P/A,Δi*,10) +  -5000(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

Incremental cahs flow (Y-X) = -30,000 + 9000(P/A,Δi*,10) + ( -5000(P/F,Δi*,10))

To find i%, then

-30,000 + 9000(P/A,Δi*,10) + ( -5000(P/F,Δi*,10)) = 0

-30,000 + 9000(P/A,Δi*,10) -5000(P/F,Δi*,10) = 0

9000(P/A,Δi*,10) -5000(P/F,Δi*,10) = 30000

Dividing by 1000

9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 30

Using trail and error method

When i = 10%, value of 9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 53.37339

When i = 15%, value of 9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 43.93299

When i = 20%, value of 9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 36.92472

When i = 25%, value of 9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 31.59766

When i = 26%, value of 9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 30.68750

When i = 27%, value of 9*(P/A,Δi*,10) - 5 *(P/F,Δi*,10) = 29.82146

using interpolation

i = 26% + (30.68750 - 30) / (30.68750 - 29.82146) *(27%-26%)

i = 26% + 0.79385%

i = 26.79385%

i = 26.79%