Question

Find the breakeven (Ai*) for the following projects (Incremental cash flow), Using interpolation. Note: Do not write the percentage sign (%) in the blank. Just write a number with two digits after decimal point like 18.32. А B -10.000 -60,000 First cost $ Annual operationg cost, $ Salvage value, $ -78,000 -65,000 6.000 11,000 Life year 3 6

Answer 1

Alternative A will be reinvested at EOY 3. We need to tabulate cash flows of both options and then find incremental Cash flow of B-A

Year	B	A	Cash Flow (B-A)
0	-60000	-10000	-60000-(-10000)=-50000
1	-65000	-78000	-78000-(-65000)=13000
2	-65000	-78000	-78000-(-65000)=13000
3	-65000	-78000-10000+6000=-82000	-82000-(-65000)=17000
4	-65000	-78000	78000-(-65000)=13000
5	-65000	-78000	78000-(-65000)=13000
6	-65000+11000=-54000	-78000+6000=-72000	-72000-(-54000)=18000

Let incremental IRR be i%, then

-50000 + 13000 * (P/A,i%,6) + 4000*(P/F,i%,3) + 5000*(P/F,i%,6) = 0

13000 * (P/A,i%,6) + 4000*(P/F,i%,3) + 5000*(P/F,i%,6) = 50000

Dividing by 1000

13* (P/A,i%,6) + 4*(P/F,i%,3) + 5*(P/F,i%,6) = 50

Using trail and error method

When i = 17%, value of 13* (P/A,i%,6) + 4*(P/F,i%,3) + 5*(P/F,i%,6) = 13*3.589185 + 4*0.624371 + 5*0.389839 = 51.106078

When i = 18%, value of 13* (P/A,i%,6) + 4*(P/F,i%,3) + 5*(P/F,i%,6) = 13*3.497603 + 4*0.608631 + 5*0.370432 = 49.755514

using interpolation

i = 17% + (51.106078-50) /(51.106078-49.755514)*(18%-17%)

i = 17% + 0.8189% = 17.8189% ~ 17.82%