Question

If Machine A has a cash flow for 5 years of -$25000; $15,000; $18,000; $12,000; $6,000 and $5,000 and Machine B has a cash flow for 5 years of -$45000; $25,000; $28,000; $12,000; $16,000 and $15,000 what is the difference between their NPW’s if MARR is 12% p y c y?

For the above question, which machine should be selected based on Delta IRR if the MARR for a company making the decision is 15% p y c y?

Answer 1

The answer is attached below.

In case of IRR, i followed TRIAL AND ERROR method out of many methods which can be used to calculate IRR

If any doubts, please send me a comment before rating my answer. I will clarify

Thanks

NET PRESENT VALUE Machine A Machine B PV Calculation PV Calculation Cashflows Cashflows Present Value D A*C Year @ 12% PV Factor Present Value @ 12% PV Factor Year В C-B D-A*C В C-B A. A Year 0 $ $ 1.0000 $ 1 1.0000 $ Year 0 -25,000 -25,000 -45,000 1 -45,000 15,000 1/(1.12) 18,000 1/(1.12)2 12,000 1/(1.12)3 6,000 1/(1.12) 25,000 1/(1.12) 28,000 1/(1.12)2 12,000 1/(1.12)3 16,000 1/(1.12) 15,000 1/(1.12)5 Year 1 0.8929$ 0.8929$ $ Year 1 $ 13,393 22,321 0.7972 $ 0.7972 $ Year 2 $ 14,349 Year 2 22,321 0.7118$ 0.7118 $ $ $ Year 3 8,541 Year 3 8,541 0.6355 $ $ $ Year 4 Year 4 0.6355 S 3,813 10,168 0.5674 $ Year 5 0.5674 $ $ 5,000 1/(1.12)5 $ Year 5 2,837 8,511 $ $ Net Present Value Net Present Value 17,934 26,864 $ Net Present Value of Machine A 17,934 $ Net Present Value of Machine B 26,864 Whos is Better : Machine B has highest NPV . Hence it is better

INTERNAL RATE OF RETURN (USING TRIAL AND ERROR METHOD) Machine A Machine B PV Calculation @ 35% PV Calculation Cashflows Cashflows 35% PV Factor @ 35% PV Factor@ 35 Present Value Present Value Year Year Year 0 $ 1.0000 S $ 1.0000 $ -25,000 Year 0 1 -45,000 1 -25,000 -45,000 25,000 1/(1.35) 28,000 1/(1.35) 12,000 1/(1.35)3 16,000 1/(1.35)4 15,000 1/(1.35) 15,000 1/(1.35) 18,000 1/(1.35) 12,000 1/(1.35)3 6,000 1/(1.35)4 5,000 1/(1.35) 0.7407 $ $ $ Year 1 Year 1 0.7407 $ 11,111 18,519 0.5487 S 0.5487 $ $ Year 2 $ Year 2 9,877 15,364 0.4064 $ 0.4064 $ Year 3 $ $ 4,877 Year 3 4,877 0.3011 $ 0.3011 $ $ Year 4 Year 4 4,817 1,806 0.2230 $ 0.2230 $ $ $ 1,115 Year 5 Year 5 3,345 $ Net Present Value Net Present Value 3,786 1,922 Machine A Machine B PV Calculation @ 50% PV Calculation @ 50% Cashflows PV Factor@ 50% Present Value Cashflows Year PV Factor@ 50 Present Value Year -25,000 Year 0 $ 1.0000 $ $ 1.0000 $ Year 0 -45,000 1 -45,000 -25,000 1 25,000 1/(1.50) 28,000 1/(1.50) 12,000 1/(1.50)3 16,000 1/(1.50)4 15,000 1/(1.50)5 15,000 1/(1.50) 18,000 1/(1.50) 12,000 1/(1.50) 6,000 1/(1.50)4 0.6667 $ 0.6667 $ $ $ Year 1 10,000 Year 1 16,667 0.4444$ Year 2 $ 0.4444 $ Year 2 8,000 12,444 $ 0.2963 $ Year 3 $ 0.2963 $ Year 3 3,556 3,556 0.1975 $ 0.1975 S $ $ Year 4 Year 4 1,185 3,160 0.1317 $ 0.1317 $ $ 5,000 1/(1.50)s Year 5 Year 5 658 1,975 $ Net Present Value Net Present Value -7,198 -1,601

MACHINE A Beginning Result Working Calculation Change in percentage Change in price 15 35% 35% + ((15*3786)/5387)% 45.54% $ 5,387 $ 3,786 Change Needed NPV : 3786-(-1601) = 3786 Percentage 50%-35% MACHINE B Calculation Beginning Result Working Change in percentage Change in price 15 ? 35% ((15*1922)/9119) % 35% 38.16% $ 9,119 1,922 Change Needed 1922 NPV 1922-(-7198) 45.54% IRR of Machine A IRR of MachineB 38.16% Whos is Better : Machine A has highest IRR. Hence it is better The MARR of company is 15% whereas Machine A and Machine B both have IRR greter than 15%. Hence both machines are good