For the data shown, what is the Delta IRR for the difference between the cash fl
ID: 2790710 • Letter: F
Question
For the data shown, what is the Delta IRR for the difference between the cash flows of the higher initial cost machine and the lower initial cost machine? The increase in costs and benefits trend does not change when a new machine is put into action (The cost keep rising at 4% every year and the benefits increase by 5% every year for the 12 year project life).
Around 17%
Around 23%
Around 37%
Around 41%
Machine A Machine B Initial cost $65,000 $17,500 Life in years 12 6 Salvage after life 20% 15% Benefits per year $34,000 $11,400 Costs per year $12,900 $6,800 Inflation 4% Increase in benefits 5%Explanation / Answer
Machine A Initial cost -65000 using formula for PV of growing annuity PV of costs -- (12900/(IRR-0.04))*(1-((1+0.04)/(1+IRR))^12) PV of benefits (34000/(IRR-0.05))*(1-((1+0.05)/(1+IRR))^12) PV of Salvage(PV of single sum) 65000*20%/((1+r)^12*(1.05)^12) Setting the above to 0, -65000-((12900/(r-0.04))*(1-((1+0.04)/(1+r))^12))+((34000/(r-0.05))*(1-((1+0.05)/(1+r))^12))+((65000*0.20)/((1+r)^12*(1.05)^12))=0 we get IRR as 36.67% Machine B Initial cost -17500 using formula for PV of growing annuity PV of costs (6800/(IRR-0.04))*(1-((1+0.04)/(1+IRR))^6) PV of benefits (11400/(IRR-0.05))*(1-((1+0.05)/(1+IRR))^6) PV of Salvage(PV of single sum) 17500*15%/((1+r)^6*(1.05)^6) -17500-(6800/(r-0.04))*(1-((1+0.04)/(1+r))^6)+(11400/(r-0.05))*(1-((1+0.05)/(1+r))^6)+((17500*0.15)/((1+r)^6*(1.05)^6)=0 we get IRR as 21.17% Difference in IRR =36.67-21.17= 15.5 ANSWER: Around 17% is nearer.