Question

Some particulars for a project are as follows:

Capital Cost ($ Mn)	1000
Annual Operating cost ($ Mn/yr)	10% of Capital Cost
Annual Benefits ($Mn/yr)	400
Useful Life (years)	20
Interest/Discount rate (percent)	10

a) What is the Life Cycle Cost (LCCs) of the project – expressed in present value and future value terms?

b) What is the Life Cycle Cost (LCCs) of the project – with year 10 as the base year? c) What is the NPV of the project with year 15 as the base year?
d) What is the Pay-back (PB) period for this project?
e) What is Equivalent Annual Cost (EAC) for this project?

f) At what discount rate will this project become unviable?

Answer 1

1 a). Life Cycle Costs 1 in present value terms Particulars (Amt. in S Mn) a).Initial cost b).Anmual operating costs c).PVAF (10%, 20years) d).PV of Annual costs [b*c] e).Total Life Cycle Costs [a+d 1,000 1,000*10%. 100 р.а. 8.5136 851.36 1,851.36 PVAF 1-(1+r)^-n }/r = [1-(1+0.1)^-201/0.1 =8.5136 2 in future value terms Particulars a).Initial cost b).Annual operating costs 1,000*10%= c).FVAF (10%, 20years) d).PV of Annual costs [b*c] e).Total Life Cycle Costs [a+d] (Amt. in S Mn) 1,000 100р.а. 6.7275 672.75 1,672.75 FV - PY(1+r) ^п = 1(1+0.1)^20 = 6.7275 b). Life Cycle Costs with 10 years as the base year 1 in present value terms Particulars (Amt. in S Mn) 1,000 .Initial cost 100 p.a b).Ammual operating costs 1,000*10%= c).PVAF (10%, 10years) d).PV of Annual costs b*c e).Total Life Cycle Costs [a+d 6.1446 614,46 1,614.46 PVAF 1-(1+r)^-n ]/r = /1-(1+0.1)^-101/0.1 =6.1446 2 in future value terms Particulars (Amt. in S Mn) a).Initial cost b).Annual operating costs 1,000*10%= c).FVAF (10%, 10ycars) d).PV of Annual costs [b*c e).Total Life Cycle Costs [atd] 1,000 100 р.а. 2.5937 259.37 - 1,259.37 = 1(1+0.1)^10 = 2.5937 FV PV(1+r)^n c). Computing NPV Cash flows p.a.= Annual benefits - Annual costs $400 $100 $300 Cash flows PVAF @10%, 15 years Disc. Cash flows Year 1 to 15 300 7.6061 2,282 Total cash inflows- Initial cash out flow 2,282 1,000 10

2 NPV 1,281.83 d). Payback period of the project. Year Cash flow Net Invested Cash -1,000 1 300 -700 2 300 -400 300 3 -100 300 200 300 5 500 Payback period 3 years [ 200/300] 3 years +0.67 3.67 years e). Equivalent Annual Cost(EAC) Particulars a). Initial Cost of Capital b). PV of Annual Cost $100*8.5136 c). Total (a+b) d). PV e). Equivalent Annual Cost (EAC) (Amt. in S Mn) 1,000 851.36 1,851.36 20 years) .5136 c/d= 217.4591 f). Computing IRR The project will be unviable at the rate above IRR PVAF @14%, 20 Disc. Cash Disc. Cash Cash flows Year PVAF @10%, 20 years flows flows years 1to 8.5136 2,554 20 300 6.6231 1,986.93 Total cash inflows 2,554 1,986.93 Initial cash outflow 1,000 1,000 NPV= 1,554.08 986.93

3 By interpolation Higher NPV Higher NPV - Lower NPV Difference in IRR Lower rate + discount rate 1,554.08 1,554.08-986.93 4% 10% + 1,554.08 10%+ *4% 567.15 2.7402 4% 10%+ 10%10.96% IRR 20.96% or 21% Therefore, the minimum rate of return shall be 20.96% or 21%. Above which the project will be unviable. Summary NPV 1.281,83 IRR 20.96% Payback period(in years) 3.67 3 4 EAC (in $) 217.46 Present value(in S) 1,851.36 5 Life Cycle Costs Future Value(In 1,672.75 Present value(in Life Cycle Costs(10 6 S) 1,614.46 Future Value(In years) $) 1,259.37 Notes: All amounts are in $ millions