Question

1. A manufacturing company is considering the installation of a standby power supply system. A used generator can be installed for £ 18,000; while a completely new generator can be installed for £ 24,000. Annual operating costs are estimated to be £ 8200 for the used generator and £7000 for the new one. Both generators are anticipated to survive for 20 years with zero salvage value at that time. Yearly maintenance costs of the used and new generators are £ 1500 and £ 500 respectively. The minimum acceptable rate of return is 15%.

• Construct the netcash flow of the two generators.                                   
• Find the internal rate of return of the net cash flow and recommend the best economical choice.                                                                                                       
• What should be the initial cost of the used generator to make the two alternatives even at an interest rate of 12%?    

                                                           

Answer 1

1)	Net installation cost (New-Old) = 24000-18000 =	6000
	Net annual operating cost (New-Old) = 8200-7000 =	1200
	Net yearly maintenance costs (New-Old) = 1500-500 =	1000
	The annual net savings = 1200+1000 =	2200
2)	IRR is that discount rate for which NPV = 0.
	Hence, 0 = -6000+2200*PVIFA(r,20)
	where r = IRR.
	Solving for r
	PVIFA(r,20) = 6000/2200 = 2.7273
	PVIFA for 37% = 2.6977
	PVIFA for 36% = 2.7718
	r (IRR) = 36+(2.7718-2.7273)/(2.7718-2.6977) =	36.60%
	AS THE IRR OF THE NET CASH FLOWS (INCREMENTAL
	CASH FLOWS) IS GREATER THAN THE MARR OF 15%,
	THE ALTERNATIVE HAVING THE HIGHER INITIAL
	INVESTMENT IS TO BE SELECTED.
3)	The two alternatives would be even if the NPV of the
	differential cash flows is equal to 0, with the discount
	rate of 12% (that is IRR should be 12%).
	As the annual savings is not changed, the initial cost
	has to be changed, such that NPV = 0 with 12% discount
	rate.
	For this the difference in initial investment should be
	equal to the PV of the net annual savings = 2200*(1.12^20-1)/(0.12*1.12^20) =	16433
	The initial cost of the used generator should be 24000-16433 =	$      7,567