Question

Machine A costs $38,000 to purchase and is worth $8,000 in 6 years at the end of its service life. Machine B costs $17,000 to purchase and is worth $3,000 in 3 years at the end of its service life. Assume that these machines are needed for 18 years (required service period). Each machine can be repurchased at the same price in the future, and assume the annual maintenance cost of each machine is negligible. Use 11% annual interest rate. What is the Present Total Cost of the machine that should be purchased? Enter your answer as a positive number.

Answer 1

For period of 18 years ,Machine A will be purchased 3 times that is:Today(costing 38000) , at end of 6 years(38000-8000from sale of old =30000) and at end of 12 years(38000-8000= 30000) .At last 8000 salvage will be recovered from last machine

For period 18 years ,Machine B will be purchase 6 times that is :Today (costing 17000),at end of year 3(17000-3000= 14000) ,at end of year 6 ,at end of year 9 ,at end of year 12 and at end of year 15 .At last 3000 salvage will be recovered from last machine

	Machine A	B
Present value of cost incurred to purchase machine (cash outflow)	cost incurred today +[PVF11%,6*CF]+[PVF11%,12*CF]	cost incurred today +[PVF11%,3*CF]+[PVF11%,6*CF]+[PVF11%,9*CF]+[PVF11%,12*CF]+[PVF11%,15*CF]
	38000+[.53464*30000]+[.28584*30000] 38000+16039.2+8575.2 62614.4	17000+[.73119*14000]+[.53464*14000]+[.39092*14000]+[.28584*14000]+[.20900*14000] 17000+10236.66+ 7484.96+ 5472.88+4001.76+ 2926 47122.26
less:present value of salvage recovered at end of year1 8 (cash inflow)	[.15282*8000] (1222.56)	[.15282*3000] (458.46)
Total cost of machine purchased	61391.84	46663.8

**find present value factor from table at11%

machine B should be purchased as its total cost is lower :46663.8 (rounded to 46664)