Question

A firm will choose one of two projects. Both projects have useful lives of 10 years. Project A has an initial cost of $10,000, annual fuel cost of $500 per year, maintenance cost of $100 at the end of year 1 that increases by $25 per year thereafter, a salvage value of $1,000, and annual benefits of $2,300. Project B has an initial cost of $13,000, annual fuel cost of $400 per year, maintenance cost of $100 at the end of year 1 that increases by 10% per year thereafter, a salvage value of $2,000, and annual benefits of $2,500. Evaluate the present worth using an interest rate of 8 percent, compounded annually. 3 (a). (1 pt.) What is the present value of the fuel cost for Project A ($)? (b). (1 pt.) What is the present value of maintenance cost for Project A ($)? (c). (1 pt.) What is the present value of the salvage value for Project A ($)? (d). (1 pt.) What is the present worth of annual benefits for Project A ($)? (e). (1 pt.) What is the present worth of project A ($)? (f). (1 pt.) What is the present value of the fuel cost for Project B ($)? (g). (1 pt.) What is the present value of the maintenance cost for Project B ($)? (h). (1 pt.) What is the present value of the salvage value for Project B ($)? (i). (1 pt.) What is the present worth of the annual benefits for Project B ($)? (j). (1 pt.) What is the present worth of Project B ($)?

Answer 1

Solution A: Present value of fuel cost of Project A:

Year	Fuel Cost	Discounting Factor @ 8%	Present Value of Fuel Cost
1	500	0.9259	462.96
2	500	0.8573	428.67
3	500	0.7938	396.92
4	500	0.7350	367.51
5	500	0.6806	340.29
6	500	0.6302	315.08
7	500	0.5835	291.75
8	500	0.5403	270.13
9	500	0.5002	250.12
10	500	0.4632	231.60
			3,355.04

Present value of fuel cost of Project A is $3,355.04.

Solution B: Present value of Maintenance cost of Project A:

Year	Maintenance Cost	Discounting Factor @ 8%	Present Value of Maintenance Cost
1	100	0.9259	92.59
2	125	0.8573	107.17
3	150	0.7938	119.07
4	175	0.7350	128.63
5	200	0.6806	136.12
6	225	0.6302	141.79
7	250	0.5835	145.87
8	275	0.5403	148.57
9	300	0.5002	150.07
10	325	0.4632	150.54
			1,320.43

Present value of Maintenance cost of Project A is $3,355.04.

Solution C: Present value of salvage value of Project A:

= Salvage value of Project A at the end of 10th Year * discounting factor @ 8% for 10th year

= $1000 * 0.4632

= $463.19

Solution D: Present value of Annual Benefits of Project A:

Year	Annual Benefits	Discounting Factor @ 8%	Present Value of Annual Benefits Cost
1	2500	0.9259	2,314.81
2	2500	0.8573	2,143.35
3	2500	0.7938	1,984.58
4	2500	0.7350	1,837.57
5	2500	0.6806	1,701.46
6	2500	0.6302	1,575.42
7	2500	0.5835	1,458.73
8	2500	0.5403	1,350.67
9	2500	0.5002	1,250.62
10	2500	0.4632	1,157.98
			16,775.20

Present value of Annual Benefits of Project A is $16,775.20

Solution E: Present value of Worth of Project A:

Year	Annual Benfits	Fuel Cost	Maintenance Cost	Net Benefit	Discounting Factor @ 8%	Present Value of Fuel Cost
1	2500	500	100	1900	0.9259	1,759.26
2	2500	500	125	1875	0.8573	1,607.51
3	2500	500	150	1850	0.7938	1,468.59
4	2500	500	175	1825	0.7350	1,341.43
5	2500	500	200	1800	0.6806	1,225.05
6	2500	500	225	1775	0.6302	1,118.55
7	2500	500	250	1750	0.5835	1,021.11
8	2500	500	275	1725	0.5403	931.96
9	2500	500	300	1700	0.5002	850.42
10	2500	500	325	1675	0.4632	775.85
10	1000			1000	0.4632	463.19
					PV of Net Benefits	12,562.93
					(-) PV of Initial Investment	10,000.00
					Present worth of Project A	2,562.93