Question

A new furnace for your small factory will cost $36,000 to install and will require ongoing maintenance expenditures of $1,000 a year. But it is far more fuel efficient than your old furnace and will reduce your consumption of heating oil by 3,300 gallons per year. Heating oil this year will cost $2 a gallon; the price per gallon is expected to increase by $.50 a year for the next 3 years and then to stabilize for the foreseeable future. The furnace will last for 20 years, at which point it will need to be replaced and will have no salvage value. The discount rate is 6%.

a. What is the net present value of the investment in the furnace? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.)

b. What is the IRR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

c. What is the equivalent annual cost of the furnace? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

d. What is the equivalent annual savings derived from the furnace? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a. Calculation of Net Present value of New Furnace -

Year	Initial investment	Saving in fuel		Saving in $	Maintinance	Depriciation	Total Exp.	Profit	less Tax	Profit after tax	add Depriciation	Cash flow	Dis. @ 6%	PV
0	36000												1	-36000
1		3300	2	6600	1000	1800	2800	3800	0	3800	1800	5600	0.943396	5283.019
2		3300	2.5	8250	1000	1800	2800	5450	0	5450	1800	7250	0.889996	6452.474
3		3300	3	9900	1000	1800	2800	7100	0	7100	1800	8900	0.839619	7472.612
4		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.792094	8356.588
5		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.747258	7883.574
6		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.704961	7437.334
7		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.665057	7016.353
8		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.627412	6619.201
9		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.591898	6244.529
10		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.558395	5891.065
11		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.526788	5557.608
12		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.496969	5243.027
13		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.468839	4946.252
14		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.442301	4666.275
15		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.417265	4402.146
16		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.393646	4152.968
17		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.371364	3917.895
18		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.350344	3696.127
19		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.330513	3486.912
20		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550	0.311805	3289.54
													NPV	76015.5

b. Calculation of IRR -

Year	Initial investment	Saving in fuel	Rate	Saving in $	Maintinance	Depriciation	Total Exp.	Profit	less Tax	Profit after tax	add Depriciation	Cash flow
0	36000											-36000
1		3300	2	6600	1000	1800	2800	3800	0	3800	1800	5600
2		3300	2.5	8250	1000	1800	2800	5450	0	5450	1800	7250
3		3300	3	9900	1000	1800	2800	7100	0	7100	1800	8900
4		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
5		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
6		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
7		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
8		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
9		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
10		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
11		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
12		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
13		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
14		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
15		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
16		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
17		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
18		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
19		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
20		3300	3.5	11550	1000	1800	2800	8750	0	8750	1800	10550
											IRR	24.22%

c. Calcualtion of equivalent cost of furnace -

Initial investment *1 + PVIFA(6%,20)

36000*1 + 1000*11.46992

= 36000 + 11469.92

= 47469.92

Equivalent annual cost of furnace = 47469.92/11.46992

= 4138.64

d. Calculation of Equivalent annual savings from the furnace -

Year	Initial investment	Saving in fuel	Rate	Saving in $	Dis. @ 6%	PV
0	36000				1
1		3300	2	6600	0.943396	6226.42
2		3300	2.5	8250	0.889996	7342.47
3		3300	3	9900	0.839619	8312.23
4		3300	3.5	11550	0.792094	9148.68
5		3300	3.5	11550	0.747258	8630.83
6		3300	3.5	11550	0.704961	8142.29
7		3300	3.5	11550	0.665057	7681.41
8		3300	3.5	11550	0.627412	7246.61
9		3300	3.5	11550	0.591898	6836.43
10		3300	3.5	11550	0.558395	6449.46
11		3300	3.5	11550	0.526788	6084.40
12		3300	3.5	11550	0.496969	5740.00
13		3300	3.5	11550	0.468839	5415.09
14		3300	3.5	11550	0.442301	5108.58
15		3300	3.5	11550	0.417265	4819.41
16		3300	3.5	11550	0.393646	4546.61
17		3300	3.5	11550	0.371364	4289.26
18		3300	3.5	11550	0.350344	4046.47
19		3300	3.5	11550	0.330513	3817.43
20		3300	3.5	11550	0.311805	3601.34
Total					12.46992	123485.42

Equivalent annual saving = 123485.42/12.46992

= 9902.66

Please comment in case of any wrong answer.