Question

A new furnace for your small factory will cost $40,000 and a year to install, will require ongoing maintenance expenditures of $2,800 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 3,700 gallons per year. Heating oil this year will cost $3 a gallon; the price per gallon is expected to increase by $0.50 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 8%.

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 payback period? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

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

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

f. Compare the PV of the difference between the equivalent annual cost and savings to your answer to part (a). Are the two measures the same or is one larger?

Answer 1

a) Statement showing NPV

Particulars	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	NPV = sum of PV
Cost of new furnance	-40000
Cost of heating oil per gallon		3.0	3.5	4.0	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5	4.5
Consumption of heating oil (in gallon)		3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700	3700
Savings in cost of heating oil [Cost of heating oil per gallon x consumtion)		11100	12950	14800	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650	16650
Less: Maintenance cost		2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800	2800
Annual cash flow	-40000	8300	10150	12000	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850
PVIF @ 8%	1.0000	0.9259	0.8573	0.7938	0.7350	0.6806	0.6302	0.5835	0.5403	0.5002	0.4632	0.4289	0.3971	0.3677	0.3405	0.3152	0.2919	0.2703	0.2502	0.2317	0.2145
PV	-40000	7685	8702	9526	10180	9426	8728	8081	7483	6928	6415	5940	5500	5093	4715	4366	4043	3743	3466	3209	2971	86202

Thus NPV =

b) IRR is the rate at which NPV is 0

Assume r = 29%

Particulars	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	NPV = sum of PV
Annual cash flow	-40000	8300	10150	12000	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850
PVIF @ 29%	1.0000	0.7752	0.6009	0.4658	0.3611	0.2799	0.2170	0.1682	0.1304	0.1011	0.0784	0.0607	0.0471	0.0365	0.0283	0.0219	0.0170	0.0132	0.0102	0.0079	0.0061
PV	-40000	6434	6099	5590	5001	3877	3005	2330	1806	1400	1085	841	652	506	392	304	236	183	142	110	85	78

Assume r = 30%

Particulars	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	NPV = sum of PV
Annual cash flow	-40000	8300	10150	12000	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850	13850
PVIF @ 8%	1.0000	0.7692	0.5917	0.4552	0.3501	0.2693	0.2072	0.1594	0.1226	0.0943	0.0725	0.0558	0.0429	0.0330	0.0254	0.0195	0.0150	0.0116	0.0089	0.0068	0.0053
PV	-40000	6385	6006	5462	4849	3730	2869	2207	1698	1306	1005	773	594	457	352	271	208	160	123	95	73	-1377

Using interpolation we can find r

r	NPV
29%	78
30%	-1377
1%	1455
?	78

=78/1455

=0.05%

Thus IRR = 29%+0.05% = 29.05%

c) Statement showing cummulative cash flow

Year	Annual cash flow	cummulative cash flow
1	8300	8300
2	10150	18450
3	12000	30450
4	13850	44300

Using Interpolation, we can find payback period

Year	cummulative cash flow
3	30450
4	44300
1	13850
?	9550

=9550/13850

=0.69

Thus Payback period = 3+0.69 = 3.69 years

d) Statement showing Equivalent annual cost of furnance

Particulars	Amount
Cost of furnance	40000
PVIFA (8%,20)	9.818
Equivalent annual cost	4074.11

Thus  Equivalent annual cost of furnance = 4074.11$