Question

Weekly assignment 8 (Chapter 8) Saved A new furnace for your small factory will cost $30,000 and a year to install, will require ongoing maintenance expenditures of $1,800 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 2,700 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 6%. 20 points eBook 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? Print a References b. NPV IRR Cumulative cash flows are positive in: Equivalent annual cost Equivalent annual savings Are the two measures the same or is one larger? d. f.

Answer 1

It will take a year to install so installation will be completed after a year.

The frunance will last for 20 years it means 20 year after a year of installation.

Answers are rounded to 2 decimal points

Ans a) NPV 82490.66 See the calculation below

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
Installation Cost	-30000
Maintinance Exp		-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800
Reduce Consumption of Heating Oil Gallons		2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700
This Year cost is $ 3, Increasing $0.5 for next 3 years		4	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	4.5	4.5
Total Saving of Heating Oil		10800	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150
Saving Net of Maintinance exp		9000	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350
Present Value at Discount Rate 6%	-28301.887	8009.968	8690.06	8198.169	7734.122	7296.342	6883.341	6493.718	6126.149	5779.386	5452.251	5143.633	4852.484	4577.815	4318.693	4074.239	3843.622	3626.058	3420.81	3227.179	3044.508
NPV sum of dicounted cash flow	82490.66

Ans b) IRR is 33.27% See the calculation below

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
Installation Cost	-30000
Maintinance Exp		-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800	-1800
Reduce Consumption of Heating Oil Gallons		2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700	2700
This Year cost is $ 3, Increasing $0.5 for next 3 years		4	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	4.5	4.5
Total Saving of Heating Oil		10800	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150	12150
Saving Net of Maintinance exp		9000	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350	10350
IRR is Present values of infolws and outflows are equals to 0	33.27%

Ans c) Payback period is 3.03 years See the calculation below

Instalation Exp	30000
Cash of 1st three years	29700
Remaining	300
Remaining divided total cash flow of next year	0.0289855
So Payback period is 3 years + 0-0289	3.03

Ans d) Equivalent Annual Cost

Equivalent Annual Cost = (Cost of Machine / Annuity Factor ) + Annual Maintenance Exp

Annuity Factor = 1 - (1 / (1+r)^n ) / r

Annuity Factor = (1 - (1 / (1+0.06)^20 )) / 0.06 = 11.7699

Equivalent Annual Cost = (36000 / 11.4699) + 1800 = 4938.65

Ans e) Equivalent Annual Saving  

Equivalent Annual Saving = NPV / Annuity Factor

NPV = 82490.66

Annuity Factor = 11.7699

Equivalent Annual Saving = 82490.66/ 11.7699 = 7008.612

And f) Differnece between Equivalent Annual Cost and Equivalent Annual Saving

= Equivalent Annual Saving - Equivalent Annual Cost = 7008.61 - 4938.65 = 2069.96

Hope this helps, Thanks and have a good day