Question

A new furnace for your small factory will cost $43,000 and a year to install, will require ongoing maintenance expenditures of $4,000 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 4,000 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?

a.NPV_________

b.IRR ____________%

c.Cumulative cash flows are positive in_______

d.Equivalent annual cost____________

e.Equivalent annual savings_____________

f.Are the two measures the same or is one larger?_______________

Answer 1

It will take a year to install means installation will be completed within a year

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

Answers are rounded to 2 decimal points.

Ans a) NPV is $ 85,742.79. See the Calculation below-

Particulars	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
(a)Installation Cost	-43,000
(b)Maintenance Expense		-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000
(c) Reduce Consumption of Heating oil Gallons		4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000
(d) 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
(e) Total Saving of Heating Oil [(c)*(d)]		16,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000
(f) Saving Net of Maintenance Expense [(e) +(b)]		12,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000
(g) Present Value at Discount rate 8%	-39,814.81	10,288.07	11,113.65	10,290.42	9,528.16	8,822.37	8,168.87	7,563.76	7,003.49	6,484.71	6,004.36	5,559.59	5,147.77	4,766.45	4,413.38	4,086.47	3,783.77	3,503.49	3,243.97	3,003.67	2,781.18

NPV sum of discounted cash Flow is equal to $ 85,742.79 (i.e sum of Present value of all the years).

Ans b) IRR is 31.31%. See the calculation below-

Particulars	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21
(a) Installation Cost	-43,000
(b)Maintenance Expense		-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000	-4,000
(c) Reduce Consumption of Heating oil Gallons		4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000	4,000
(d) 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
(e) Total Saving of Heating Oil [(c)*(d)]		16,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000	18,000
(f) Saving Net of Maintenance Expense [(e) +(b)]		12,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000	14,000

IRR is Present value of Inflows and Outflows which is equal to 31.31%

Ans (c) Payback Period is 3.21 years. See the calculation below-

Installation expense	43,000
Cash of 1st three years	40,000
Remaining	3,000
Remaining divided total cash flow of next year	0.214285714
So Payback period is 3 years + 0.2142	3.21

Ans (d) Equivalent Annual Cost

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

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

Annuity Factor= (1 - (1 / (1+0.08)^20 )) / 0.08= 9.8181

Equivalent Annual Cost=  (43,000 / 9.8181) + 4000 = 8,379.67

Ans (e) Equivalent Annual Saving

Equivalent Annual Saving = NPV / Annuity Factor

NPV= $ 85,742.79

Annuity Factor= 9.8181

Equivalent Annual Saving = 85,742.79/ 9.8181= 8733.13

Ans (f) Difference between Equivalent Annual Cost and Equivalent Annual Saving

Equivalent Annual Saving - Equivalent Annual Cost = 8,733.13 - 8,379.67 = 353.46