Question

A new furnace for your small factory will cost $41,000 and a year to install, will require ongoing maintenance expenditures of $3,500 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 3,800 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 10%.

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

0 2 Year 3 Savings 4 Price per gallon 1 3800 3.5 2 3800 4 3 3800 4.5 4 3800 4.5 5 3800 4.5 6 3800 4.5 7 3800 4.5 8 3800 4.5 9 3800 4.5 10 3800 4.5 11 3800 4.5 12 3800 4.5 13 3800 4.5 14 3800 4.5 15 3800 4.5 16 3800 4.5 17 3800 4.5 18 3800 4.5 19 3800 4.5 20 3800 4.5 3 17100 3500 17100 3500 17100 3500 17100 3500 17100 3500 17100 3500 13600 13600 13600 13600 13600 13600 6 Total savings 13300 15200 17100 17100 17100 17100 17100 17100 17100 17100 17100 17100 17100 17100 7 Ongoing expenses 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 3500 8 Capex -41000 9 Net cash flows -41000 9800 11700 13600 13600 13600 13600 13600 13600 13600 13600 13600 13600 13600 13600 10 NPV 69,759.67 Formula = NPV(10%,C9:V9)+B9 11 IRR 30.03% Formula = IRR(B9:V9,5%) 72 Payback period 3.43 years 13 Equivalent annual cost The equivalent annual cost of the new machine is the 20-year annuity with present value equal to $41,000. So, C*[1/.10-1/(.10*(1.10^20))]=41,000 Cx annuity factor (10%, 20 years) = $41,000 = x 8.5136 C=EAC = $4815.824 16 Equivalent annual savings $13,009.73 Formula = present value of annual savings/annuity factor (10%, 20 years) = NPV(10%,C9:V9)/8.5136 The equivalent annual annuity for this present value at 10% for 20 years is $13009.73. 19 f) Same The difference between equivalent annual savings and costs is $8193.91 ($14682.13-$4815.824). Thisvalue is equivalent to an annual annuity with a present value of $69759.67, the NPV from part (a). $8193.91 x annuity factor (10%, 20 years) = $8193.91 x 8.5136 = $9*759.67