Question

The heat loss through the exterior walls of a certain poultry processing plant is estimated to cost the owner $3,500 next year. A salesman from Superfiber Insulation, Inc., has told you, the plant engineer, that he can reduce the heat loss by 75% with the installation of $18,000 worth of Superfiber now. If the cost of heat loss rises by $190 per year ( gradent) after the next year and the owner plans to keep the present building for 14 more years, what would you recommend if the interest rate is 9% per year? Click the icon to view the interest and annuity table for discrete compounding when i= 9% per year The present equivalent value of the savings equals $ (Round to the nearest dollar.)

Answer 1

The cost of heat loss rises by $ by $190 per year (uniform gradient) The present value of Gradient , (PG) = (A/G . i%, n) = $ 190 [1/I - n/(1 + i)^n - 1] = $190[1/0.09 - 14/(1.09)^14 -] = $190(11.11 - 14/(3.3417 - 1) = $190 (11.11 - 14/2.3417) = $190(11.11 - 5.9785) = $190 times 5.1315 = $974.985 therefore PG = $974.99 Total estimated costs = $3500 + $974.99 $ 4474.99 \r\n pv = $ 4474.99 (PV 1 FA @ i.n) = $4474.99 (PV1FA@9%14) = $4474.99[1.09^14 - 1)/ 0.09 times 1.09^14)] = $4474.99 [(3.3417 - 1)/(0.09 times 3.3417)] = $4474.99 [2.3417/0.300753] = $4474.99 times 7.7849 = $34837.35 Total heat loss without insulation = $34837.35 Heat loss cost with insulation = (1 - 0.75) times $34837.35 = 0.25 times $34837.35 = $ 8709.34 I ation cost = $ 18,000 present worth cost for heat loss with installed superfiber = $18,000 + $8709.34 = $26,709.34 Installing superfiber insulation is recommended