Question

We are evaluating a project that costs $1,374,000, has a six-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 87,400 units per year. Price per unit is $34.45, variable cost per unit is $20.70, and fixed costs are $754,000 per year. The tax rate is 30 percent, and we require a return of 11 percent on this project.

Calculate the base-case operating cash flow and NPV. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

  

Base-case operating cash flow	$
NPV	$

  

What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

  

Sensitivity of NPV            $

  

If there is a 500-unit decrease in projected sales, how much would the NPV drop? (Input your answer as a positive value. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

NPV drop            $

  

What is the sensitivity of OCF to changes in the variable cost figure? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

  

Sensitivity of OCF            $

  

If there is $1 decrease in estimated variable costs, how much would the increase in OCF be? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

  

Increase in OCF

Answer 1

Answer a.

Initial Cost = $1,374,000
Life of Project = 6 years

Annual Depreciation = Initial Cost / Life of Project
Annual Depreciation = $1,374,000 / 6
Annual Depreciation = $229,000

Operating Cash Flow = [(Selling Price-Variable Cost)*Unit Sales - Fixed Costs]*(1-tax) + tax*Depreciation
Operating Cash Flow = [($34.45 - $20.70)*87,400 - $754,000]*(1 - 0.30) + 0.30 * $229,000
Operating Cash Flow = $447,750 * 0.70 + 0.30 * $229,000
Operating Cash Flow = $382,125

NPV = -$1,374,000 + $382,125 * PVA of $1 (11%, 6)
NPV = -$1,374,000 + $382,125 * (1 - (1/1.11)^6) / 0.11
NPV = -$1,374,000 + $382,125 * 4.2305
NPV = $242,579.81

Answer b.

If unit sales decreased by 500 units:

Operating Cash Flow = [(Selling Price-Variable Cost)*Unit Sales - Fixed Costs]*(1-tax) + tax*Depreciation
Operating Cash Flow = [($34.45 - $20.70)*86,900 - $754,000]*(1 - 0.30) + 0.30 * $229,000
Operating Cash Flow = $440,875 * 0.70 + 0.30 * $229,000
Operating Cash Flow = $377,312.50

NPV = -$1,374,000 + $377,312.50 * PVA of $1 (11%, 6)
NPV = -$1,374,000 + $377,312.50 * (1 - (1/1.11)^6) / 0.11
NPV = -$1,374,000 + $377,312.50 * 4.2305
NPV = $222,220.53

Sensitivity of NPV = (New NPV - Old NPV) / (New Unit Sales - Old Unit Sales)
Sensitivity of NPV = ($222,220.53 - $242,579.81) / (86,900 - 87,400)
Sensitivity of NPV = $40.719

Answer c.

If sales drops by 500 units, then NPV will drop by $20,359.28 ($242,579.81 - $222,220.53)

Answer d.

If variable cost per unit decreased by $1.00 units:

Operating Cash Flow = [(Selling Price-Variable Cost)*Unit Sales - Fixed Costs]*(1-tax) + tax*Depreciation
Operating Cash Flow = [($34.45 - $19.70)*87,400 - $754,000]*(1 - 0.30) + 0.30 * $229,000
Operating Cash Flow = $535,150 * 0.70 + 0.30 * $229,000
Operating Cash Flow = $443,305

Sensitivity of OCF = (New OCF - Old OCF) / (New Variable cost per unit - Old Variable cost per unit)
Sensitivity of OCF = ($443,305 - $382,125) / ($19.70 - $20.70)
Sensitivity of OCF = -$61,180

Answer e.

Increase in OCF = New OCF - Old OCF
Increase in OCF = $443,305 - $382,125
Increase in OCF = $61,180