Question

Consider a project to supply Detroit with 40,000 tons of machine screws annually for automobile production. You will need an initial $5,800,000 investment in threading equipment to get the project started; the project will last for six years. The accounting department estimates that annual fixed costs will be $700,000 and that variable costs should be $200 per ton; accounting will depreciate the initial fixed asset investment straight-line to zero over the six-year project life. It also estimates a salvage value of $680,000 after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $300 per ton. The engineering department estimates you will need an initial net working capital investment of $580,000. You require a 18 percent return and face a marginal tax rate of 30 percent on this project.

  

a-1	What is the estimated OCF for this project?

  

OCF

$

  

a-2	What is the estimated NPV for this project? (Round your answer to 2 decimal places. (e.g., 32.16))

  

NPV

$

b.

Suppose you believe that the accounting department’s initial cost and salvage value projections are accurate only to within ±15 percent; the marketing department’s price estimate is accurate only to within ±10 percent; and the engineering department’s net working capital estimate is accurate only to within ±5 percent. What is your worst-case and best-case scenario for this project? (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))

  

Worst-case	$
Best-case	$

Answer 1

a-1. OCF = NI + depreciation

= [Qty*(selling price - variable cost) - fixed cost]*(1-tax%) + depreciation_perYear*(tax%) ...(1)

= [40,000*(300-200) - 700,000]*(1-30%) + 5,800,000/6*(30%)

= $ 2,600,000

a-2. NPV

= - Initial Investment - Initial Working Capital + PV(OCF)_{yr1_to_yr6} + PV(FreedUpWorkingCapital_yr6) + PV[SalvageValue (1-tax%)]_yr6 ...(2)

= -5,800,000 - 580,000 + [2.6M/1.18 + 2.6M/1.18² +2.6M/1.18³ +2.6M/1.18⁴ +2.6M/1.18⁵ +2.6M/1.18⁶] + [580,000 + 680,000*(1-30%)]/1.18⁶

=  -5,800,000 - 580,000 + 9,093,766.656 + [580,000 + 680,000*(1-30%)]/1.18⁶

= 3,104,942.361 =$ 3,104,942.36 (rounded)

{Note: we can calculate following in financial calculator:

[2.6M/1.18 + 2.6M/1.18² +2.6M/1.18³ +2.6M/1.18⁴ +2.6M/1.18⁵ +2.6M/1.18⁶]

PMT=2,600,000, N=6, I/Y=18, Compute (CPT) PV and we get PV=-9,093,766.656}

b. worst case

we will get worst case when we have high initial cost (+15%), high working capital (+5%), price estimate is low (-10%), salvage value is low (-15%),

Using (1) & making adjustments for worst case values, our OCF_worst

= [40,000* (300*0.9 - 200) - 700,000]*(1-30%) + 5,800,000(1.15)/6*(30%)

= $1,803,500

Using (2) & making adjustments for worst case values, our NPV_worst

= -5,800,000*1.15 - 580,000*1.05 + [1,803,500/1.18 + 1,803,500/1.18² +1,803,500/1.18³ +1,803,500/1.18⁴ +1,803,500/1.18⁵ +1,803,500/1.18⁶] + [580,000*1.05 + 680,000*(1-15%)(1-30%)]/1.18⁶

= -5,800,000*1.15 - 580,000*1.05 + 6,307,926.217 + [580,000*1.05 + 680,000*(1-15%)(1-30%)]/1.18⁶

= -595,604.3749 = $ -595604.37 (rounded)

b. best case

we will get worst case when we have low initial cost (-15%), low working capital (-5%), price estimate is high (+10%), salvage value is high (+15%),

Using (1) & making adjustments for best case values, our OCF_best

= [40,000* (300*1.1 - 200) - 700,000]*(1-30%) + 5,800,000(0.85)/6*(30%) = 3,396,500

Using (2) & making adjustments for best case values, our NPV_best

= -5,800,000*0.85 - 580,000*0.95 + [3,396,500/1.18 + 3,396,500/1.18² +3,396,500/1.18³ +3,396,500/1.18⁴ +3,396,500/1.18⁵ +3,396,500/1.18⁶] + [580,000*0.95 + 680,000*(1.15)(1-30%)]/1.18⁶

= -5,800,000*0.85 - 580,000*0.95 + 11,879,607.1 + [580,000*0.95 + 680,000*(1.15)(1-30%)]/1.18⁶

= 6,805,489.103 = $ 6,805,489.10 (rounded)