You are working on a bid to build two city parks a year for the next three years

Question

You are working on a bid to build two city parks a year for the next three years. This project requires the purchase of $180,000 of equipment that will be depreciated using straight-line depreciation to a zero book value over the 3-year project life. The equipment can be sold at the end of the project for $34,000. You will also need $20,000 in net working capital for the duration of the project. The fixed costs will be $16,000 a year and the variable costs will be $168,000 per park. Your required rate of return is 15 percent and your tax rate is 40 percent. What is the minimal amount you should bid per park?

Please include a detailed description along with the answer. Thanks!

Explanation / Answer

NPV = PV of Benefits - PV of Costs

PV of Benefits include OCF, Salvage Value after tax, and the Return of NWC

PV of Costs include CAPEX and the Investment in NWC

OCF = N.I. + D. EBIT = N.I./(1-Tax rate)

SALES = Variable Costs + Fixed Costs + Depreciation + EBIT

ASSUMPTIONS

# of years : 3

#of Parks (Unit) :2

Variable Costs/unit : $168,000

Fixed Costs : $16,000

CAPEX : $180,000

Salvage : 0

Sale Value : $34,000

Depreciation is straight line to salvage value = (180,000-0)/3 = $60,000/yr.

NWC Investment : $20,000

Tx Rate : 40%

WACC : 15%

YEARS

0 1 2 3

OCF OCF OCF OCF

∆NWC (20,000) ------ ------- 20,000

CAPEX (180,000) _____ _____ 34,000

----------------------------------------------------------------------------------

CFFA (200,000) OCF OCF OCF +54,000/(1.15)^3

ie 54000/(1.15)^3= 35,506 â†-------------------------------------------------------↑

NPV = (164,494) + OCF/(1.15) + OCF/(1.15)^2 + OCF/ (1.15)^3

At break even, NPV = 0, thus PV of the Benefits = PV of the Costs

PV of OCF (an annuity) = PV Costs

ie OCF *{1/(1.15) +1/(1.15)^2+1/(1.15)^3} = 164,494

We have PV = 164494, Rate=i = 15%, nper=n = 3, FV = 0, PMT = ?

So OCF = PMT(rate,nper,PV,FV) = PMT(15%,3,164494,0) = $72,045

Annual OCF = $72,045 needed to break even

OCF = NI + Dep; NI = OCF – Dep

= $72,045 – 60,000

= $12,045

EBIT = NI/(1-tax rate) = $12,045/(1-0.4) = $20,075

ANNUAL SALES = Var. Costs + Fixed Costs + Depreciation + EBIT

= (2*168000) + 16000 + 60000 + 20075

= 432075

Break Even Unit Price = Annual Sales/ # of units = 432075/2 = $216,037.50

SO Minimal Bid for Park should be $216,037.50

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