Consider a project to supply 100 million postage stamps per year to the U.S. Pos
ID: 2765334 • Letter: C
Question
Consider a project to supply 100 million postage stamps per year to the U.S. Postal Service for the next five years. You have an idle parcel of land available that cost $1,900,000 five years ago; if the land were sold today, it would net you $2,100,000 after tax. The land can be sold for $2,300,000 after taxes in five years. You will need to install $5.4 million in new manufacturing plant and equipment to actually produce the stamps; this plant and equipment will be depreciated straight-line to zero over the project's five-year life. The equipment can be sold for $500,000 at the end of the project. You will also need $600,000 in initial net working capital for the project, and an additional investment of $50,000 in every year thereafter. Your production costs are 0.5 cents per stamp, and you have fixed costs of $1,050,000 per year. If your tax rate is 34 percent and your required return on this project is 12 percent, what bid price should you submit on the contract? (Do not round intermediate calculations and round your final answer to 5 decimal places, (e.g., 32.16161))Explanation / Answer
Step 1: Calculate the Operating Cash Flow at which NPV is Zero
NPV is the difference between the present value of cash inflows and cash outflows. The equation for NPV = 0 in this case is given below:
NPV = 0 = -Initial Investment - Opportunity Cost of Land - Initial Working Capital + Operating Cash Flow*PVIFA(Years,Percentage) - Working Capital Each Year*PVIFA(Years,Percentage) + (After-Tax Salvage Value + Recovery of Working Capital + Sale Value of Land)/(1+Required Return)^Years
where PVIFA is the Present Value Interest Factor for an Annuity which can be derived from the Present Value Tables
________
Using the values provided in the question, we get,
After-Tax Salvage Value = Sales Value of Equipment at the End of 5 Years*(1-Tax Rate) = 500,000*(1-34%) = $330,000
NPV = 0 = -5,400,000 - 2,100,000 - 600,000 + Operating Cash Flow*PVIFA(12%,5) - 50,000*PVIFA(12%,4) + (330,000 + (600,000 + 4*(50,000)) + 2,300,000)/(1+12%)^5
On Solving, we get,
NPV = 0 = -8,100,000 + Operating Cash Flow*PVIFA(12%,5) - 50,000*3.0373 + 1,946,274.12
Operating Cash Flow = 6,305,593.35/3.6048 = $1,749,232.96
__________
Step 2: Calculate the Bid Price
The bid price can be calculated with the use of following equation for operating cash flow.
Operating Cash Flow = [((Price - Variable Cost)*Quantity) - Fixed Cost)]*(1-Tax Rate) + Depreciation*Tax Rate
Substituting Values, we get,
1,749,232.96 = [(Price - .005)*(100,000,000) - 1,050,000]*(1-34%) + 34%*(5,400,000)/5
On Solving, we get,
1,749,232.96 = [100,000,000Price - 500,000 - 1,050,000]*66% + 367,200
1,749,232.96 = 66,000,000Price - 1,023,000 + 367,200
Price = (1,749,232.96 + 1,023,000 - 367,200)/66,000,000 = $.03644 (answer)
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