Your company has been approached to bid on a contract to sell 4,500 voice recognition (VR) computer keyboards a year for four years. Due to technological improvements, beyond that time they will be outdated and no sales will be possible. The equipment necessary for the production will cost $4.1 million and will be depreciated on a straight-line basis to a zero salvage value. Production will require an investment in net working capital of $98,000 to be returned at the end of the project, and the equipment can be sold for $278,000 at the end of production. Fixed costs are $643,000 per year, and variable costs are $158 per unit. In addition to the contract, you feel your company can sell 9,800, 10,700, 12,800, and 10,100 additional units to companies in other countries over the next four years, respectively, at a price of $325. This price is fixed. The tax rate is 40 percent, and the required return is 10 percent. Additionally, the president of the company will undertake the project only if it has an NPV of $100,000. What bid price should you set for the contract?

contract price per year = $1,007,298.39 (for 4,500 units)

$223.844 per unit

Explanation:

initial outlay = $4,100,000 + $98,000 = $4,198,000

depreciation expense per year = $4,100,000 /  4 = $1,025,000

resale value = $278,000

after tax resale value = $278,000 x (1 - 40%) = $166,800

total revenue:

year 1 = (4,500 x P) + (9,800 x $325) = 4,500P + $3,185,000

year 2 = (4,500 x P) + (10,700 x $325) = 4,500P + $3,477,500

year 3 = (4,500 x P) + (12,800 x $325) = 4,500P + $4,160,000

year 4 = (4,500 x P) + (10,100 x $325) = 4,500P + $3,282,500

total variable costs:

year 1 = (4,500 + 9,800) x $158 = $2,259,400

year 2 = (4,500 + 10,700) x $158 = $2,401,600

year 3 = (4,500 + 12,800) x $158 = $2,733,400

year 4 = (4,500 + 10,100) x $158 = $2,306,800

fixed costs per year = $643,000

cash flow year 1 = [(4,500P + $3,185,000 - $1,025,000 - $2,259,400 - $643,000) x (1 - 40%)] + $1,025,000 = 2,700P + $579,560

cash flow year 2 = [(4,500P + $3,477,500 - $1,025,000 - $2,401,600 - $643,000) x (1 - 40%)] + $1,025,000 = 2,700P + $669,740

cash flow year 3 = [(4,500P + $4,160,000 - $1,025,000 - $2,733,400 - $643,000) x (1 - 40%)] + $1,025,000 = 2,700P + $938,096

cash flow year 4 = [(4,500P + $3,282,500 - $1,025,000 - $2,306,800 - $643,000) x (1 - 40%)] + $1,025,000 + $98,000 + $166,800 = 2,700P + $874,420

present value of cash flows:

CF₁ = 2,700P + $579,560 / 1.1 = 2,454.55P + $526,872.73

CF₂ = 2,700P + $669,740 / 1.1² = 2,231.40P + $553,504.13

CF₃ = 2,700P + $938,096 / 1.1³ = 2,028.55P + $704,805.41

CF₄ = (2,700P + $874,420) / 1.1⁴ = 1,844.14P + $597,240.63

since NPV = $100,000 at least, then

$100,000 = -$4,198,000 + 2,454.55P + $526,872.73 + 2,231.40P + $553,504.13 + 2,028.55P + $704,805.41 + 1,844.14P + $597,240.63

$100,000 = -$1,815,577.10 + 8,558.64P

8,558.64P = $1,915,577.10

P = $1,915,577.10 / 8,558.64 = $223.844

the contract price per year = $223.844 x 4,500 = $1,007,298.39

explanation:

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