An automobile tier II supplier has been offered a contract to supply a gearbox to a car company. The initial price of the gearbox is $389, and the car company is ready to give a contract to the supplier to supply 500,000 gearboxes in the first year, increasing by 2% every year, if the supplier is ready to bring down the price of the gearbox every year by $7.50 over the 12-year life of the contract.
1. How much is the contract worth to the supplier at 6% interest?



:

The contract is worth $1,622,970,237.98

Explanation:

Given

Number of Years = 12

Initial Price = $389

Initial Units = 500,000

Unit Increment = 2%

Price Decrement = $7.5

At Year 0:

$389 * 500,000 = $194,500,000

The Initial price would continue to decrease by $7.5

And the Initial units would continue to increase by 2%.

So,

At Year 1:

($389 - $7.5) * (500,000 * 2% + 500,000)

= $381.5 * 510,000 = $194,565,000

At Year 2:

($381.5 - $7.5) * (510,000 * 2% + 510,000)

= $374 * 520,200 = $194,554,800

At Year 3:

($374 - $7.5) * (520,200 * 2% + 520,200)

= $366.5 * 530,604 = $194,466,366

At Year 4:

$359 * $541,216 = $194,296,5736

At Year 5:

$351.5 * $552,040 = $194,042,2017

At Year 6:

$344 * $563,081 = $193,699,9368

At Year 7:

$336.5 * $574,343 = $193,266,3649

At Year 8:

$329 * $585,830 = $192,737,96810

At Year 9:

$321.5 * $597,546 = $192,111,13011

At Year 10:

$314 * $609,497 = $191,382,12412

At Year 11:

$306.5 * $621,687 = $190,547,113

Calculating present worth of contract (at 6%)

By adding the result of 0.06 * present value at each year.

Net Present Value = $1,622,970,237.98

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