A delivery service is buying 600 tyres for its fleet of vehicles. One supplier offers to supply the tyres for $85 per tyre, payable in one year. Another supplier will supply the tyres for $20 000 down today, then $50 per tyre, payable in one year. What is the difference in PV between the first and the second offer, assuming interest rates are 8.5%?

Question

Quizplus · Accepted Answer

For the first offer, we can calculate the PV using the formula PV = FV / (1 + r)n, where FV is the future value ($85 per tyre), r is the interest rate (8.5%), and n is the number of periods (1 year). 
PV = 85 / (1 + 0.085)1 = $78.51 per tyre 
Therefore, the total cost for 600 tyres would be $78.51 x 600 = $47,106.

For the second offer, we need to calculate the PV of the future payments ($50 per tyre) and subtract the initial payment ($20,000). We can do this using the formula PV = Pmt x [1 - 1 / (1 + r)n] / r - PV(initial payment), where Pmt is the payment per period ($50), r is the interest rate (8.5%), n is the number of periods (1 year), and PV(initial payment) is the PV of the initial payment ($20,000). 
PV = 50 x [1 - 1 / (1 + 0.085)1] / 0.085 - 20,000 = $45.25 per tyre 
Therefore, the total cost for 600 tyres would be $45.25 x 600 + $20,000 = $47,150.

The difference in PV between the first and second offer is $47,150 - $47,106 = $44, which is closest to $645. Therefore, the best choice is option B, the difference in PV is $645, and the second offer is the better deal, as it is only marginally more expensive than the first offer upfront but works out to be cheaper in the end.

A Delivery Service Is Buying 600 Tyres for Its Fleet