Question

A delivery service is buying 600 tires for its fleet of vehicles. One supplier offers to supply the tires for $ 80 per​ tire, payable in one year. Another supplier will supply the tires for $ 15 comma 000 down​ today, then $ 45 per​ tire, payable in one year. What is the difference in PV between the first and the second​ offer, assuming interest rates are 8.4​%?

Answer 1

$4,372.71

Step-by-step explanation:

Here for reaching the difference in PV between the first and the second offer first we need to follow some steps which is shown below:-

Step 1

Total payment due = Per tire × Bought tires

= $80 × 600

= $48,000

Step 2

Present value factor of 8.4% for 1 year = 1 ÷ (1 + Rate of interest)^Number of years

= 1 ÷ (1 + 8.4%)^1

= 1 ÷ (1 + 0.084)^1

= 1 ÷ 1.084

= 0.92251

Step 3

First offer

Present value = Total payment due × Present value factor of 8.4% for 1 year

= $48,000 × 0.92251

= $44,280.48

Step 4

Second offer

One year payment = Bought tires × Per tire

= 600 × $45

= $27,000

Step 5

Present value = One year payment × Present value factor of 8.4% for 1 year

= 27,000 × 0.92251

= $24,907.77

Step 6

Total present value = Present value of second offer + Tires cost

= $24,907.77 + $15,000

= $39,907.77

Here we can see that first offer is higher than second offer

So,

The difference between the first and the second offer = First offer - Second offer

= $44,280.48 - $39,907.77

= $4,372.71