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Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $250 000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $5 000 (paid at the end of each month). Your firm can borrow at 5% APR with quarterly compounding.
-The effective annual rate on your firm's borrowings is closest to:
A)5.13%
B)5.09%
C)5.06%
D)5.12%

Question

Quizplus · Accepted Answer

We need to calculate the effective annual rate on the firm's borrowings to compare the cost of purchasing versus leasing the delivery truck. The formula for effective annual rate is:

EAR = (1 + (APR/m))^m - 1

where APR is the annual percentage rate, m is the number of compounding periods per year, and EAR is the effective annual rate.

In this case, APR = 5%, m = 4 (since compounding is quarterly), so:

EAR = (1 + (0.05/4))^4 - 1 = 0.0509 or 5.09%

Now, we can compare the cost of purchasing versus leasing the truck. If we purchase the truck, the upfront cost is $250,000. If we lease the truck, the total lease payments over five years would be:

Total lease payments = 5 years x 12 months/year x $5,000/month = $300,000

Since the total lease payments are higher than the upfront cost of purchasing, it is better to purchase the truck. Therefore, the best choice is to purchase the delivery truck for $250,000 upfront.

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