Question

) 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 $240,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4800 (paid at the end of each month). Your firm can borrow at 7.80% APR with quarterly compounding.

The present value (PV) of the lease payments for the delivery truck is closest to ________.

A) $190,506

B) $238,132

C) $285,758

D) $333,385

Answer 1

B) $238,132

Step-by-step explanation:

Firstly, we calculate the effective annual rate (EAR) which can be estimated as shown below:

EAR =
`(1+(rate)/(periods))^(period) - 1`

rate = 7.80%; periods = 4 (quarterly)

EAR = (1+ 0.078/4)^4 - 1 = (1+0.0195)^4 - 1 = (1.0195)^4 - 1 = 1.08031 - 1 = 0.08031

Then,

Monthly rate = [(1+EAR)^(1/12)] - 1 = [(1+0.08031)^(1/12)] - 1 = [(1.08031)^(0.0833)] - 1 = 1.006458 - 1 = 0.006458

Thus, if we use the formula for PVA, to estimate the PV. Where I = 0.6458; N = 60 (5 years × 12 months/yr); FV = 0; PMT = $4800, the PV = $238,132.