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​ $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of​ $4000 (paid at the end of each​ month). Your firm can borrow at​ 6% APR with quarterly compounding.

The present value of the lease payments for the delivery truck is closest​ to $____.

Answer 1

The present value of the lease payments for the delivery truck is closest​ to $207,050.

Step-by-step explanation:

First we need to calculate the monthly discount rate for the lease arrangement.

EAR = (1 + APR / k)
`^(k)`- 1

= (1 + 0.06 / 4)
`^(4)` - 1 = 0.06136 or 6.14%

Monthly rate = (1 + EAR)(
`(1)/(12)`) - 1

= (1.06136)
`^{(1)/(12)}` - 1 = 0.004975 = 0.4975%

Now we can apply the PVA formula in excel or calculate the PV of the lease or by a calculator:

I = 0.4975

N = 60 (5 years × 12 months/yr)

FV = 0

PMT = $4000

PV = 207,051.61.