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

Answer:

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

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)($\frac{1}{12}$) - 1

= (1.06136)$^{\frac{1}{12}}$ - 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.