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. should you purchase the delivery truck or lease it? why?

Answer 1

First we need to calculate the monthly discount rate for the lease arrangement (EAR):

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

= (1 + .06 / 4)^4 – 1

 = .06136 or 6 .14%

Monthly rate = (1 + EAR)^(1/12) – 1

= (1.06136)^(1/12) - 1

= .004975 = 0.4975%

Now we can apply the formula for the PV of a constant annuity:

I = .4975

N = 60 = (5 years × 12 months/yr)

FV = 0

PMT = $4000 (lease payment)

Compute PV = 207,051.61

Answer:  Therefore you should purchase the new delivery truck.