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?

Question

Brooke Foley

Business

1 December, 05:16

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?

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Answers (1)

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Brian Douglas · 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.