Buy or Lease a new delivery truck

[Jill]

I think I have the problem structured correctly for the option to buy but the lease does not appear correct the payment does not look right. Or maybe I am missing a step because the PV is only 4K. Please help me, I think this will be the last one... :?

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 $4,000 (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?

The effective annual rate on your firm's borrowing is:
EAR = (1 + APR / k) k - 1 = (1 + .06 / 4)4 - 1 = .06136 or 6.14%

Purchase truck:
N = 5 (12 X 5) = 60 months
I = .06136
FV= 0
PV= 200,000
Compute payment

P = C (1/r) (1-(1/ (1+r) N))

200000/ (1/.06136) (1-1/ (1.061360) ^60
= 200000/16.29726206 (1-(1/35.62566402)
= 200000 / (16.29726206) (1-(.0280696522)
= 200000/ (16.29726206) (.9719303478)
= 200000/15.83980216

PMT = $12, 626.42


The monthly discount rate lease is:
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 = 0.498%

PV= 4000
I = .498 = .004975
FV= 0
N = 5 yrs 5/12 = 60 months

P = C (1/r) (1-(1/ (1+r) N))

4000/1/1.004975(1-(1/(1.004975)^ 60)
4000/ (201.0050251)(1-(1/1.34683842)
4000/(201.0050251)(1-(.7424795619)
4000/(201.0050251)/(.2575204381)
4000/(51.76290213)

= 77.2727541995

Thanks again,
Jill

 

[Jill]

Re: Buy or Lease

Let's back track to the lease option the montly payment would be 4K , right so I am not solving for payments. Do I need to find out what value of 4K is for 5yrs with .498 discount rate?

 

[Denis]

> The effective annual rate on your firm's borrowing is:
> EAR = (1 + APR / k) k - 1 = (1 + .06 / 4)4 - 1 = .06136 or 6.14%
Correct.

> 200000/ (1/.06136) (1-1/ (1.061360) ^60
> PMT = $12, 626.42
No. You must use .06136 / 12 as rate; that'll give you a payment of $3,879.22
If you repay 12,626.42 for 60 months, that's a total of $757,585: YIKES!!

> The monthly discount rate lease is:
> EAR = (1 + APR / k) k - 1 = (1 + .06 / 4)4 - 1 = .06136 or 6.14%
No need to do anything with lease amount...
Simply compare it (4000 more expensive than 3879.22); so borrow, don't lease.