Question 253065: . A corporation may obtain a machine either by leasing it for 6 years (the useful life) at an annual rent of $3,300 or by purchasing the machine for $12,000. Which alternative is preferable if the corporation can invest money at 8% per annum?
Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If they buy the machine, it costs them $12,000 today.
if they lease the machine, then are making installment payments at $3,300 per year for 6 years.
The present value of those payments at 8% per year for 6 years is equal to $15,255.50.
On a cash flow basis, it's cheaper to buy the machine than to lease it.
If you look at it from a future worth basis, here's what's happening.
When you buy the machine, you are paying $12,000 today, but you have an extra $3,300 in your pocket for 6 years that you can invest at 8% a year.
That investment each year is worth $24,208.56 at the end of the 6 years.
When you lease the machine, you keep your $12,000 which earns you $19042.49188 at the end of the 6 years, but you do not have the $3,300 to invest each year because that is being used to pay off the machine.
You earn more in 6 years from the payments you didn't have to make then from the 12,000 you would have been able to keep had you made the payments.
here's a year by year accounting from a future worth basis.
plan 1 is buying the machine. in this plan you get to keep 3300 per year that you can invest at 8%.
end of year 1 you have $3300.
end of year 2 you have $3300 * 1.08 = 3564 + 3300 = 6864
end of year 3 you have 6864 * 1.08 = 7413 + 3300 = 10713
end of year 4 you have 10713 * 1.08 = 11570 + 3300 = 14870
end of year 5 you have 14870 * 1.08 = 16059 + 3300 = 19359
end of year 6 you have 19359 * 1.08 = 20908 + 3300 = 24208
I truncated to the nearest dollar when showing you the results but kept the small change when doing the calculations on the calculator.
plan 2 is leasing the machine. in this plan you get to keep your 12000 but you do not have 3300 per year that you can invest anymore because it is being used to pay off the lease on the machine.
end of year 1 you have 12000 * 1.08 = 12960
end of year 2 you have 12960 * 1.08 = 13996
end of year 3 you have 13996 * 1.08 = 15165
end of year 4 you have 15165 * 1.08 = 16325
end of year 5 you have 16325 * 1.08 = 17631
end of year 6 you have 17631 * 1.08 = 19042
the present worth analysis takes all that into considereation.
present worth of 12,000 = 12,000
present worth of 3300 for 6 years = 15,255
if the plan is a winner on a present worth basis, it will also be a winner on a future worth basis.
you just have to be careful how to look at the impacts of each plan versus the other.
simplest thing to do is to present worth all cash flows for each plan which I did first.
revenues in each plan are positive.
costs in each plan are negative.
there were no revenues in either of these plan so we were just comparing costs.
plan 1 cost was 12,000 up front.
plan 2 cost was 3300 per year for 6 years present worthed at 8% per year.
if you need formulas i can supply them.
just let me know.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! .08*12000*6=5760 money invested at 8% for six years
6*3300=19800
12000+5760=17760
19800 is larger than 17760
if they purchase it it will cost 12000+5760
cost plus interest not earned
if they rent it will cost 19980-interest earned
696 interest 1 year 8700 on 12000-3300
432 interest 2 year 5400 on 8700-3300
168 3 year 2100 on 5400-3300
0 4 year 00000 on 2100-3300
696+432+168 =1296 interest for three years
19980-1296=18684 cost for leasing+interest for 3 years on the remainder of 12000
cost for purchasing=12000+5760(interest lost)=17760
so it still comes out better to buy it
actual costs
18684 versus 12000
Since the leasing is so much more than purchase the interest for six years really don't come into play here.
It would be significant if the leasing were cheaper.
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