Companies often face the choice of buying or leasing equipment. Suppose a piece
ID: 2728963 • Letter: C
Question
Companies often face the choice of buying or leasing equipment. Suppose a piece of equipment costs $20,000. Typically, companies depreciate the value of their equipment over 5 years for tax purposes.
(a) Suppose you pay cash for the equipment. The total cost over 5 years is the principal plus 5 years of compound interest. If savings interest rate is 3% per year compounded monthly, what is the total cost of the equipment for the 5 year period?
(b) Suppose instead the company borrows the cost from a bank. The bank will charge 5% interest per year. How much is the future value of the $20,000 that the bank plans to have at the end of the 5 years, again using monthly compounding?
(c) The bank gets its money from depositors. If the bank has to pay off the depositors the amount in (a), then how much profit does the bank make from the loan at the end of 5 years?
(d) Now the company has to make monthly payments in order to re-pay the loan. This can be calculated by equating the future value of the $20,000 at 5% interest to the future value of an ordinary annuity paying 5% interest. Calculate the monthly payment using
P(1 + )nt = m[ (1 + )nt – 1]/(r/n)
(e) Finally, the company could lease the equipment at $650 per month for the 5 years. Now if you did the problem right, the cost of plan (e) > plan (b) > plan (a). So why would someone choose plan (b) over plan (a)?
(f) Plan (d) is the most expensive option. So why would someone choose plan (d) over two other cheaper options?
Explanation / Answer
For calculating componded amount payable, we use, A = P (1+i)n
where, A = Amount
P = Principle
i = Interest for the time period
n = number of years X time period
(a) Suppose we pay cash at the beginning, opportunity cost for purchase of the equipment is 3% i.e., Interest lost on $20000
Cost of the equipment = Compounced amount at the end of 5 years
= P(1+i)n
= $20000[1+ (0.03/12)]5x12
= $ 23232.34
(b) If the company borrows @5%, then A = P(1+i)n
= $20000[1+(.05/12)]5x12
= $ 25672.29
(c) That means the bank receives repayment @ 5% and pays interest to depositors @ 3%
Profit to the bank = (b) above - (a) above
= $25672.29 - $23232.34
= $ 2439.95
(d) Monthly EMI = Amount/PVAF(5%/12 , 5yearsx12)
= $20000/PVAF(0.00417, 60 )
= $20000/52.9856
= $377.46
(e) If company leases it out for $650 per month, then total inflow for 5 years = $650x12monthsx5years
= $39000
If company opts for option (a), profit = $39000- $23232.34
= $15767.66
If company opts for option (b), profit = $39000- $25672.29
= $13327.71
Option (b) would be opted
(i) if there are financial crunches and cannot afford for the initial outlay of $20000
(ii) the opportunity cost of the company is higher than the Bank interest rate i.e., the company can earn more than 5% on $20000 for 5 years
(f) plan (d) would be choosen if the company wishes to minimize its interest expenses and has surplus cash to pay off the installments
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