Question

our firm is purchasing a new telephone system, which will last for four years.There are two alternatives: purchase outright or lease. If the system is purchased, there is an upfront cost of 150K. If the system is leased from the manufacturer, then the firm must pay 4K at the end of each month for four years. Your firm can borrow from its local bank at an interest rate of 5% APR with semiannual compounding. With alternative is best?

Can someone explain how they figured out the monthly payment of 3,450.9 if take the loan and got a total cost of 173,867 for leasing. I'm not sure how to do it.

Answer 1

Total Value of Purchasing Option			150 K
Total Value of Leasing Option
Toal Monthly Payment		PMT	4K
No of Payments		N	48 Months
Interest Rate		I/Y
Annual Borrowing Rate		5%
Semi Annual		2.50%
Effective Annual Borrowing
Rate with SemiAnnual Compounding
Formula	(1*1.025*1.025)-1*100
	5.0625
So therefore I/Y comes out to be 5.0625 %
Monthly I/Y		5.0625/12
	=	0.421875
Using Financial Calculator Present Value of Leasing Option is
		173478.47
Leasing Cost Comes out to be 173478.47 while cash Cost is 150000
Therefore, Purchase Outright is better

Explanation for Bank Option:

In the Second Option cost of leasing Option is 173867 and Total Period N is 48, and PMT is 3450.90. Bank has calculated the Present value of the Total Amount Paid with their effective interest rate over the period.