Question

Hansus Enterprises is a start-up small business specializing in software systems for machine-based high-school student tutoring in science and math. Sheryl Hansus, the owner, has spoken with lenders to obtain a loan of $50,000 now (year 0), and the same amount in years 3 and 6. Two different repayment schedules are available. They are: Schedule A: Pay a uniform amount of $19,500 in years 3 through 12. Schedule B: Pay a uniform amount of $20,000 in years 1 through 6, with “balloon” payments of an additional $20,000 in year 2 and a final amount of $40,000 in year 7. To assist in the decision of which schedule to select, determine the following: (a) Total amount repaid for each schedule. Which is smaller? (b) The equivalent annual worth of the loan amounts and of the repayments at i = 5% per year over a 12-year evaluation period. Which schedule has the smaller loss per year? Why is this the case?

Answer 1

	Schedule A
Year	Cash flow	Amount $	PV at 5%	Discounted Value $
0	Loan Amount	50,000.00	1	50,000.00
1	Annual repayment	-	0.9524	-
2	Annual repayment	-	0.9070	-
3	Additional loan amount	50,000.00	0.8638	43,191.88
3	Annual repayment	(19,500.00)	0.8638	(16,844.83)
4	Annual repayment	(19,500.00)	0.8227	(16,042.70)
5	Annual repayment	(19,500.00)	0.7835	(15,278.76)
6	Additional loan amount	50,000.00	0.7462	37,310.77
6	Annual repayment	(19,500.00)	0.7462	(14,551.20)
7	Annual repayment	(19,500.00)	0.7107	(13,858.29)
8	Annual repayment	(19,500.00)	0.6768	(13,198.37)
9	Annual repayment	(19,500.00)	0.6446	(12,569.87)
10	Annual repayment	(19,500.00)	0.6139	(11,971.31)
11	Annual repayment	(19,500.00)	0.5847	(11,401.25)
12	Annual repayment	(19,500.00)	0.5568	(10,858.33)
	Net Present Value of Loan			(6,072.25)
	Present Value of loan repayment			(136,574.90)
	Schedule B
Year	Cash flow	Amount $	PV at 5%	Discounted Value $
0	Loan Amount	50,000.00	1	50,000.00
1	Annual repayment	(20,000.00)	0.9524	(19,047.62)
2	Annual repayment	(40,000.00)	0.9070	(36,281.18)
3	Additional loan amount	50,000.00	0.8638	43,191.88
3	Annual repayment	(20,000.00)	0.8638	(17,276.75)
4	Annual repayment	(20,000.00)	0.8227	(16,454.05)
5	Annual repayment	(20,000.00)	0.7835	(15,670.52)
6	Additional loan amount	50,000.00	0.7462	37,310.77
6	Annual repayment	(20,000.00)	0.7462	(14,924.31)
7	Annual repayment	(40,000.00)	0.7107	(28,427.25)
	Net Present Value of Loan			(17,579.03)
	Present Value of loan repayment			(148,081.68)
	Repayment amount in Schedule A is smaller than amount in Schedule B.
	Present value annuity factor in Schedule A = 10.4733
	Present value annuity factor in Schedule B = 7.3964
	Equivalent Annual Net worth of Schedule A = (6,072.25/10.4733) = ( 579.78)
	Equivalent Annual Net worth of Schedule B = (17,579.03/7.3964) = ( 2,376.70)