Question

A company is trying to structure a loan with the Bank of California. The company would like to purchase a property for $2.5 million. The property is projected to produce a first-year NOI of $200,000. Loan: The lender will allow an 80 percent LTV loan on the property. It also requires a DCR in the first year of at 1.25. The contract (or the accrual) rate of interest on the loan is 12 percent. The lender is willing to allow the loan to negatively amortize; however, the loan will mature at the end of the five-year period. All loan payments are to be made monthly, and every year will be 10 percent higher than in the previous year. (I.e., loan payments in months 13-24 are 10 percent higher than in months 1-12. Loan payments in months 25-36 are 10 percent higher than in months 13-24. And so on for five years.) a. Calculate the loan balance be at the end of the fifth year. Show and explain all calculations.

Here is an Accrual loan condition, a.k.a negative amortization loan. Pay rate < Accrual Rate.

b. If the property value does not change, what will the loan-to-value ratio be at the end of the five-year period? Calculate. Show and explain all calculations.

c. Calculate what the monthly loan payment would instead need to be in order for the loan balance at the end of the first year to be equal to the loan balance at the beginning of the first year. Show a loan amortization table for this case, just for the first year: what would be the total loan payment? The principal payment? The interest payment?

Calculate. Show and explain all calculations

Answer 1

Loan amount = LTV ratio * Property value = 80%*2.5 million = $2,000,000

Total Payment for the first year = NOI/Debt service ratio = 200,000/1.25 = $160,000

Payment per month for the first year = 160000/12 = $13,333.33

Payment per month for the 2nd year = 13333.33*(1.10) = 14666.67

Payment per month for the 3rd year = 14666.67*(1.10) = 16133.33

Payment per month for the 4th year = 16,133.33*(1.10) = 17746.67

Payment per month for the 5th year = 17746.67*(1.10) = 19521.33

b)

Month	Opening Balance	Interest payment	Total Payment	Principal repayment	Ending balance	Loan to Value ratio
1	2,000,000.00	20,000.00	13,333.33	(6,666.67)	2,006,666.67	80.27%
2	2,006,666.67	20,066.67	13,333.33	(6,733.33)	2,013,400.00	80.54%
3	2,013,400.00	20,134.00	13,333.33	(6,800.67)	2,020,200.67	80.81%
4	2,020,200.67	20,202.01	13,333.33	(6,868.67)	2,027,069.34	81.08%
5	2,027,069.34	20,270.69	13,333.33	(6,937.36)	2,034,006.70	81.36%
6	2,034,006.70	20,340.07	13,333.33	(7,006.73)	2,041,013.43	81.64%
7	2,041,013.43	20,410.13	13,333.33	(7,076.80)	2,048,090.23	81.92%
8	2,048,090.23	20,480.90	13,333.33	(7,147.57)	2,055,237.80	82.21%
9	2,055,237.80	20,552.38	13,333.33	(7,219.04)	2,062,456.85	82.50%
10	2,062,456.85	20,624.57	13,333.33	(7,291.24)	2,069,748.08	82.79%
11	2,069,748.08	20,697.48	13,333.33	(7,364.15)	2,077,112.23	83.08%
12	2,077,112.23	20,771.12	13,333.33	(7,437.79)	2,084,550.02	83.38%
13	2,084,550.02	20,845.50	14,666.67	(6,178.83)	2,090,728.85	83.63%
14	2,090,728.85	20,907.29	14,666.67	(6,240.62)	2,096,969.48	83.88%
15	2,096,969.48	20,969.69	14,666.67	(6,303.03)	2,103,272.50	84.13%
16	2,103,272.50	21,032.73	14,666.67	(6,366.06)	2,109,638.56	84.39%
17	2,109,638.56	21,096.39	14,666.67	(6,429.72)	2,116,068.28	84.64%
18	2,116,068.28	21,160.68	14,666.67	(6,494.02)	2,122,562.30	84.90%
19	2,122,562.30	21,225.62	14,666.67	(6,558.96)	2,129,121.25	85.16%
20	2,129,121.25	21,291.21	14,666.67	(6,624.55)	2,135,745.80	85.43%
21	2,135,745.80	21,357.46	14,666.67	(6,690.79)	2,142,436.59	85.70%
22	2,142,436.59	21,424.37	14,666.67	(6,757.70)	2,149,194.29	85.97%
23	2,149,194.29	21,491.94	14,666.67	(6,825.28)	2,156,019.57	86.24%
24	2,156,019.57	21,560.20	14,666.67	(6,893.53)	2,162,913.10	86.52%
25	2,162,913.10	21,629.13	16,133.33	(5,495.80)	2,168,408.89	86.74%
26	2,168,408.89	21,684.09	16,133.33	(5,550.76)	2,173,959.65	86.96%
27	2,173,959.65	21,739.60	16,133.33	(5,606.26)	2,179,565.91	87.18%
28	2,179,565.91	21,795.66	16,133.33	(5,662.33)	2,185,228.24	87.41%
29	2,185,228.24	21,852.28	16,133.33	(5,718.95)	2,190,947.19	87.64%
30	2,190,947.19	21,909.47	16,133.33	(5,776.14)	2,196,723.32	87.87%
31	2,196,723.32	21,967.23	16,133.33	(5,833.90)	2,202,557.22	88.10%
32	2,202,557.22	22,025.57	16,133.33	(5,892.24)	2,208,449.46	88.34%
33	2,208,449.46	22,084.49	16,133.33	(5,951.16)	2,214,400.62	88.58%
34	2,214,400.62	22,144.01	16,133.33	(6,010.67)	2,220,411.30	88.82%
35	2,220,411.30	22,204.11	16,133.33	(6,070.78)	2,226,482.08	89.06%
36	2,226,482.08	22,264.82	16,133.33	(6,131.49)	2,232,613.56	89.30%
37	2,232,613.56	22,326.14	17,746.67	(4,579.47)	2,237,193.03	89.49%
38	2,237,193.03	22,371.93	17,746.67	(4,625.26)	2,241,818.30	89.67%
39	2,241,818.30	22,418.18	17,746.67	(4,671.52)	2,246,489.81	89.86%
40	2,246,489.81	22,464.90	17,746.67	(4,718.23)	2,251,208.05	90.05%
41	2,251,208.05	22,512.08	17,746.67	(4,765.41)	2,255,973.46	90.24%
42	2,255,973.46	22,559.73	17,746.67	(4,813.07)	2,260,786.53	90.43%
43	2,260,786.53	22,607.87	17,746.67	(4,861.20)	2,265,647.73	90.63%
44	2,265,647.73	22,656.48	17,746.67	(4,909.81)	2,270,557.54	90.82%
45	2,270,557.54	22,705.58	17,746.67	(4,958.91)	2,275,516.44	91.02%
46	2,275,516.44	22,755.16	17,746.67	(5,008.50)	2,280,524.94	91.22%
47	2,280,524.94	22,805.25	17,746.67	(5,058.58)	2,285,583.53	91.42%
48	2,285,583.53	22,855.84	17,746.67	(5,109.17)	2,290,692.69	91.63%
49	2,290,692.69	22,906.93	19,521.33	(3,385.59)	2,294,078.29	91.76%
50	2,294,078.29	22,940.78	19,521.33	(3,419.45)	2,297,497.74	91.90%
51	2,297,497.74	22,974.98	19,521.33	(3,453.64)	2,300,951.38	92.04%
52	2,300,951.38	23,009.51	19,521.33	(3,488.18)	2,304,439.56	92.18%
53	2,304,439.56	23,044.40	19,521.33	(3,523.06)	2,307,962.62	92.32%
54	2,307,962.62	23,079.63	19,521.33	(3,558.29)	2,311,520.92	92.46%
55	2,311,520.92	23,115.21	19,521.33	(3,593.88)	2,315,114.79	92.60%
56	2,315,114.79	23,151.15	19,521.33	(3,629.81)	2,318,744.61	92.75%
57	2,318,744.61	23,187.45	19,521.33	(3,666.11)	2,322,410.72	92.90%
58	2,322,410.72	23,224.11	19,521.33	(3,702.77)	2,326,113.49	93.04%
59	2,326,113.49	23,261.13	19,521.33	(3,739.80)	2,329,853.30	93.19%
60	2,329,853.30	23,298.53	19,521.33	(3,777.20)	2,333,630.50	93.35%

Loan to value ratio = 2333,630.50/2500,000 = 93.35%

c) For laon value to stay constant, the amount of payment should be equal to the amount of interest accrued, such that there is no principal balance repayment. The first year amortization schedule will be:

Month	Opening Balance	Interest payment	Total Payment	Principal repayment	Ending balance
1	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
2	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
3	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
4	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
5	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
6	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
7	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
8	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
9	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
10	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
11	2,000,000.00	20,000.00	20,000.00	0.00	2,000,000.00
	TOTAL	220,000.00	220,000.00	0.00