Description
Question:
A property that can be purchased for $1.7 million has an expected first-year net operating income of $190,000. An investor is considering two loan alternatives:
LOAN A: a 70% loan-to-value ratio, with interest at 7.5% per annum; the loan will require level monthly payments to amortize the principal over 20 years.
LOAN B: an 80% loan-to-value ratio, with interest at 8% per annum; this loan will require level monthly payments to amortize the principal over 25 years.
For each loan, determine:
1) The expected before-tax cash flow (NOI – annual debt service) as a percentage of the equity investment
2) The actual before-tax cash flow as a percentage of the equity investment, if the actual net operating income falls 10% below expectations
3) The percentage by which actual net operating income can fall below expectations before it is just sufficient to provide for annual debt service
Answer:
Property Price = $ 1700000
Loan A: Loan to Value Ratio = 70%
Investor’s Equity = 30% and Loan =70% (of the purchase price)
Investor’s Equity = 0.3 x 1700000 = $ 510000 and Loan = $ 1190000
Interest Rate = 7.5% per annum or 0.625% per month
Loan Period = 20 years or 240 months.
Let monthly repayments be Ka $
Therefore, 1190000 = Ka x (1/0.00625) x [1-{1/(1.00625)^(240)}]
Ka = $ 9586.56 per month
Annual Debt Service = 12 x Ka = $ 115038.72
Annual NOI = $ 190000
Before Tax Cash Flow (BTCF) = NOI – Annual Debt Service = $ 74961.28
BTCF as % of Investor’s Equity = (74961.78 / 510000) x 100 = 14.698 %
Actual NOI = 0.9 x Expected NOI = 0.9 x 190000 = $ 171000
Actual BTCF = Actual NOI – Annual Debt Service = 171000 – 115038.72 = $ 55961.28
Actual BTCF as % of Investor’s Equity = (55961.28 / 510000) x 100 = 10.973 %
Let the % by which NOI needs to fall so as to just cover the annual debt service be x
Therefore, [1 – (x/100)] x 190000 = 115038.72
[1 – (x/100)] = (115038.72 / 190000)
x = 39.453 %
Loan B: Loan to Value Ratio = 80%
Investor’s Equity = 20% and Loan =80% (of the purchase price)
Investor’s Equity = 0.2 x 1700000 = $ 340000 and Loan = $ 1360000
Interest Rate = 8% per annum or 0.666% per month
Loan Period = 25 years or 300 months.
Let monthly repayments be Kb $
Therefore, 1360000 = Ka x (1/0.00666) x [1-{1/(1.00666)^(300)}]
Kb = $ 10489.49 per month
Annual Debt Service = 12 x Kb = $ 125873.88
Annual NOI = $ 190000
Before Tax Cash Flow (BTCF) = NOI – Annual Debt Service = $ 64126.12
BTCF as % of Investor’s Equity = (64126.12 / 340000) x 100 = 18.86 %
Actual NOI = 0.9 x Expected NOI = 0.9 x 190000 = $ 171000
Actual BTCF = Actual NOI – Annual Debt Service = 171000 – 125873.88 = $ 45126.12
Actual BTCF as % of Investor’s Equity = (45126.12 / 340000) x 100 = 13.272 %
Let the % by which NOI needs to fall so as to just cover the annual debt service be y
Therefore, [1 – (x/100)] x 190000 = 125873.88
[1 – (x/100)] = (125873.88 / 190000)
y = 33.75 %
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