# Solved Question: A property that can be purchased for \$1.7 million

## 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

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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