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

Show all work as well as the formulas you used.

Answer 1

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 %