You are considering the purchase of a quadruplex apartment building. Effective gross income during the first year of operations is expected to be $33,600 ($700 per month per unit). First-year operating expenses are expected to be $13,440 (at 40 percent of EGI). Ignore capital expenditures. The purchase price of the quadruplex is $200,000. The acquisition will be financed with $60,000 in equity and a $140,000 standard fixed-rate mortgage. The interest rate on the debt financing is 8 percent and the loan term is 30 years. Assume, for simplicity, that payments will be made annually and that there are no up-front financing costs.

a. What is the overall capitalization rate?
b. What is the effective gross income multiplier?
c. What is the equity dividend rate (the before-tax return on equity)?
d. What is the debt coverage ratio?
e. Assume the lender requires a minimum debt coverage ratio of 1.2. What is the largest loan that you could obtain if you decide that you want to borrow more than $140,000?

(a) The overall capitalization rate 10.08%

(b) The effective gross income multiplier is 5.95

(c) The equity dividend rate 12.87 %

(d) The debt coverage ratio $1.62

(e) The largest loan that you could obtain is $189,130

Explanation:

(a).

NOI = EGI – operating expenses= $33,600 – $13,440= $20,160

NOI / Market price = $20,160 / $200,000 = 10.08 %

(b).

Market price / Effective gross income = $200,000 / $33,600 = 5.95

(c).

Debt service = $12,436, as calculated below

N=30, I/YR=8, PV=$140,000 , PMT=? , FV =0

Before-tax cash flow = NOI - Debt service

                               = $20,160 - $12,436

                                 = $7,724

Equity dividend rate = Before-tax cash flow / equity invested

                                 = $7,724 / $60,000

                                 = 12.87 %

(d).

Debt Coverage Ratio = NOI / debt service

                                    = $20,160 / $12,436

                                   = $1.62

(e).

Debt service must be such that the following relationship holds:

(NOI/DEBT SERVICE) ≥1.2

But, debt service is equal to the loan amount times the mortgage constant (contract interest rate plus principal amortization). Thus, we can rewrite the above expression as

(NOI/LOAN AMOUNT*MORTGAGE CONSTANT) ≥1.2

(NOI/1.2* MORTGAGE CONSTANT)=LOAN AMOUNT

20160/(1.2*0.0888)=LOAN AMOUNT

The mortgage constant is the stated interest rate plus the first-year principal payment divided by the loan amount (1,236/140 000 = .0088), or .0888.

$189,130 = loan amount

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