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ou are considering the purchase of a quadruplex apartment building. Effective gr

ID: 2814086 • Letter: O

Question

ou 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?

Explanation / Answer

a. Overall Capitalization Rate

Effective gross income for first year

Gross Income - 33600

- Operating Exps - (13440)

Effective gross income = 20,160

Capitalization rate = Effective gross income/Purchase price of quadraplex

= 20160/200000 * 100

= 10.08%

b. Gross income multiplier

Effective gross income multiplier = Market price / Effective gross income

= 200000/33600

= 5.95

c. Equity Dividend Rate

Debt service cost = For 140000 @ 8% for 30 years

A = P(r(1+r)^n)/(1+r)^n - 1

= 140000(0.08(1+0.08)^30/(1+0.08)^30 - 1

= $12,332

So, Before-tax cash flow = NOI - Debt service

= $20,160 - $12,332

= $7828

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

= $7,828 / $60,000

= 13.05% approx.

d. Debt coverage ratio

DCR= NOI / debt service cost

= $20,160 / $12,332

= 1.63

e. Here, debt service is equal to the loan amount times the mortgage constant (contract interest rate plus principal amortization).

The mortgage constant is the stated interest rate plus the first-year principal payment divided by the loan amount.

Now, @ 140000, first year interest payment will be

I = PNR/100

= 140000*8%

= $11200

If he wants to keep debt service cost @ 1.2,

debt service cost will be = NOI/DCR

= 20160/1.2

= 16800

A = P(r(1+r)^n)/(1+r)^n - 1

16800 = P(0.08(1+0.08)^30/(1+0.08)^30 - 1

P = 16800*9.87/0.8696

= $190,680