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
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