You are considering the purchase of a quadruplex apartment. Effective gross income (EGI) 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 eight 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.
- What is the overall capitalization rate?
- What is the effective gross income multiplier?
- What is the equity dividend rate (the before-tax return on equity)?
- What is the debt coverage ratio
- Assume the lender requires a minimum debt coverage ratio of 1.2. What is the largest loan that you could obtain if you decide to borrow more than $140,000?
. What is the overall capitalization rate?
Solution: NOI = EGI – operating expenses
= $33,600 – $13,440
= $20,160
NOI / Market price = $20,160 / $200,000 = 10.08 percent
- What is the effective gross income multiplier?
Solution: Market price / Effective gross income = $200,000 / $33,600 = 5.95
- What is the equity dividend rate (the before-tax return on equity)?
Solution:
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 percent
- What is the debt coverage ratio?
Solution: DCR= NOI / debt service
= $20,160 / $12,436
= 1.62
- Assume the lender requires a minimum debt coverage ratio of 1.2. What is the largest loan that you could obtain if you decide to borrow more than $140,000?
Solution: Debt service must be such that the following relationship holds:
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
Rearranging,
or,
For our problem,
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
