Anne Hathaway has just bought the Shakespeare Apartments in the growing communit
ID: 2797195 • Letter: A
Question
Anne Hathaway has just bought the Shakespeare Apartments in the growing community of Elizabethtown. The price was $600,000 or $15,000 per unit. Ms. Hathaway assumed the original mortgage. The performance of the property over the past three years has averaged:
Rent Revenue (PGI) $100,000
Less Vacancy & Collection Loss (3%) (3,000)
EGI $97,000
Less: Operating Expenses (41,560)
Net Operating Income $55,440
After analyzing the rents of the Essex House and The Raleigh properties nearby, Ms. Hathaway feels she can raise the unit rents by $10 per month; however, this will increase the vacancies to 5%. She will then be able to refinance the property and withdraw $140,126.73 of tax-free (actually tax-deferred) monies.
The mortgage she assumed on purchase was originally $540,000 at 7½% annual interest payable in level monthly installments over 21 years. The mortgage was eight years old at the time of Ms. Hathaway’s purchase. The new mortgage would be for 25 years at 8½% annual interest payable in level monthly installments.
9. What is the amount of the new mortgage?
10. What is the loan-to-value ratio on the new mortgage?
11. What is the before tax cash flow under the new mortgage?
12. What is the amount of Ms. Hathaway’s equity investment with the new mortgage?
13. What do you believe Ms. Hathaway’s equity yield will be (approximately) with the new mortgage?
14. If she refinances, will Ms. Hathaway enjoy positive or negative leverage?
15. Do you think Ms. Hathaway should refinance the property and, if so, why?
Just need to know how to put on financial calculator thanks
Explanation / Answer
Assumed Mortgage =$540,000
Interest =7.50% per year or 0.625% per month
Time =21 years or 252 monthly periods
Monthly Payment =PMT(0.00625, 252, 540000) =$4,261.50
Annual Debt Service = $4261.50x12 =$51,138
Mortgage balance when she assumed =$540,000x(1.0065)96 - 4261.50x{(1.0065)96-1)/0.0065}
=$540,000x1.8187 - 4261.50x{(1.8187 -1)/0.00625}
=$1,005,811 - 558,236
=$423,873
3.) Current Rate of Interest =8.50% or 0.7083% monthly
Number of Payments Due =(21-8)x12 =156
Market Value of Assumed Loan = PV(0.007083, 156, 4261.50) =$401,571
4.) Loan to Value Ratio on the assumed Mortgage = 540,000/ 600,000 =0.90
5.) Effective Constant on Mortgage = Annual Debt Service/Mortgage Amount =51,138/540,000 =0.0947 or 9.47%
6.) Before Tax Cash Flow with Assumed Mortgage = Net Operating Income - Annual Debt Service
=$ 55,440 - 51,138
=$ 4,302
7.) Hathway's Down Payment =$600,000 - 540,000 =$ 60,000
8.) Number of Units =600,000/15,000 =40
Total Rent Increase Impact =$10 x 40 =$400
New Rent Revenue =$100,000 + 400=$100,400
New Vacancy Costs =5% of 100,400 =$0.05 x 100,400 =$5,020
New Estimated Gross Income =$100,400 - 5,020 =$95,380
Operating Expenses =$ 41,560
Net Operating Income =$95,380 - 41,560 =$53,820
9.) Loan Outstanding after 8 years = $423,873
10.) Loan to Value Ratio on the New Mortgage = 423,873/ 600,000 =0.7065
11.) New Interest =8.50% per year or 0.708% per month
Time =25 years or 300 monthly periods
Monthly Payment =PMT(0.00708, 300, 423873) =$3,413.14
Annual Debt Service =$3413.14x12 =$40,958
Before Tax Cash Flow with New Mortgage = Net Operating Income - Annual Debt Service
= $ 53,820 - 40,958
= $ 12,862
12.) Equity Component under New Mortgage =$600,000 - 423,873=$176,127
13.) Monthly Equity Yield Rate =(600,000/176,127)1/300 - 1 = 1.004094 - 1 =0.004094
Annual Equity Yield Rate = 0.004094 x 12 =0.0491 or 4.91%
14.) If she refinances, she will enjoy positive leverage only if the property prices have appreciated in the last 8 years.
15.) As the property prices have not appreciated, it does not make sense to refinance her existing mortgage loan.
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