A real estate investor has the following information on an apartment building: P
ID: 2776163 • Letter: A
Question
A real estate investor has the following information on an apartment building:
Purchase Price is $1,125,000 with acquisition costs of $50,000
33,600 leasable square feet
Initial rent of $1.5/sq. ft. per month and will increase at the beginning of each year for 5 percent per year. For example, the first year rent from month 1 to month 12 is $1.5/sq. ft., the 2nd year rent from month 1 to month 12 is $1.575 ($1.5*(1+5%)), and so on.
Vacancy rate of 5% of gross rent per month.
Operating expenses are 25% of effective gross income
Three financing choices:
1. Mortgage with 75% LTV ratio, 20 years, monthly payments and 5% annual rate;
2. Mortgage with 80% LTV ratio, 20 years, monthly payments and 6% annual rate;
3. Mortgage with 85% LTV ratio, 20 years, monthly payments and 6.5% annual rate;
Holding period is 3 years (36 months) and the capital improvement expenditure is assumed to be $20,000 at the end of the first year only (12 months).
Expected increase in value is 50% in total when sold in year 3 (36 months), 5% selling expenses
80% depreciable with monthly depreciation.
Investor’s tax rate is 33%, and capital gain tax rate is 15%.
Questions:
1. Compute equity after-tax cash flows from month 1 to month 36 for each financing choice.
2. What is the equity after-tax annual return (internal rate of return) for each financing choice and which choice would you like to make?
Comment
Explanation / Answer
Mortgage with 75% LTV, Monthly Payments and 5% annual Rate
Loan amount = $1,125,000 * 0.75 = $ 843,750
Interest rate = 5%/12 = 0.4167% or 0.004167
Period =20 years or 20*12 – 240 months
EMI = 843,750 * [ (0.004167 * (1.004167)^240)/(1.004167)^240 -1)]
= 843,750 * [(0.004167 * 2.712856)/(2.712856 -1)] = 843,750 * 0.0113045/1.712856
= 843,750 * 0.00659978 = $ 5,568.56
Loan o/s after 36 months = 843750 * [(1.004167)^240 – (1.004167)^36)/(1.004167)^240 -1)]
= 843750 * [(2.712856 – 1.1614861)/(2.712856-1)]
= 843750 * (1.5513699/1.712856) = $ 764,202.22
Loan O/s Afer 12 months = 843750 * 1.6616899/1.712856= 818,545.67
Interest for first year = 5568.56 *12 – (843750 – 818545.67) = 66822.72 - 25204.33
= 41618.39
Loan O/s After 24 months = 843750 * 1.60791/1.712856 = 792,051.00
Mortgage with 80% LTV, Monthly Payments and 6% annual Rate
Loan amount = $1,125,000 * 0.80 = $ 900,000
Interest rate = 6%/12 = 0.5% or 0.005
Period =20 years or 20*12 – 240 months
EMI = 900,000 * [ (0.005 * (1.005)^240)/(1.005)^240 -1)]
= 900,000 * [(0.005 * 3.310204)/(3.310204 -1)] = 900,000 * 0.016551/2.310204
= 900,000 * 0.0071643 = $ 6,447.88
Loan o/s after 36 months = 900,000 * [(1.005)^240 – (1.005)^36)/(1.005)^240 -1)]
= 900,000 * [(3.310204 – 1.1966805)/(3.310204-1)]
= 900,000 * (2.113523/2.310204) = $ 823,377.99
Loan O/S after 12 months = 900000 *2.248526/2.310204 = 875971.80
Loan O/s after 24 months = 900,000 * 2.183044/2.310204 = 850461.60
Mortgage with 85% LTV, Monthly Payments and 6.5% annual Rate
Loan amount = $1,125,000 * 0.85 = $ 956,250
Interest rate = 6.5%/12 = 0.5417% or 0.005417
Period =20 years or 20*12 – 240 months
EMI = 956,250 * [ (0.005417 * (1.005417)^240)/( 1.005417)^240 -1)]
= 956,250 * [(0.005417 * 3.656738)/( 3.656738 -1)] = 900,000 * 0.019809/2.656738
= 956,250 * 0.007456 = $ 7,129.77
Loan o/s after 36 months = 956,250 * [(1.005417)^240 – (1.005417)^36)/( 1.005417)^240 -1)]
= 956,250 * [(3.656738 – 1.214686)/( 3.656738-1)]
= 956,250 * (2.44205/2.656738) = $ 878,977.19
Loan O/s after 12 months = 956250 * 2.589762/2.656738 = 932143.03
Loan O/s after 24 months = 956250 * 2.5183/2.656738 = 906421.48
Calculation of Cash flows under the financing options Year 1 Year 2 Year 3 Monthly rental 47880.00 50274.00 52787.70 Annual Rental 574560.00 603288.00 633452.40 Operating Expenses 143640.00 150822.00 158363.10 Depreciation (1125000*80%)/36 300000.00 300000.00 300000.00 Capital Improvement Expenditure 20000.00 Interest Financing Option I 41618.39 40328.05 38973.94 Financing Option II 53346.36 51864.36 50290.95 Financing Option III 61450.27 59835.69 58112.95 EBIT Option I 69301.61 112137.95 136115.36 Option II 57573.64 100601.64 124798.35 Option III 49469.73 92630.31 116976.35 Tax (33%) Option I 22869.53 37005.52 44918.07 Option II 18999.30 33198.54 41183.46 Option III 16325.01 30568.00 38602.20 Net Income Option I 46432.08 75132.43 91197.29 Option II 38574.34 67403.10 83614.89 Option III 33144.72 62062.31 78374.15 Net Cast Flow (NI - Loan Pmt + Depn) Financing Option I 279609.36 308309.71 324374.57 Financing Option II 261199.78 290028.54 306240.33 Financing Option III 247587.48 276505.07 292816.91 Project Cash flows under different financing options & IRR Year 0 Year 1 Year 2 Year 3 Financing Option I Purchase Price -1125000 Acquisition Costs -50000 Net Cash Flow 279609.36 308309.71 324374.57 Net realisation on sale of property 1362656.25 Total Cash Flows -1175000 279609.3587 308309.707 1687030.821 Internal Rate of Return 30% Financing Option II Purchase Price -1125000 Acquisition Costs -50000 Net Cash Flow 261199.78 290028.54 306240.33 Net realisation on sale of property 1362656.25 Total Cash Flows -1175000 261199.7788 290028.539 1668896.585 Internal Rate of Return 28% Financing Option III Purchase Price -1125000 Acquisition Costs -50000 Net Cash Flow 247587.48 276505.07 292816.91 Net realisation on sale of property 1362656.25 Total Cash Flows -1175000 247587.4791 276505.068 1655473.165 Internal Rate of Return 27% As IRR of financing option I viz., Mortgage of LTV75% at 5% is higher than others, the same can be opted for working year 1 year2 year3 Total leasable area (sq ft) 33600 Vacancy rate 5% Rent (Per Sqft) per month 1.5 1.575 1.65375 Lease growth rate (per annum) 5% Monthly retnal = leasable area * rent* (1-vacancy rate) Operating expenses at 25% of gross income Financing Choices Option I Option II Option III Loan Amount 843750 900000 956250 Monthly Instalment 5568.56 6447.88 7129.77 Loan O/s after 12 months 818545.67 875971.8 932143.03 Loan O/s after 24 months 792051 850461.6 906421.48 Loan O/s after 36 months 764202.22 823377.99 878977.19 Interest for First Year 41618.39 53346.36 61450.27 Interest for Second Year 40328.05 51864.36 59835.69 Interest for third year 38973.94 50290.95 58112.95 Property Value 1125000 Appreciation after 3 years 50% Sale Value 1687500 Less Selling Expenses 1603125 Capital Gains Tax 15% Net Resale realisation 1362656.25Related Questions
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