Question

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An investor would like to purchase a new apartment property for $2 million. However, she faces the decision of whether to use 70 percent or 80 percent financing. The 70 percent loan can be obtained at 10 percent interest for 25 years. The 80 percent loan can be obtained at 11 percent interest for 25 years, NOI is expected to be $190,000 per year and increase at 3 percent annually, the same rate at which the property is expected to increase in value. The building and improvements represent 80 percent of value and will be depreciated over 275 years (1 - 27.5 per year). The project is expected to be sold after five years. Assume a 36 percent tax bracket for all income and capital gains taxes. a. What would the BTIRR and ATIRR be at each level of financing (assume monthly mortgage amortization)? BTIRR ATIRR 70% Loan 80% Loan b. What is the break-even interest rate (BEIR) for this project?

Answer 1

a. Computation of BTIRR and ATIRR

Valuation of IRR at 70% finance level
Years	Cash Flow	Value of Property	Interest(10%)	Net cash flow before tax	Tax	After tax CF
0	-20,00,000.0	20,00,000.00	0	-20,00,000.0		-20,00,000.00
1	1,90,000.00	20,60,000.00	140000	50,000.0	18,000.0	32,000.00
2	1,95,700.00	21,21,800.00	140000	55,700.0	20,052.0	35,648.00
3	2,01,571.00	21,85,454.00	140000	61,571.0	22,165.6	39,405.44
4	2,07,618.13	22,51,017.62	140000	67,618.1	24,342.5	43,275.60
5	2,13,846.67	23,18,548.15	140000	23,92,394.8	1,41,262.1	22,51,132.69
			IRR	5.89%		3.85%

Valuation of IRR at 80% finance level
Years	Cash Flow	Value of Property	Interest(11%)	Net cash flow before tax	Tax	After tax CF
0	-20,00,000.0	20,00,000.00	0	-20,00,000.0		-20,00,000.00
1	1,90,000.00	20,60,000.00	176000	14,000.0	5,040.0	8,960.00
2	1,95,700.00	21,21,800.00	176000	19,700.0	7,092.0	12,608.00
3	2,01,571.00	21,85,454.00	176000	25,571.0	9,205.6	16,365.44
4	2,07,618.13	22,51,017.62	176000	31,618.1	11,382.5	20,235.60
5	2,13,846.67	23,18,548.15	176000	23,56,394.8	1,28,302.1	22,28,092.69
			IRR	4.19%		2.74%

b. Break Even Interest Rate

The break even interest rate (BIR) is the level of interest rate at which the effect of borrowed funds on the investors’ equity return, and therefore the leverage effect, switches from positive to negative. More specifically:

If the mortgage interest rate is HIGHER than BIR ==> Negative Leverage

If the mortgage interest rate LOWER than BIR ==> Positive Leverage

In other words, Break even interest rate means maximum interest rate before negative Financial Leverage.

According to Brueggeman and Fisher (1993) BIR can be calculated as:

BIR = After-Tax IRR on Total Funds Invested/(1-investor’s tax rate).

Here,

AT 70% fund

BIR=0.0385/(1-0.36)

=0.0601

=6%

At 80% Level

BIR=0.0274/(1-0.36)

=0.0429

=4.29%

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