Question

An investor would like to purchase a new apartment property that costs $2 million with an initial year NOI of $190,000, and an expected growth rate of 3% per year (in income and value).

The building and improvements represent 80% of value and will be depreciated over (1 ÷ 27.5 per year). Assume a 36% tax bracket for all income and capital gains taxes. The investor faces the decision of whether to use 70% or 80% financing.

The 70% loan can be obtained at 10% interest for 25 years. The 80% loan can be obtained at 11% interest for 25 years.Develop a 10-year pro forma.

(a) Use the pro forma to determine the before-tax IRR (BTIRR) and after-tax IRR (ATIRR) for each level of financing (assume monthly mortgage amortization).

(b) What is the break-even interest rate (BEIR) for this project?

(c) What is the marginal cost of the 80% loan? What does this mean?

(d) Does each loan offer favorable financial leverage? Which would you recommend?

Answer 1

Net operating income represent the cash flow before the factors such as taxes and finance costs.

a. Value of property for 5 years will be calculated with the help of the following formula

= V * (1 + i )ⁿ

where , V = Value of the property , i = growth rate , n= number of years.

V= $ 2000000 , i = 0.03 , n = 5 years

Putting the value , we get

2000000 (1+0.03)⁵

2000000 (1.03)⁵

$ 2318548

Value of propert after 5 years will be $ 2318548.

Interest per annum when loan is 70 % financing , will be calculated with the help of following formula.

Interest per annum = Value of property * interest rate * Loan proportion

Value of property = $ 2000000 * 0.10 * 0.70

= $ 140000

Interest per annum is $ 140000.

Calculation of internal rate of return before tax

Working

Internal rate of return before tax is 5.89% .

Calculation of internal rate of return after tax.

after tax internal rate of return is 3.85 %.

Interest per annum when loan is 80 % financing.

Interest per annum = Value of property * Loan financing * interest rate

= $ 2000000 * 0.80 * 0.11

= $ 176000

Calculation of before tax internal rate of return

Calculation

Calculation of IRR after tax

Working

After tax IRR is 2.74 %.

b . Break even interest rate (when loan is 70 %) will be calculated as

Break even interest rate = After tax interest rate

1 - Tax rate

= 3.85 %

1- 36 %

= 6.01 %

Break even interest rate is 6.01 % .

Break even interest rate (when loan is 80 %) will be calculated as

Break even interest rate =

After tax interest rate

1 - Tax rate

2.74 %

1- 36 %

= 4.28 %

c. Marginal cost will be calculated as

Marginal cost = Interest rate on 80 % loan - Interest rate on 70 % loan

= 11 % - 10 %

= 1 %

Marginal cost for 80 % loan is 1 %.

d.

From the above table , it is clear that loan offers favourable financial leverage when loan financing is 70 %.