Question

The asking price for the property is $1,000,000; rents are estimated at $200,000 during the first year and are expected to grow at 5% per year. Vacancies and collection losses are expected to be 10% of rents. Operating expenses will be 35% of effective gross income. Capital expenditures will be 5% of effective gross income. A 30-year fixed rate loan fro 70 percent of the purchase price can be obtained at 10% interest rate. The property is expected to appreciate at 3% per year and is expected to be owned for seven years and then sold. The sale cost is 6% of the sale price.

The investor tells you he would also like to know how tax considerations affect your investment analysis. You determine that the building represent 90% of value and would be depreciated over 27.5 years. The potential investor indicates that he is in the 28% tax bracket. Capital gains tax rate is 20% while depreciation recapture tax rate is 25%.

A) Write down the cash flows pro forma for year 1 to 7

B) What is the investors expected before-tax internal rate of return on equity invested? Show work.

C) What is the investors expected after-tax internal rate of return on equity invested (ATIRR)? Show work.

Use financial calculator

Answer 1

(A) Cash Flow pro forma

Years	1	2	3	4	5	6	7
Rental Income	200,000	200,000	200,000	200,000	200,000	200,000	200,000
Increment	(1+5%)^0	(1+5%)^1	(1+5%)^2	(1+5%)^3	(1+5%)^4	(1+5%)^5	(1+5%)^6
Total Rental Income (A)	200,000	210,000	220,500	231,525	243,101	255,256	268,019
Vacancies and Collection losses (10%)* (A)	(20,000)	(21,000)	(22,050)	(23,153)	(24,310)	(25,526)	(26,802)
Gross Income (B)	180,000	189,000	198,450	208,372	218,791	229,730	241,217
Operating expenses (35%) (C)	(63,000)	(66,150)	(69,458)	(72,930)	(76,577)	(80,406)	(84,426)
Interest Expense (70%*10%* $ 1 Mn) (D)	(70,000)	(70,000)	(70,000)	(70,000)	(70,000)	(70,000)	(70,000)
Profit before tax and Dep (E=B-C-D)	47,000	52,850	58,992	65,442	72,214	79,324	86,791
Net of Tax (1-28%)*E	33,840	38,052	42,474	47,118	51,994	57,113	62,490
Savings on account of dep (F) (WN#1)	8,182	8,182	8,182	8,182	8,182	8,182	8,182
Cash flow from Operating activities (G = E+F)	42,022	46,234	50,656	55,300	60,176	65,295	70,672
Capex (5%)	(9,000)	(9,450)	(9,923)	(10,419)	(10,940)	(11,487)	(12,061)
Sale proceeds (WN#2)							1,156,081
Capital Gain Tax (WN#3)							(77,034)
Net Cash Flows	33,022	36,784	40,733	44,881	49,236	53,808	1,137,658

WN#1 Calculation of Savings on account of Depreciation Expense;

Purchase Value of Asset = 1,000,000

Building Block in above (90%) = 900,000

Life of asset = 27.5 Years

Annual Depreciation = 900,000/27.5 = 32,727

Savings (@25% recapture tax rate) = 32,727*25% = $ 8,182

Note - Depreciation on Capex is ignored.

WN#2 Calculation of Net Proceeds from Sale of Asset

Particulars	Value
Purchase Cost ($)	1,000,000
Annual Increment	3% p.a.
Holding Period	7 years
Sale Consideration net of cost => (1,000,000*(1+3%)^7)*(1-6%)	1,156,081

Note - Capex is ignored.

WN#3 Capital Gains

Particulars	Value
Purchase Price	1,000,000
Depreciation for 7 Years [32,727*7] (WN#1)	(229,089)
Book Value at the end of 7 years  (A)	770,911
Sale Consideration net of Cost (WN#2) (B)	1,156,081
Capital Gains (B-A)	385,170
Capital Gain Tax (20%)	77,034

Note - Capex is ignored.

(B)Calculating Equity IRR (before-tax) using a financial calculator.

Years	0	1	2	3	4	5	6	7
Profit before tax and Dep (E) (Part A)		47,000	52,850	58,992	65,442	72,214	79,324	86,791
Capex		(9,000)	(9,450)	(9,923)	(10,419)	(10,940)	(11,487)	(12,061)
Sale Proceeds								1,156,081
Net Cash Inflow before tax		38,000	43,400	49,069	55,023	61,274	67,837	1,230,811
Equity Cash Flow	(300,000)
IRR	32%

(C) Calculating Equity IRR (after-tax) using a financial calculator.

Years	0	1	2	3	4	5	6	7
Equity Cash Flow	(300,000)
Net Cash Flows (Part A)		33,022	36,784	40,733	44,881	49,236	53,808	1,137,658
IRR (After tax)	29%