# Decimate Real Estate

At least try to complete the problem without looking, but it’s from CFAI volume 5, Page 17 (reading 46) if you get lost. Good luck. 1. NOI is 64,000 2. Price is 525,000 3. Improvements make up 85.9% of the price. Using a 27.5-year life, SLD gives 16,399 annual tax depreciation. 4. Equity cont.: 131,250 5. Debt cont.: 30-year 8% fixed rate mortgage for 393,750. Monthly payment: 2,889.20. LTV ratio: 75% 6. 36% marginal income tax; 20% capital gains tax; 25% recaptured depreciation tax. 7. Required after-tax return: 12% 8. Holding period: 4 years. NOI expected to grow over holding period 5% annually. Market value at end of year 4 is 777,924. Selling costs are 7% of sales price (market value). Outstanding loan balance at end of year 4 is 378,862. 9. Annual compounding used for the equity TVM calculations. A. Determine taxes payable (years 1 through 4) B. Determine after-tax cash flow (years 1 through 4) C. Determine after-tax equity reversion (end of year 4) D. Calculate NPV of the investment (12%) E. Calculate IRR of the investment F. Explain using the NPV and IRR rules why an investor would or would not invest in this real estate venture.

I took a stab at it, and got caught with the equity reversion calc, I just blanked out. For A: Yr 1 5839.1534 Yr 2 7089.4362 Yr 3 8405.4765 Yr 4 9790.8311 For B: Yr 1 10380.7171 Yr 2 12603.4422 Yr 3 14943.0692 Yr 4 17405.922

What’s the growth in NOI? What’s the interest payment per year?

chad17 Wrote: ------------------------------------------------------- > What’s the growth in NOI? What’s the interest > payment per year? Growth in NOI is given as 5% a year. I took the mortgage info, converted everything into a monthly figure and used my calculator’s “amort” function to find the interest payments for periods 1-12, 13-24, 25-36, 37-48.

I just went to check the formulas, looks like I messed up with ATCF, and probably taxes paid as well. Damnit!

Dude, I use Schweser and in that it says: Interest expense has been determined from a loan amortization schedule. Since you are not asked to construct an amortization table on the exam, this would either be given on the exam, or the loan would be interest only.

chad17 Wrote: ------------------------------------------------------- > Dude, I use Schweser and in that it says: > > Interest expense has been determined from a loan > amortization schedule. Since you are not asked to > construct an amortization table on the exam, this > would either be given on the exam, or the loan > would be interest only. I hope that’s the case, I actually learned this method for L1 when calculating lease payments.

Good job on A! (NOI - Dep. - Interest paid) * marginal tax rate = Income tax payable Thank god interest paid is given. At this point, re-learning how to construct an amortization table would probably put me over the edge! However, are we positive we won’t need to know how to do this for mortgage backed securities? B. should be: NOI - Debt service - Tax payable (from A) = ATCF Yr 1 = 23,491 Yr 2 = 25,441 Yr 3 = 27,484 Yr 4 = 29,627 C is CAPITAL GAINS: (Sales price - Selling costs) - (Purchase price - Accumulated dep.) - Recaptured dep* (777,924 - (777,924 * 0.07)) - (525,000 - 65,596) - 65,596 = 198,469 *property appreciates over holding period, depreciation must be recaptured TAXES: Tax on capital gain: 198,469 * 0.20 = 39,694 Tax on recap depreciation: 65,596 * 0.25 = 16,399 Total taxes due on sale: 16,399 + 39,694 = 56,093 AFTER TAX EQUITY REVERSION: Sales price - Selling expenses - Balance on debt - Total taxes due on sale 777,924 - (777,924 * 0.07) - 344,607 - 56,093 = 288,514 D. Yr 1 23,491 / 1.12 Yr 2 25,441 / (1.12)^2 Yr 3 27,484 / (1.12)^3 Yr 4 (29,627 + 288,514) / (1.12)^4 Sum: 263,022.44 Equity outlay: 131,250 NPV: 131,752.44 E. Use calculator to obtain IRR ~ 37.14% F. Decision is to buy based on NPV and IRR, which are greater than zero and 12%, respectively.

cjones65 Wrote: ------------------------------------------------------- > Good job on A! > > (NOI - Dep. - Interest paid) * marginal tax rate = > Income tax payable > > I have a question for you that I got stuck on > myself: How did you calculate interest paid? It > should have been Yr1: 31,381, Yr2: 31,108, Yr3: > 30,812, Yr4: 30,492. You seem to have gotten it > correct, but I was wondering the best way to > calculate it since it’s kind of important for the > whole problem! > > B. should be: > > NOI - Debt service - Tax payable (from A) = ATCF > > Yr 1 = 23,491 > Yr 2 = 25,441 > Yr 3 = 27,484 > Yr 4 = 29,627 > > C is > > CAPITAL GAINS: > (Sales price - Selling costs) - (Purchase price - > Accumulated dep.) - Recaptured dep* > > (777,924 - (777,924 * 0.07)) - (525,000 - 65,596) > - 65,596 = 198,469 > > *property appreciates over holding period, > depreciation must be recaptured > > TAXES: > Tax on capital gain: > 198,469 * 0.20 = 39,694 > > Tax on recap depreciation: > 65,596 * 0.25 = 16,399 > > Total taxes due on sale: > 16,399 + 39,694 = 56,093 > > AFTER TAX EQUITY REVERSION: > Sales price - Selling expenses - Balance on debt - > Total taxes due on sale > > 777,924 - (777,924 * 0.07) - 344,607 - 56,093 = > 288,514 > > D. > > Yr 1 23,491 / 1.12 > Yr 2 25,441 / (1.12)^2 > Yr 3 27,484 / (1.12)^3 > Yr 4 (29,627 + 288,514) / (1.12)^4 > > Sum: 263,022.44 > Equity outlay: 131,250 > NPV: 131,752.44 > > E. Use calculator to obtain IRR ~ 37.14% > > F. Decision is to buy based on NPV and IRR, which > are greater than zero and 12%, respectively. I used my calculator (TIBA2+, using the following functions: n= 360 i = 8/12 = .67 PV =393750 PMT = -2889.2 Hit 2nd AMORT: P1 = 1 P 2 = 12 Scroll down to interest = 31,381 Go back to P1, enter: P1 = 13 P2 = 24 Scroll down to interest = 31,108 Repeat for years 3 and 4

can someone clarify exactly what debt service means please? thanks joe

p + I

thanks

Joe, It’s just your mortgage payment *12, so in this case annual debt service would be 2889.20 * 12 = 34,670.38

schweser uses mortgage balance to be purchase price - accumulated depreciation - tax on recaptured depreciation. in here where on earth did the 344,607 come from??? thanks in advance cheers joe

Good exercise, depreciation recapture caught me. 344,607 is the selling price (777924 * (1-.07)) - Mortgage amount after principal payment (use the amortization table in your calculator) of 378862.37