# SS13 - Real Estate Valuation

Try the following question to test your knowledge. I will post the answers later. 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.

let me have a try tax: 8581.818182 10629.81818 12780.21818 15038.13818 CFAT: 52528.98182 53680.98182 54890.58182 56160.66182 ERAT: 285822.5469 calculated on a excel during work time…just 4 fun~

Remember seeing this. Do we have to know how to calc an amortisation schedule here…ie when calulating Income tax payable from NOI - how do we get the interest paid portion?

For calculating after-tax cf (NOI - Annual Debt Service - Tax payable = After-tax CF) how would you calculate the debt service to get the after-tax CF? Kalo1: You would get the interest payment by first finding out the interest expense on each month then subracting the monthly payment to get the amount that will go into your principal (which would be a much smaller number than the interest expense at the beginning). Then subtract the principal paid portion from the loan. Now you have your lowered principal. With that you multiple the interest for month two from the lowered principal (the 2nd month interest would be lower than the first as it is from a lowered principal amt). Now you have the 2nd month interest payment and subtract that from your monthly payment of 2,889.20 to get the amount that will go into lowering your principal. repeat the process for month 3 to 12. Then you’ll get your interest paid for the year. It is very unlikely that the test will ask you to caculate this… maybe to the 2nd or 3rd month (if it is asking for monthly after tax cf, or 2nd, 3rd year if asking for yearly after-tax cf).

Answers to help: A (NOI - Dep. - Interest paid) * marginal tax rate = Income tax payable N = 360 I = 8/12 PV = 393,750 PMT = 2,889.20 Interest Yr 1 = 31,381 Yr 2 = 31,108 Yr 3 = 30,812 Yr 4 = 30,492 Yr 1 5839.15 (64,000 – 16,399 – 31,381) * 0.36 Yr 2 7089.43 (64,000 – 16,399 – 31,108) * 0.36 Yr 3 8405.47 Yr 4 9790.83 B NOI - Debt service - Tax payable (from A) = ATCF where Debt service = Mortgage payment x 12 2889.2 * 12 = 34,670.38 Yr 1 = 23,491 (64,000 – 34,670.38 – 5,839.15) Yr 2 = 25,441 Yr 3 = 27,484 Yr 4 = 29,627 C 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.

ahh~~~ so thats how debt service is calculated.

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Thanks ASM299 but do you have the calc to get the below interest payments. The book omits this which makes me think if this came up in the exam they will give you the interest payments (if interest only) and also the debt servicing value when getting to ERAT. Interest Yr 1 = 31,381 Yr 2 = 31,108 Yr 3 = 30,812 Yr 4 = 30,492 Cheers

I don’t think interest per year can be calculated without a full schedule, or by doing an amortization function with your calculator, right?

it can be done with the Amort button on your calc. Use PV=-393750 N=360 I/Y=8/12 CPT PMT =2889.20 2nd Amort P1=1 Down Arrow P2=12 BAL=390460.75 PRN=3289.25 INT=31381 P1=13 P2=24 PRN=3562.25 INT=31108 25,36 PRN=3857.92 INT=30812 37,48 4178 30492

Why is depreciation calculated based on the improvement cost and not the total cost? Looks weird to me.

it is not weird. this is exactly the example in the text book (douglas Manor, or whatever).

I’m guessing the property is not depreciated ( land is not depreciated ) . However improvements are capital expenditures which are depreciated over the estimated life of the investment

legendary…although probably wont need it. cheers cpk

true, but there is more than improvement on this building. They didn’t say here but they are assuming that basically the land cost is \$525000 - 451,000 = \$74k. The point is that we should depreciate based on total price minus land.