# 2 Alternative investment pricing questions!! Challenging

Ariel Andres, CFA, is contemplating the purchase of a shopping mall. The average annual after tax cash flow for the next ten years is expected to be \$30K. The property cost \$750K. Andres will put down 23% and borrow the rest. In 10 years, the property will be sold netting \$350K after taxes. What is the approximate yield on the shopping mall? A13.8% B20.35% C17.2% D15.3% ======================================================== AN invetor made the following information about a purchaseL Bought an office building for \$500K using 90% financing. The borrowing cost was 10% They received \$29K at the year end from rentals They sold the building for \$520K at the end of the year Assuming a flat tax rate on income and capital gains of 25% what was the return on equity? A8% B5% C-3% D6%

D for the second one

a. CFo = -172.5 CF1 = 30 F1=9 CF2=380 F2=1 Calculate IRR 21.14% Choice B? 2nd question: 29 - 45 = -16 ( 1-.25) = -12 (total NI) Sold for 520, left over balance on property = 450 so 70 gain Capital gains removed and left with 52.5 Spent 50 on the property (his down payment) so HPR = (-12 + 52.5) / 50 -1 = -19% Cannot select any choice!!!

cpk… you shouldnt pay capital gains on your own intital equity… I started out the same NI = -12000 Gain = 20000*.75 = 15000 Return = 3000 Equity = 50000 6% Correct?

for the second one, the answer is D

B and C? 2nd one bought for 500 finance 90% = 450, interest = 45 returnat end of year 1 = (520 - 450 - 45 + 29) * .75 =40.5 NPV of investment = -50 + 40.5 / 1.1 = -13.18 Return = -13.18 / 50 = -.2636

chadtap, very clear thinking, impressive. I wonder if there is a systematic approach over this kind of question at all? Or do I have to do it case by case? For question 1, though it looks similar as 2, the approach is quite different. the answer gives C. I still have no idea how can one reach that answer in a sensible way.

Im getting B and D. Do you habe the solution for the first one?

I’m saying A on the first one. Since interest is deductible for tax purposes (450,000 amount borrowed * .10) = 45K in interest expense exceeding capital gains and interest. salce proceeds +520,000 rental proceeds + 29,000 princ. repay - 450,000 interest pmt. - 45,000 -------------- 54,000 54,000/(initial inv=50,000) = 8%

I’m saying A on the second one. Since interest is deductible for tax purposes (450,000 amount borrowed * .10) = 45K in interest expense exceeding capital gains and interest. salce proceeds +520,000 rental proceeds + 29,000 princ. repay - 450,000 interest pmt. - 45,000 -------------- 54,000 54,000/(initial inv=50,000) = 8%

Capital gain needs to pay tax guys! 4000 gain after tax is 3,000, 3,000/50,000 = 6% so D!

I think Chad is bang on target on the 2nd one…but whats with the 1st question…I can’t hit any of the choices. Can someone shed some light on that.

Chad and cpk, When you have negative income (-16), why would you pay tax on it? You seem to get the right answer, but… the government doesn’t subsidize your losses, does it? You made -16 in a year, the government gives you +4 (no way) so you end up with -12?? I believe you would get a loss carry-forward instead. Even if the tax rate is the same for both income and capital gains, you wouldn’t lump the two categories to calculate the total tax payable. You keep them separate. So in this case you wouldn’t pay taxes on the income, but you would still pay tax on the capital gains. So I’m looking at: Income: -16 Cap Gain: +15 Investment: -50 Return: - 1/50 = -2% What am I missing?

but you get to write off your losses against other gains

delhirocks, That makes sense. Should we assume that the investor has other income unless stated otherwise? In the industry I work in, this can be an assumption that makes or breaks a deal - some projects have tax credits that you can only use if you have high enough income.

dehli this is how i did the first one cfo=23%750k=-172500 cf1=30000 f=10 cf2=350000 cpt irr=20.04% ?

florin, why cf1=30000 f=10 cf2=350000 cpt irr=20.04% ? and not cf1=30000f=9 cf2=380000

barthezz makes more sense what you are saying i dont know why the answer is off though…

florin i’ve seen too many wrong worded examples on this forum … I’m looking forward to the next problem and put this one ad Acta.

Sorry ppl, I forgot to post the answers. Answer for 1: 17.2% Approximate yield = (Ave annual cash flow + annualized capital gain)/average investment, where annualized capital gain=[(ending price-cost)/years] and average investment = (ending price +cost)/2. Cost is equl to the ivnestor’s equity contribution In this example, cost =0.25*750k=187500, thus approximate yield=[(3000+(350000-187500)/10)/[(350000+187500)/2]=46250/268750=0.172 Answer for 2: Equity = 500,000(0.1)=50000 interest cost=450000*0.1=45000 capital gain=520000-500000=20k atcf=(income+capital gain-interest)(1-tax rate) atcf=(29k+20k-45K)(1-0.25)=3k 3k/5k=6% does any one buy the first answer? coz I don’t! it seems to be so unsystematic~~