FIN 3332- Risk, return, time value of money notes

FIN 3332- Risk, return, time value of money notes - Ch 17...

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Unformatted text preview: Ch. 17- Risk, Return and Time Value of Money 9 l7 Risk and Retum-measure returns on real estate as percentage rates of return, with benefits to be received in the future. Since these filture benefits are uncertain, there is risk involved in investing in real estate. The greater the risk, the greater the required return. A. Types of Risk Investors compensate for: 1. Business Risk—uncertainty arising from changing economic conditions. LIMA“ UNJ} ““55; 2. Financial Risk-uncertainty from possibility of defaulting on borrowed l1 l:IT funds. 3. Purchasing Power Risk-inflation. 4. Liquidity Risk-not being able to convert investment to cash. B. Time Value of Money-investors must consider timing of flows, since a dollar to be received in the future is not worth as much as a dollar to be received today. 1. Dollar today can be invested, where dollars received in the future lose potential interest (opportunity cost) 2. Dollars received in future are worth less than today's dollars because inflation reduces purchasing power. 3. Risk in not receiving the future dollars. 11. Time Value of Money Formulas-revolves around 6 fimctions of a dollar. Always 4 variables, with 3 known and the unknown being solved for: periods I —_—_l PV F\/ In % interest (compound -I- or discount 4—) A. Future Value of a Single Sum: FV = PV (1 + i)“ Pufi ‘00 ex. if invest $100 in savings account paying 5%, compounded annually, what is " value at end of 2 years? IV: C :1 FV=$100(1+.05)2 _ . =$100 (1.05)(1.05) WM ’0 =$100(1.1025) = $110.25 Can use formula, table or calculator to solve. If have more compounding periods, adjust equation: FV = PV(1+ Um)“ where m = number of periods per year. B. Present Value of a Single Sum-exactly opposite of FV, where now determine what dollar to be received in future is worth today: 1 Pv=1=v [—-—] (1 + i)n i: \j : mold ex. parents leave you $100,000 to be received in 5 years- If someone willing to (- buy that right now with a required yield of 15% annually, what is your inheritance .. 9 worth today“? :1: [y : hS ' HAT-lb PV*$100 OOOE—1—] ’ (1+.15)5 PV = $100,000 (.4971767) = $49,717.67 C. Future Value of an Annuity-when make a series of payments, could compound each payment into the future, or use a formula instead: (1+i)n - 1 W. : PMT If] 1 V : 0 ex. deposit $100 per month in an account at the end of the month, earning 5% NAT“ ‘0 0 interest, compounded monthly. What is the value at the end of 20 years? INZSIR (1+fi)20x12 _ 1 a ————11———-#—— N JJJM 3x FV=$100[ 05 1 E = $100 (411.0337) = $41,103.37 D. Sinking Fund Factor-amount of deposit necessary to accumulate a given future value based on an assumed compounding and interest rate over a period of time: 9691i Q0395. : (J- m- xix—5L Nit): F. r Ewes: Li FJA PMT=[ l (1+i)" — 1]FV ex. how much do you need to save each month to retire in 35 years? Present Value of an Annuity-most important real estate time value of money configuration. Used in real estate finance, valuation and investment to determine present value of a stream of payments to be received in the future. 1 1 '(1+i)“ 1 PV, = PMT ex. you have won the lottery for $8,000,000! You have the option of taking 50% of the money in a lump sum distribution today, or taking a payment of $320,000 per year for the next 25 years. Assuming an 8% annual available return, and $339k ignoring tax effects, what option should you take? Ofim n l 1 l— 25 Pv: fl $320,000 .08 = (10.67478) $320,000 = $3,415,928 Mortgage Constant-typically used in valuation and mortgage finance, where the MC is the inverse of the PVa. The MC is the factor that will give the periodic payment necessary to amortize (pay back principal as well as provide a return o_n the investment by the lender) the loan. PMT= PV 1- . 0+1)" ex. You borrow $80,000, agreeing to pay it back over 30 years in monthly installments, paying 8% interest, compounded monthly. What are your payments to principal and interest? 1 1 1__,_..__ .08 1+— 0 ( 12)36 g 12 PMT = $80,000 = $80,000 (.007338) = $587.01 Related Mortgage Mathematics-several other concepts that follow from time value of money calculations: Total interest paid over life of loan: INT = ($587.01 x 360) — $80,000 = $211,323.60 — $80,000 = $131,323.60 PI'I'I payment-lender often requires payment to cover not only principal and interest, but tax and insurance escrow as well. If taxes = $1,200/year and insurance = $600/year, what is total PITT payment? $1,200 + $600 Escrow = m = $150/m0 12 mt PITI = $587.01 + 5150 = $737.01 Portion going to principal and interest-part of monthly payment goes to returning principal and part goes to interest. Portion going to interest = PV(i/12). Ex. Int; .—. $80,000 (.08/12) = $80,000 (.006667) Nfll (13139 Nrfib 00 EN: (My; PMiSQMl 0121870 boas E. El '[. Chainfifiigfi $242. and) 3M hJ tb‘blllos? . WY: 91701 NEH-.6 2:07.10 = $533.33 two and Prim : $587.0] - $533.33 3 $53.68 Second Month: Lon“ Int; = $80,000-$53.68 (.08/ 12) = $79,946.32 (.006667) = $532.97 MT and Prim = $537.01 - $532.97 = $54.04 Could do this for every month of loan term-called amortization schedule. Mortgage Balance Remaining-of interest to know the balance owing at any point (ex-selling property and need to know payoff) - could get from amortization schedule or use formula: MBR = PMT (PV..i%,n-j) wherej = period in which prepaying ex. MBR after 6 years: MBR = $587.01 (PV,,.08/12,288) = $587.01 (127.86839) = $75,060.02 (calculator = $75,060.24) Would use same methodology to calculate balloon payment. Discount Points-by definition, 1 point equals 1 percent of loan amount. Paid at closing to raise lender's yield. Ex. 8%, 30 year monthly loan with 1/1 (1 point origination fee and 1 discount point) on an $80,000 loan. What is the dollar value of the points, and what is the lender's effective yield? $ Points = $80,000 (.02) = $1,600 Lender advances $80,000 - $1,600 = $78,400, and is paid back the full $80,000 over the 30 years (i.e. assumes no prepayment), which raises yield: Net Loan = PMT (PVa,i%,360) $78,400 = $587.01 (PV.,?%,360) Esq-360°} [lUO>F. NM27l WSW"? ol FV: 75mm Wick 15M} ?%= 8.214% Discount Points with assumed prepayment — if loan is paid off before end of term, yield to lender (and cost to borrower) will change. Reason is that the APR calculation spreads points over the entire loan period, but if they are paid back sooner, this will change the yield. Ex. — assume the same facts above ($80,000, 8%, 30 year fixed rate mortgage with 1 point origination fee and 1 discount point at close), what will the yield be if the loan is prepaid at the end of 6 years? Net LoanzPMT(Pv,,i%,72) + MBR(PV5,i%,72) $78,400=$587.01(PV,,?%,72) + $75 ,060.24(PVs,i%,72) I} IN” 17%: 8.437% «kg, we PM W (M we) 79 0},ng M3? Jitttgl’c 9W1}? M31975 '9‘)“ Wank N? \9 -\3\ i/Yr—(l .15.“! u. ’fiK/fi“ at, Wok mt mm. W B 7r) mil/3: 'lOblL- £1,005 ‘- W4 :Lry-n;(g5§§) PMT:@ Q70. lLI M5“- 00% ' Newt/H1000 l‘rgpwxl‘ ZS‘yFJ F0 MERE 0:7l r107 05 Nabobo week emrrmxn W;71f\01.0‘n Mzto :N- we W17 Flu-£700; [EQR N271 PW:- ‘SCU ,o\ W: 75,060)“. Wok 1N4} ?%=8.214% Discount Points with assumed prepayment — if loan is paid off before end of term, yield to lender (and cost to borrower) will change. Reason is that the APR calculation spreads points over the entire loan period, but if they are paid back sooner, this will change the yield. Ex. — assume the same facts above ($80,000, 8%, 30 year fixed rate mortgage with 1 point origination fee and 1 discount point at close), what will the yield be if the loan is prepaid at the end of 6 years? Net Loan=PMT(PV3,i%,72) + MBR(PV§,i%,72) $78,490=$587.01(Pv,,?%,72) + "lake, ink/0951* PAYS lmvx (“le w,‘7 pw'tlt) ‘ buyer‘s M‘Fl’ Wrath \‘WTSMM: fijziook N"?- \§ '\3\ i'Tr/iqmi $00K low «gr “@1571. War 19 7 r) $75,060.24(PVs,i°/o,72) my. D. ?% = 8.437% riff. iD‘Jt’l .__ an): 100k“ IWoo 1 (3le :[email protected] PMV:@ {170. “I My: ontlnuk’blmoo Prepaid“ 1S\,l’3 F0 mojtbbzmom N350 wet waVMJ7 f‘J:Y7\,%07,Db 0250 IN- 12:: “\17 ...
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