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Unformatted text preview: [1(1/1.01)/.01] besides investment is PV) if NPV is less than PV than its worth less than it cost, therefore not a good investmentl.Investing in bank at insured rate:(amount to invest)*(1+r)PV of an investment:(CF at Date 1)/(1+r)NPV:Cost+PVCompounding:Loan Amount*(1+r)2 Future Value of an Investment: (CF to be invested today)*(1+r)t How much to lend today to get $1 in 2y:PV*(1+r)2 =$1Present Value of an Investment: (CF at Date T)/ (1+r)t PV=FV/(1+disc. Rate)tNPV=Co+(C1/1+r)+(C2/1+r2)+Compounding Periods (semiannually):(deposit amount)*(1+r/2)2 where 2 is the number of compounding periods. EAR:(1+r/m)m1, m= times compoundedAPR:r*(365/# days)Future value with compounding:(initial investment)*(1+r/m)mT Continuous Comounding: (initial investment)*erT, e=2.718 PV when Pay X at end of T year @ rate of R: X*(1/erT)=PVPV of Perpetuity: [C/(1+r)]+ [C/(1+r)2]+ [C/(1+r)3] or C/r PV of Growing Perpetuity:(CF/rg)Price of stock today:[dividend about to pay]+[future dividend/rg] future dividend= dividend*1+gPresent Value of an Annuity:C/rC/r*[1/(1+r)t]Future Value of anAnnuity:C*[(1+r)t 1/r]investment that will pay $1,000/year for 10 years.earn a rate of 9% per year on similar investments, how much willing to pay for thisannuity?:10 into N, 9 into I/Y, and 1000 (a cash inflow) into PMT. Now press CPTPVto solve for the present value. The answer is 6,417.6577. Again, this is negative because it represents the amount you would have to pay (cash outflow) today to purchase this annuity.If borrowing $1000 each year for 10 years at a rate of 9%, and thenpaying back the loan immediate after receiving the last payment.How to repay?All we need to do is to put a 0 into PVto clear it out, and then press CPTFVto find that the answer is 15,192.92972 (a cash outflow).Present Value of 4yr college:(expense)*[1(1/1+r)4/r], take PV/(1+r)last deposit> PV at Date 0. C*A17.14=PV @Date 0, solve for C, where A17.14 is a 17 yr annuity at 14%.B. Present Value Annuity Problems In a present value annuity problem, Assume N = 5, I/Y = 8%, PMT = $ 1, and PV = $ 3.9927. Clear: [2nd] [CLR TVM]. 1. Present Value:Input 5 [N], 8 [I/Y] , and 1[+/] [PMT]. Press [CPT] [PV]. 2. Payment:Input 5 [N], 8 [I/Y] , and 3.9927 [PV]. Press [CPT] [PMT]. 3. Interest Rate: Input 5 [N], 1[+/] [PMT], 3.9927 [PV]. Press [CPT] [I/Y]. This is the interest rate implicit in the cash flow stream and the PV. It is the Internal Rate of Return of the annuity. 4. Number of Payments: Input 8 [I/Y], 1[+/] [PMT], and 3.9927 [PV]. Press [CPT] [N]. C. Future Value Annuity Problems Assume N = 5, I/Y = 8%, PMT = $ 1, and FV = $ 5.8666. Clear: [2nd] [CLR TVM].1. Future Value: Input 5 [N], 8 [I/Y] , and 1 [+/] [PMT]. Press [CPT] [FV]. 2. Payment: Input 5 [N], 8 [I/Y] , and 5.8666 [FV]. 1....
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 Spring '11
 Zhu
 Finance, Investing

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