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FIN422 Cheat sheet - [1(1/1.01.01 besides investment is PV...

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[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 investment l. Investing in bank at insured rate: (amount to invest)*(1+r) PV of an investment: (CF at Date 1)/(1+r) NPV: -Cost+PV Compounding: 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 =$1 Present Value of an Investment: (CF at Date T)/ (1+r) t PV=FV/(1+disc. Rate) t NPV=-C o +(C 1 /1+r)+(C 2 /1+r 2 )+… Compounding Periods (semiannually): (deposit amount)*(1+r/2) 2 where 2 is the number of compounding periods. EAR: (1+r/m) m -1, m= times compounded APR: r*(365/# days) Future value with compounding: (initial investment)*(1+r/m) mT Continuous Comounding: (initial investment)*e rT , e=2.718 PV when Pay X at end of T year @ rate of R: X*(1/e rT )=PV PV of Perpetuity: [C/(1+r)]+ [C/(1+r) 2 ]+ [C/(1+r)3] or C/r PV of Growing Perpetuity: (CF/r-g) Price of stock today: [dividend about to pay]+[future dividend/r-g] future dividend= dividend*1+g Present Value of an Annuity: C/r-C/r*[1/(1+r) t ] Future Value of an Annuity: 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 this annuity?: 10 into N , 9 into I/Y , and 1000 (a cash inflow) into PMT . Now press CPT PV to 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 then paying back the loan immediate after receiving the last payment. How to repay? All we need to do is to put a 0 into PV to clear it out, and then press CPT FV to 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*A 17 .14 =PV @Date 0, solve for C, where A 17 .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].
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