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This 0 page Class Notes was uploaded by Domingo Parker on Sunday November 1, 2015. The Class Notes belongs to FIN 3113 at Oklahoma State University taught by Richard Buchanan in Fall. Since its upload, it has received 45 views. For similar materials see /class/232773/fin-3113-oklahoma-state-university in Finance at Oklahoma State University.
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Date Created: 11/01/15
There are three types of Time Value of Money scenarios Lump Sum Periodic Level Payments and Uneven Cash Flow Streams Lump Sum means literally a lump of money either paid or received one time only The lump sum can be a Present Value paid or received today now or it can be a Future Value that will be received after the passage of a determined number of time periods usually stated in years Interest is either paid or received on the lump sum The interest can be Simple interest that when due is removed from the transaction Or the interest due can be left unpaid or un received compounded onto the principal amount and becoming subject to interest just like the original lump sum An amount that will not be received until some future date is worth less today ie it s present value results from negative compounding from the amount to be received in the future called discounting How often interest is compounded discounted depends on the frequency of interest calculations ie quarterly interest gets compounded every three months quarterly monthly would be added to principal at the end of each month and so forth Calculator operation for Lump Sum problems happens in the keys N IY PV PMT and PV where any four variables are entered and CPT followed by keying the unknown variable produces an answer N the TOTAL number of compounding periods 2 years x compounding periods per year between the PV and FV dates eg 5 years with quarterly compounding would result in 20 being entered as N ie 5 x 4 Likewise 3 years of daily compounding would result in N1095 ie 3 x 365 IYthe PERIODIC interest rate 2 annual interest rate compounding periods per year eg 12 annually compounding quarterly would result in 3 being entered as IY ie 124 Likewise an annual rate of 6 compounded daily would result in IY 0164 ie 6365 IY is entered as a percentage not a decimal PV 2 the present value is how much the transaction is worth now TODAY For instance if I borrow 5000 today that I m going to pay back some time in the future PV5000 Likewise if I deposit 1000 into an account today that will be withdrawn some time in the future the PV 1000 Whether the amount is positive or negative depends on whether it is being put into positive or taken out of negative my pocket PMT is always entered as 0 when doing Lump Sum problems FV the value of the transaction at some future date after a known number of interest compounding periods LUMP SUM Examples 1 N U 4 U1 0 l 00 You borrow 10000 today on a 3 year term loan with interest at 5 per year compounded annually How much will you have to pay the bank in 3 years when the loan is due N 3 x 1 3 IY 51 5 PV 10000 PMT 0 because you re not making payments CPT FV and see 1157625 which is what you ll owe in three years You borrow the 10000 from a banker that only charges 49 interest but compounded it daily How much will you have to pay at the end of three years if you borrow from this bank N 3 X 365 1095 IY 49 365 0134 PV 2 10000 PMT still is 0 CPT FV 2 1158343 If the interest rate in 2 was lower than in 1 why d you pay more at the end of 3 years Abe promised to give his favorite son Jake 100000 ten years from today Esau Jake s brother offered Jake 10000 today if Jake would let him have the 100000 in ten years What kind of annual return will Esau make on this deal if Jake sells him Abe s 100000 that doesn t come in for 10 years N 10 PV 2 10000 PMT 0 EV 100000 CPT lY 258925 In 4 above if Esau can get 20 at the bank how much better or worse off will he be in 10 years if Jake takes his offer N 10 IY 20 PV 2 10000 PMT 0 CPT FV 2 6191736 is what Esau would have if he only earned the 20 at the bank so he ll be 100000 less 6191736 or 3808263 better off Jake has a special deal with a really big banker who will pay him 30 interest compounded quarterly How much better or worse off will Jake be today if he takes the 10000 Esau is offering HINT How much is what he give ups worth today if takes Esau s deal N 10 x 4 40 IY 304 2 75 PMT 0 EV 100000 CPT PV 2 554194 2 the value to him today of 100000 he d get in 10 years If he takes the 10000 he ll be 10000 less the 554194 what the 100000 would be worth to him today or 445806 better off in today s dollars Okay the answer in 6 doesn t seem like very much of a difference does it So how much better off would Jake be 10 years from today if he took Esau s deal N 40 lY 304 2 75 PV 2 10000 PMT 0 CPT FV 18044239 so he d be 8044239 better off in 10 years quite a bigger number than that petty 445806 huh Just out of curiosity is there any relationship between the 445806 that Jake would be better off today and the 8044239 that he d he better off in 10 years ie what would 445806 be worth in 10 years if it earned 30 compounded quarterly Periodic Level Payments mean the same amount called payment occurs repeatedly at unchanging intervals If the payments continue for a de ned time ie a xed number of payments the stream of payments is called an Annuity If the payments occur at the END of each interval it s called an ORDINARY annuity and if the payments occur at the BEGINNING of each interval it s called an ANNUITY DUE The same statements about interest as used for Lump Sums apply to annuities and are repeated here Interest is either paid or received on the accumulated payments The interest can be Simple interest that when due is removed from the transaction Or the interest due can Compound interest left unpaid or un received compounded onto the accumulating payments and likewise becoming subject to interest How often interest is compounded discounted depends on the frequency of interest calculations ie quarterly interest gets compounded every three months quarterly monthly would be added to principal at the end of each month and so forth N number of payments that will occur 2 years x number of payments per year eg if payments are semi annually for 5 years the N 5 x 2 10 lY 2 annual interest rate number of payments per year if payment interval and compounding frequency are the same eg 4 payments per year occur and compounding is quarterly eg if the annual interest rate is 10 and payments are quarterly then lY 104 2 25 IF the payment interval and the frequency are NOT the same eg 4 payments per year occur and annual interest rate of 6 is compounded monthly things get complicated and you must use the following formula to find IY IY 1 nominal annual rate compounding periods per yr mm mmdmg Fem per year payment periods per year 1 X S0 IY 1 0612124 1 x 100 15075 I WILL NOT PUT A PROBLEM LIKE THIS ON THE EXAM BUT YOU SHOULD KNOW HOW TO DO IT PV 2 if computed the present value today of a stream of future payments But if in addition to the payments I make a deposit into an account today that amount will be entered as PV Whether the amount is positive or negative depends on whether it is being put into positive or taken out of negative my pocket PMT is the amount of each periodic amount that occurs Set the calculator to END or BEG as appropriate by touching 2quotd then PMT BGN then T and ENTER SET until you see the desired END or BEG then touch 2quotd and CPT QUIT FV If computed FV is the value of the PV and PMTs at some future date after a known number of payments occurs and interest is compounded left to accumulate and also earns interest If entered FV is an amount that is needed to J be reached at some time in the future as a result of the PV and PMTs that are made and Interest that is earned and compounded to the accumulating amount that nally becomes the FV ANNUITY EXAMPLES You borrow 10000 today on a 3 year loan with payments to be made and the end of each month and interest at 5 per year compounded monthly How much will you have to pay the bank monthly N 3 x 1236 lY 5124167 PV 10000 FV 0 because the loan will be paid off at the end of 3 years CPT PMT and see 29971 Same facts as 1 above except the payments are due at the beginning of each month What s the monthly payment CPT PMT 29846 Same facts as 1 above except you convince the banker that you can pay one final amount of 2000 at the end of the 3rel year called a balloon payment How much would your monthly payment be PV 2000 CPT PMT 24810 Abe promised to give his favorite son Jake 1000 at the w of every month for ten years Esau Jake s brother offered Jake 100000 today if Jake would let him have the monthly payments for the next ten years What kind of annual return will Esau make on this deal if Jake sells him the payments he ll be receiving for the next for 10 years N 10 x12 2 120 PV 2 100000 PMT 1000FV 0 CPT lY 3114 per month x 12 3737 annually In 4 above if Abe told Jake that in addition to the monthly payments at the end of the 10 h year he d also give him 25000 then how much should Esau pay Jake for the deal if he wants the same 3737 annual return based on monthly compounding N120 lY 3114 PMT 1000 FV25000 CPT PV 2 11721455 Same facts as in 5 above except that Esau wants to buy the deal for an amount so that he makes a 6 return compounded semi annually How much should he pay Oh boy Now we have monthly payments and semi annual compounding so we have to use the formula to find lY 100 x 1 nominal annual rate compounding periods per yr wmpoummg my payment periods 1 Thus IY 100 x 1 0622 12 1 4939 Everything else stays the same CPT PV 2 10421614 It makes sense that he d pay less ie 104216 than the 117215 if he wants a higher return with more frequent compounding doesn t it N U 4 U1 0 PERPETUITY ie there is no N the payments go on forever Well you can t use N lY PV PMT and there is no FV because forever eliminates FV You have to use a very simple formula for perpetuities PV 2 PMTPeriodic Rate Example How much would you pay for a never ending stream of monthly payments of 100 if you wanted a 10 annual return PV 2 100 1012 12000 UNEVEN STREAMS OF CASH FLOWS When the payments are not level ie each payment is a different amount you re confronted with an uneven stream of cash ows You have to use the Cash Flow register in your calculator to solve this type of problem and the keys are CF NPV and IRR You ll also use the 2m1 and CEC keys to clear work This concept is best taught with examples 1 Consider a stream of cash ows that looks like this End of rst year 1000 end of second year 2000 end of third year 3000 If you required a 5 annual return what would you be willing to pay for this stream of cash ows Hit CF then Hit 2 then CEC Now you ll see CEO 2 0 and CEO is the PV which is what we re solving for so just hit the i key and see C01 Key in 1000 which is your rst cash ow and hit Enter hit the i key and see F01 which is the frequency ie number of times that C01 happened it only happened once which is the default so hit the i key and see C02 Key in 2000 the second cash ow hit ENTER hit i key and see F02 1 which is the correct number of times it happened so hit i key to go to C03 key in 3000 hit ENTER hit i key and see F03 default is 1 which is correct That was the last cash ow Now you re looking for amount you d pay which is PV so hit NPV and you must input the interest rate you want to use which is 5 so key in 5 hit ENTER Now hit i key to get back to NPV hit CPT and see 535795 That s what you d pay 2 Same deal as 1 above except you re going to receive the 3000 not just in the third year but also in the fourth fth and sixth years What s it worth Need to change F03 from 1 to 4 So hit i key until you get to F03 key 4 hit ENTER Hit NPV and repeat from 1 above and see 1241528 3 Same deal as 2 above except you can buy the cash ows for 11000 What would be your return if you paid 11000 at CFO Okay put in the price as CFO and be sure to put a negative sign in front of the 11000 you re taking out of your pocket to buy it with by keying in 11000 then hitting to change it to negative hit ENTER Hit IRR hit CPT see 84155 which is the return Using the TI BAII PLUS to calculate IRR and NPV First clear previous work by Touch CF key39 then Touch 2 key39 then Touch CLR Work key Data from previous cash ow calculations have now been cleared from the calculator ENTERING CASH FLOW DATA 1 Touch CF key and display shows CF 0 039 key in the amount of the initial investment required then touch the key39 Touch ENTER key 2 Next touch the down arrow key and display shows COl39 key in the rst cash ow amount if it is a receipt source let it be positive39 if it is a payment use then touch the key if for a particular year it is zero then touch 0 now touch ENTER key 3 Touch the down arrow key and the display shows FOll Touch ENTER key if C01 occurs only one time Ifit occurs more than once enter as a number the number of times is occurs ie the frequency then touch ENTER 4 Touch the down arrow key and the display shows CO2 key in the second cash ow amount refer to above touch ENTER key 5 Touch the down arrow key and the display shows F02 1 Touch ENTER key if C02 occurs only one time If it occurs more than once enter as a number the number of times is occurs ie the frequency then touch ENTER 6 Continue repeating steps 2 and 3 same as 4 and 5 until all cash ows have been entered CALCULATING THE INTERNAL RATE OF RETURN Now touch the IRR key39 then touch the CPT key39 WAIT while the calculator computes the internal rate of return a er a few seconds see IRR a number that is the internal rate of return CALCULATING THE NET PRESENT VALUE 1 Touch the NPVkey39 see I and enter with number key pad the required rate of return ie the discount rate applicable to the problem as a percentage ie 7 is entered as 7 NOT 07 touch ENTER key 2 Touch the down arrow see NPV in the display39 Touch CPT39 WAIT while the calculator computes the net present value39 a er a few seconds see NPV a number that is the net present value 3 To calculate NPV with a different discount rate you don t need to reenter all the cash ows Simply touch the down arrow see I the previous discount rate used39 key in the new discount rate on the number key pad and touch ENTER touch the down arrow and see NPV the previous NPV39 touch CPT and wait while the calculator computes the net present value using the new discount rate you just entered
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