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# BUSINESS FINANCE FIN 3715

LSU

GPA 3.99

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This 30 page Class Notes was uploaded by Arthur Dicki on Tuesday October 13, 2015. The Class Notes belongs to FIN 3715 at Louisiana State University taught by Staff in Fall. Since its upload, it has received 21 views. For similar materials see /class/222544/fin-3715-louisiana-state-university in Finance at Louisiana State University.

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Date Created: 10/13/15

Chapter 6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute loan payments Be able to find the interest rate on a loan Understand how interest rates are quoted Understand how loans are amortized or paid off l 1 Chapter Outline 39 Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows Annuities and Perpetuities r Comparing Rates The Effect of Compounding Loan Types and Loan Amortization Multiple Cash Flows Future Value Example 61 Find the value at year 3 of each cash flow and add them together Today s year 0 CF 3 N 8 IN 7000 PV CPT FV 98 Year 1 CF 2 N 8 IN 4000 PV CPT FV 466560 Year 2 CF 1 N 8 IN 4000 PV CPT FV 4320 Year 3 CF value 4000 Total value in 3 years 881798 466560 4320 4000 2180358 Value at year 4 1 N 8 W 2180358 PV CPT FV 2354787 Multiple Cash Flows FV Example 2 0 Suppose you invest 500 in a mutual fund today and 600 in one year lfthe fund pays 9 annually how much will you have in two years YearO CF12 N 500 PV 9 IN CPT FV 59405 Year l CF21 N 600 PV 9 IN CPT FV 65400 Total FV 59405 65400 124805 Multiple Cash Flows Example 2 Continued How much will you have in 5 years if you make no further deposits First way Year 0 CF 5 N 500 PV 9 IN CPT FV 76931 Year 1 CF 4 N 600 PV 9 IN CPT FV 84695 Total FV 76931 84695 161626 Second way use value at year 2 3 N 424805 PV 9 W CPT FV 161626 Multiple Cash Flows FV Example 3 0 Suppose you plan to deposit 100 into an account in one year and 300 into the account in three years How much will be in the account in five years ifthe interest rate is 8 Year l CF 4 N 100 PV 8 IN CPT FV 05 Year3 CF 2 N 300 PV 8 IN CPT FV 34992 Total FV 13605 34992 48597 Multiple Cash Flows Present Value Example 63 Find the PV of each cash flow and add them Year1 OF N 1 lY 12 FV 200 CPT PV 17857 Year2 OF N 2 IN 12 FV 400 CPT PV 31888 Years OF N 3 IN 12 FV 600 CPT PV 42707 Year 4 OF N 4 IN 12 FV 800 CPT PV 50841 Total PV 17857 31888 42707 50841 143293 2 4 400 600 800 200 Example 63 Timeline 318 88 427 07 50841 1 432 93 Multiple Cash Flows Using a Spreadsheet 0 You can use the PV or FV functions in Excel to find the present value or future value of a set of cash flows 0 Setting the data up is half the battle if it is set up properly then you can just copy the formulas 0 Click on the Excel icon for an example Multiple Cash Flows PV Another Example 0 You are considering an investment that will pay you 1000 in one year 2000 in two years and 3000 in three years If you want to earn 10 on your money how much would you be willing to pay N 1Y 10 FV 1000CPT PV 90909 N 2 IN 10 FV 2000 CPT PV 465289 N 3 IN 10 FV 3000 CPT PV 225394 PV 90909 165289 225394 481593 0040 Multiple Uneven Cash Flows Using the Calculator Another way to use the nancial calculator for uneven cash ows is to use the cash flow keys Press CF and enter the cash ows beginning with year 0 You have to press the Enter key for each cash ow Use the down arrow key to move to the next cash ow The F is the number oftimes a given cash ow occurs in consecutive periods Use the NPV key to compute the present value by entering the interest rate for l pressing the down arrow and then computing the answer Clear the cash flow worksheet by pressing CF and then 2 d CLR Work eon Decisions Decisions Your broker calls you and tells you that he has this great investment opportunity If you invest 100 today you will receive 40 in one year and 75 in two years If you require a 15 return on investments of this risk should you take the investment Use the CF keys to compute the value of the investment CF CFEl 0 C01 40 F01 1 002 75 F02 1 NPV15CPT NPV 9149 No the broker is charging more than you would be willing to pay 5042 Saving For Retirement You are offered the opportunity to put some money away for retirement You will receive five annual payments of 25000 each beginning in 40 years How much would you be willing to invest today if you desire an interest rate of 12 Use cash flow keys CF CFD 0 CO1 0 F01 39 C02 25000 F02 5 NPV 12 CPT NPV 108471 5043 Saving For Retirement Timeline 0 25K 25K 25K 25K 25K L J l I Notice that the year 0 cash ow 0 CF0 0 E The cash ows in years 17 39 are 0 C01 0 F01 39 J The cash ows in years 40 7 44 are 25000 C02 25000 F02 5 5044 Quick Quiz Part I Suppose you are looking at the following possible cash flows Year 1 CF 100 Years 2 and 3 CFs 200 Years 4 and 5 CFs 300 The required discount rate is 7 What is the value of the cash flows at year 5 What is the value of the cash flows today What is the value of the cash flows at year 3 5045 Annuities and Perpetuities Defined Annuity finite series of equal payments that occur at regular intervals Ifthe first payment occurs at the end ofthe period it is called an ordinary annuity Ifthe first payment occurs at the beginning of the period it is called an annuity due Perpetuity infinite series of equal payments Ecrie Annuities and Perpetuities 39 39 Basic Formulas Perpetuity PV C r Annuities If PVC 1rt r r 5047 Annuities and the Calculator 0 You can use the PMT key on the calculator forthe equal payment 0 The sign convention still holds 0 Ordinary annuity versus annuity due You can switch your calculator between the two types by using the 2quotd BGN 2quotd Set on the TI BAII Plus If you see BGN or Begin in the display of your calculator you have it set for an annuity due Most problems are ordinary annuities Bola Annuity Example 65 39 You borrow money TODAY so you need to compute the present value 48 N 1 IN 632 PMT CPT PV 2399954 24000 Formula 0 PV 632 2399954 5049 Annuity Sweepstakes Example 0 Suppose you win the Publishers Clearinghouse 10 million sweepstakes The money is paid in equal annual endof year installments of 33333333 over 30 years lfthe appropriate discount rate is 5 how much is the sweepstakes actually worth today 30 N 5 IN 33333333 PMT CPT PV 512415029 5072 Buying a House You are ready to buy a house and you have 20000 for a down payment and closing costs Closing costs are estimated to be 4 ofthe loan value You have an annual salary of 36000 and the bank is Willing to allow your monthly mortgage payment to be equal to 28 of your monthly income The interest rate on the loan is 6 per year With monthly compounding 5 per month for a 30year fixed rate loan How much money will the bank loan you How much can you offerforthe house 50721 Buying a House Continued Bank loan Monthly income 36000 12 3000 Maximum payment 283000 840 3012 360 N 5 IN 840 PMT CPT PV 14o105 Total Price Closing costs 04140105 5604 Down payment 20000 5604 14396 Total Price 140105 14396 154501 50722 Annuities on the Spreadsheet Example The present value and future value formulas in a spreadsheet include a place for annuity payments Click on the Excel icon to see an h example 50723 Quick Quiz Part H You know the payment amount for a loan and you want to know how much was borrowed Do you compute a present value or a future value You want to receive 5000 per month in retirement If you can earn 075 per month and you expect to need the income for 25 years how much do you need to have in your account at retirement 50724 Finding the Payment Suppose you want to borrow 20000 for a new car You can borrow at 8 per year compounded monthly 812 66667 per month If you take a 4year loan What is your monthly payment 412 48 N 20000 PV 66667 IN CPT PMT 48826 50725 Finding the Payment on a Spreadsheet Another TVM formula that can be found in a spreadsheet is the payment formula PMTratenperpvfv The same sign convention holds as forthe PV and FV formulas Click on the Excel icon for an example 5025 Finding the Number of Payments Example 66 The sign convention matters 15 Y 1000 PV 20 PMT CPT N 93111 MONTHS 775 years And this is only if you don t charge anything more on the card 50727 Finding the Number of Payments Another Example Suppose you borrow 2000 at 5 and you are going to make annual payments of 73442 How long before you pay off the loan Sign convention matters 5 IN 2000 PV 73442 PMT CPT N 3 years 50723

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