Agenda 11/28 Review Quiz 4 Discuss interest and the time value of money Explore the Excel time value of money functions Examine the accounting measures of profitability Course Evaluations

Introduction to Interest Calculations When you borrow money you pay interest When you loan money, you receive interest When you make a payment  part of the payment is applied to interest  Part of the payment is applied to principal

Understanding time value of money Money will increase value over time if the money is invested and can make more money. If you have $1,000 today, it will be worth more tomorrow if you invest that $1,000 and it earns additional money (interest or some other return on that investment). If you have $1,000 today, it will NOT be worth more tomorrow if you put it in an envelope and hide it in a drawer. Then the time value of money does not apply. Of course, you won’t lose the $1,000 either… 3

Types of Interest Simple interest  Interest is paid only on the principal  Many certificates of deposit work this way Compound interest  Interest is added to the principal each period  Interest is calculated on the principal plus any accrued interest  Compounding can occur on different periods  Annually, quarterly, monthly, daily

Difference between simple and compound interest Assume that you have $1,000 to invest. $1,000 is the present value (PV) of your money. You can invest it and receive “simple” interest or you can earn “compound” interest. The money that you have at the end of the time you have invested it is called the “future value” (FV) of your money. 5

Future value of money Simple interest is always calculated on the initial $1,000. 5% interest on $1,000 is $50. Always $50. When interest is paid on not only the principal amount invested, but also on any previous interest earned, this is called compound interest. FV = Principal + (Principal x Interest) = (1000 x.05) = 1000 (1 + i) = PV (1 + i) 6

Simple vs. compound interest comparison YearSimple InterestCompound Interest 0$1,000 1$1,050 2$1,100$1, $1,150$1, $1,200$1, $1,250$1, $1,500$1, $2,000$2, $2,500$4, $1,000 Invested at 5% return

What about if you borrow money? If you borrow money, the lender wants to earn “compound” money on its investment. If you borrow $1000 at 10%, then you won’t pay back just $1,100 (unless you pay it back at once during the initial time period). You will pay it back “compounded”. Interest will be calculated each period on your remaining balance. 8

Amortization table $1,000 loan, pay $200 year, 10% year interest YearAmount OwedAmount Plus Interest Payment 1$1,000.00$1,100.00$ $900.00$990.00$ $790.00$869.00$ $669.00$735.90$ $535.90$589.49$ $389.49$428.44$ $228.44$251.28$ $51.28$56.41 Total Paid$1,

Types of financial questions usually asked How much will it cost each month to pay off a loan if I want to borrow $150,000 at 6% interest each year for 30 years? Assume that you need to have exactly $40,000 saved 10 years from now. How much must you deposit today in an account that pays 6% interest, compounded annually, so that you reach your goal of $40,000? If you invest $2,000 today and have accumulated $2, after exactly five years, what rate of annual compound interest was earned? 10

Some Excel financial functions 11 FunctionDescription CUMIPMTCumulative Interest Payments CUMPRINCCumulative Principal Payments FVFuture Value IPMTInterest Payment IRRInternal Rate of Return NPERNumber of periods NPVNet Present Value PMTPayment PPMTPrincipal Payment PVPresent Value RATEInterest Rate SLNStraight Line Depreciation

The PMT Function (Introduction) PMT is used to calculate the periodic payment on a loan The interest rate must be fixed There may be a residual value on the note at the end of the periods  This is often referred to as a balloon payment  An auto lease, for example, would have a residual note value

The PMT Function (Arguments 1) Rate: The first argument contains the interest rate per compounding period Nper: The second argument contains the number of periods PV: The third argument contains the present loan value FV: The fourth argument contains the future value  If the loan is paid off at the end of the periods, the value is 0 Type: The final argument indicates when payments are made  0 (the default) indicates the end of the period  1 indicates the beginning of the period

The PMT Function (Arguments 2)

The PMT Function (Example)

Other Time Value of Money Functions Here we are just solving the same equation for a different variable  RATE determines the interest rate  NPER determines the number of periods  PMT determines the payment  PV determines the present value of a transaction  FV determines the future value of a transaction

The RATE Function (Introduction) Determines the interest rate per period based on  The number of periods  The payment  The present value  The future value  The type

The RATE Function (Arguments)

The RATE Function (Example)

The NPER Function (Introduction) Determines the number of periods based on  The interest rate  The payment  The present value  The future value  The type

The NPER Function (Arguments)

The NPER Function (Example)

The FV Function (Introduction) Determines the future value of a lump sum  It’s possible for FV to account for regular cash flows (periodic payments) per period

The FV Function (Arguments)

The FV Function (Example)

The PV Function (Introduction) Determines the present value of a cash flow Like FV, regular inflows or outflows are supported

THE PV Function (Arguments)

The PV Function (Example)

The IPMT Function (Introduction) Use IPMT to calculate the interest applicable to a particular period  Use the initial balance for the present value no matter the period Use PPMT to calculate the principal applicable to a particular period The arguments to both functions are the same

The IPMT Function (Arguments)

The CUMIPMT Function (Introduction) CUMIPMT calculates the cumulative interest between two periods CUMPRINC calculates the cumulative principal between two periods The arguments to both functions are the same Functions require the analysis tool pack add-in

The CUMIPMT Function (Arguments)