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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 3 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… 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 5 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. Future value of money 6 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 + (1000 x .05) = 1000 (1 + i) = PV (1 + i) Simple vs. compound interest comparison 7 Year Simple Interest Compound Interest 0 $1,000 $1,000 1 $1,050 $1,050 2 $1,100 $1,102.50 3 $1,150 $1,157.62 4 $1,200 $1,215.61 5 $1,250 $1,276.28 10 $1,500 $1,628.89 20 $2,000 $2,653.30 30 $2,500 $4,321.94 $1,000 Invested at 5% return What about if you borrow money? 8 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. Amortization table $1,000 loan, pay $200 year, 10% year interest 9 Year Amount Owed Amount Plus Interest Payment 1 $1,000.00 $1,100.00 $200.00 2 $900.00 $990.00 $200.00 3 $790.00 $869.00 $200.00 4 $669.00 $735.90 $200.00 5 $535.90 $589.49 $200.00 6 $389.49 $428.44 $200.00 7 $228.44 $251.28 $200.00 8 $51.28 $56.41 $56.41 Total Paid $1,456.41 Types of financial questions usually asked 10 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 $2,676.45 after exactly five years, what rate of annual compound interest was earned? Some Excel financial functions Function Description CUMIPMT Cumulative Interest Payments CUMPRINC Cumulative Principal Payments FV Future Value IPMT Interest Payment IRR Internal Rate of Return NPER Number of periods NPV Net Present Value PMT Payment PPMT Principal Payment PV Present Value RATE Interest Rate SLN Straight Line Depreciation 11 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)