Presentation on theme: "FIL 240 Prepared by Keldon Bauer"— Presentation transcript:
1FIL 240 Prepared by Keldon Bauer Time Value of MoneyFIL 240Prepared by Keldon Bauer
2Cash Flow Time LinesYou win the American College Student Publishers Contest.You have the option of taking $1.4 million now or $250,000 per year for five years.Which should you take?The answer comes through taking into consideration the time value of money.
3Cash Flow Time LinesThe first step is visualizing the cash flows by drawing a cash flow time line.Time lines show when cash flows occur.Time 0 is now.12345
4Cash Flow Time Lines Outflows are listed as negatives. Inflows are positive.State the appropriate “interest rate,” which represents your opportunity costs123458%$250K
5Future ValueFuture value is higher than today, because if I had the money I would put it to work, it would earn interest.The interest could then earn interest.Compounding: allowing interest to earn interest on itself.
6Future Value - ExampleIf you invest 1,000 today at 8% interest per year, how much should you have in five years (in thousands).123458%PrincipalInterestTotalPrev. Interest-10.080.001.080.08640.08001.16640.09330.16641.25970.10080.25971.36050.10880.36051.4693
7Future ValueFor one year, the future value can be defined as:
8Future ValueThe second year, the future value can be stated as follows:
9Future ValueTherefore, the general solution to the future value problem is:
10Future ValueInterest can be seen as the opportunity growth rate of money.
11Present ValuePresent value is the value in today’s dollars of a future cash flow.If we are interested in the present value of $500 delivered in 5 years:123458%$500PV=?
12Present ValueThe general solution to this problem follows from the solution to the future value problem:
13Present ValueSince the discount rate is the opportunity cost, the present value represents what I would have to give up now to get the future value specified.
14Interest RatesIf we know the amount we need at time n and the amount we can invest at time zero, then we must only solve for the interest rate.12345?%$500$100
15Interest RatesSolving for interest rates algebraically:
17Time PeriodsIf the present value, future value and interest rate are known, but the number of time periods is not. Then n can be found algebraically:
18Time Periods - ExampleIf we use the last example of investing $100, we want $500 in future, and the current market interest is 8%, n can be found:
19Annuities Definition: A series of equal payments at a fixed interval. Two types:Ordinary annuity: Payments occur at the end of each period.Annuity due: Payments occur at the beginning of each period.
20Ordinary AnnuityExample is a regular payment of $100 for five years earning 8% interest.12345$1008%What is the future value?FV=?
21Ordinary Annuity – Future Value The future value of an ordinary annuity can be found as follows:
32Annuities - Finding Interest Rate Interest rates cannot be solved directly.Calculators search for the correct answer (there is only one correct answer).It guesses and then iteratively goes higher or lower.
33PerpetuitiesWhat would you have to pay to be paid $2,000 per year forever (given a market rate of 8%)?
34Uneven Cash Flow Streams If payments are irregular or come at irregular intervals, we can still find the PV (or FV).Take the present value (or future value) of individual payments and sum them together.
35Uneven Cash Flows - Example 12345$100$200$300$400$5008%$294.01$340.29$171.47$238.15$ 92.59$1, = Present Value
36Uneven Cash Flow - Example 12345$100$200$300$400$5008%$136.05$251.94$349.92$432.00Future Value = $1,669.91$1, = Present Value
37Finding Interest RateAs with annuities, interest rates for uneven cash flow streams cannot be solved directly.Calculators search for the correct answer, called an IRR (there may be more than one correct answer).It guesses and then iteratively goes higher or lower.
38CompoundingThe more often one compounds interest, the faster it grows.123458%-$100$146.93Annual12341056789Semi-Annual4%-$100$148.02
39Compounding Why is there a difference in future value? Because interest is earned on itself faster!How would you adjust to compound monthly?How would you make an adjustment in annuities?
40Effective Annual RateTo convert the other compounding periods to an effective annual compounding rate (EAR) use the following formula:
41Effective Annual Rate - Example 8% monthly compounding loan is equal to what in effective annual rate?
42Fractional Time Periods If you invest $100 for nine months at an EAR of 8%, how does one calculate the future value?The same way one did before.
43Amortized LoansA loan with equal payments over the life of the loan is called an amortized loan.Loan mathematics are the same as an annuity.Loan amounts are the present value.Periodic loan payments are the payments.
44Amortized LoansThe present value of a monthly loan uses the annuity formula adjusted for monthly payments:
45Amortized LoansPayments on a given loan can be found by solving for PMT in the previous equation:
46Amortized Loans - Example What is the payment on a 30 year loan of $150,000?
47Amortization Schedules Amortization schedules show how much of each payment goes toward principal and how much toward interest.The easiest way of calculating one by hand is by calculating the outstanding loan balance month-by-month, and then taking the difference in loan balance from month to month as the principal portion of the payment.
48Amortization Schedules The portion in the amortized loan formula that says n×m can be interpreted as months remaining.So to find the part of the first $1, that is paid toward the principal one would realize that at the beginning one had all $150,000 outstanding.
49Amortization Schedules After the first month, one has 359 payments left. Therefore the loan principal outstanding is:
50Amortization Schedules The difference in principal outstanding is the part of the payment that went toward principal. In this instance, 150, ,899.35=$100.65The rest of the payment went toward interest. In this instance that would be 1, =$1,000.