THE TIME VALUE OF MONEY The main function of financial management is to maximize shareholder’s wealth. * Utilization of firm’s assets must be efficient, its mean that each dollar must be profitable. The basic asumption states that “a dollar” in hand today is worth more than a dollar to be received next year because, if you had it now, you could invest it, earn interest, and end up next year it will be more than one dollar.

Future value (Fv) is the value of n years after coumpund interest has been earned, it is also called compounding. To ilustrate; suppose you had $100 deposited in a bank savings account that paid 5 % interest annually. Time frame concept Future Value Present value

How much would you have at the end of one year? PRINCIPAL + INTEREST EARNED Fv1= $100 + (0.05 x $100) Fv1= P0 + i.P0 Fv1= P0 (1 + i) Fv1= 100 (1.05)= $ 105

The future value at the end of 2 year would be: Fv2= Fv1+ Fv1.i Fv2= P0 (1+i)(1+i) Fv2 =$100 (1.05)(1.05)

Now suppose you leave your funds on deposit for 5years; how much will you have at the end of the fith year? YearAmount at the beginning of year (1+i)Amount at the end of year Interest earned 1$ $105.00$ 5 2$ $110.25$ $ $115.76$ $ $121.55$ $ $127.63$ 6.08 TOTAL INTEREST EARNED $ 27.63

FUTURE VALUE INTEREST FACTOR OF $1 Period n 3%5%7%

The table of FVIF shows that; initial amount of $100 growing at 5% a year would be $ at the end of five years. Thus you should be indifferent to the choice between $ 100 today and $ at the end of 5 years.

Relationship between future value interest factors, interest rates, and time FVIF 7% 5% 3% 1 0% Periods

1.If a firm’s earnings per share grew from $1 to $2 over a 10 year period, the total growth would be 100 percent, but the annual growth rate would be less than 10 percent. Prove it! 2.Assume that it is now January 1,2009. On January 1, 2010 you will deposit $ 1000 into a saving account paying an 8 percent interest rate. a. How much will you have in your account on January1,2014? b. What would your January1, 2014, balance be if the bank used quarterly compounding?

3. Find the interest rates, on each the following: a. You borrow $ 400 and promise to pay back $420 at the end of 1 year b. You lend $400 and receive a promise of $420 at the end of 1 year. c. You borrow $40,000 and promice to pay back $ 65,156 at the end of 10 years d. You borrow $ 4,000 and promise to make payments of $ 1, per year for 5 years.

PRESENT VALUE In general, the present value of a sum due n year in the future is the amount which, if it were on hand today. From the previous example your deposit at the end of year 5 is $ , where the interest rates is 5% annually. Finding the present value

FV5= $ ; i= 5% It means that if you are offered an income at end of year 5 of $ , you will accept this offer if maximum investment is $ 100

FUTURE VALUE OF ANNUITY An annuity is a series of equal payments at fixed interval for specified number of periods. The basic assumption of annuity is that “each payment (cash flow) is made at the end of the year”

Time line for future value of annuity 0 4 % 1 4 % 2 4% 3 $1 $1 $ FVA

From the FVA line you know that each $1invested at the end of every year during 3 years, it would be $ End of yearCompounded period 12 year= year= year= 1 total

PRESENT VALUE OF ANNUITY (PVA) (i=4%)

We have an information that the sum of interest factor of equal serial cash flow of $ 1 during 3 years is The Application of PVA One of the most important application of compound interest involves loans that are to be paid off in installments over time. Included are automobile loans, home mortgage loans, and most business debt. If a loan is to be repaid in equal periodic amounts, it is said to be an amortized loan.

Exercise A firm ABC borrows $1,000 to be repaid in 3 equal payments at the end of each of the next 3 years. The lender charges 6 percent interest rate on the loan balance that is outstanding at the beginning of each period. Calculate: 1.Determine the amount the firm must repay each year or the annual payment 2.Split or separate between principal and interest

year Beginning amount PaymentInterestPrincipal repayment Remaining Balance 1 1, , $1,000,000

PINJAMAN Rp BUNGA9% PER TAHUN ANGSURAN 4 TAHUN DALAM ANUITAS ANGSURAN ANNUITAS Rp ,314 THPINJAMAN AWALBUNGAANGSURAN POKOK SISA PINJAMAN AKHIR 1Rp Rp Rp ,314Rp ,686 2 Rp Rp ,252Rp ,434 3 Rp Rp ,615Rp ,820 4 Rp Rp ,820Rp0,000