THE TIME VALUE OF MONEYThe 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)

2)1(02 iPFv niPFvn )1(0

25.110$)05.1(100$2 2 Fv

Now suppose you leave your funds on deposit for 5years; how much will you have at the end of the fith year?

Year Amount at the beginning of year

(1+i) Amount at the end of year

Interest earned

1 $ 100 1.05 $105.00 $ 5

2 $105.00 1.05 $110.25 $ 5.25

3 $110.25 1.05 $115.76 $ 5.51

4 $115.76 1.05 $121.55 $ 5.79

5 $121.55 1.05 $127.63 $ 6.08

TOTAL INTEREST EARNED $ 27.63

FUTURE VALUE INTEREST FACTOR OF $1

Period n

3% 5% 7%

1 1.0300 1.0500 1.0700

2 1.0609 1.1025 1.1449

3 1.0927 1.1576 1.2250

4 1.1255 1.2155 1.3108

5 1.1593 1.2763 1.4026

The table of FVIF shows that; initial amount of $100 growing at 5% a year would be $127.63 at the end of five years. Thus you should be indifferent to the choice between $ 100 today and $ 127.63 at the end of 5 years.

Relationship between future value interest factors, interest rates, and time

FVIF

7%

5%

3%

1 0%

1 2 3 4 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 yearb. 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 yearsd. You borrow $ 4,000 and promise to make payments of $ 1,028.36 per year for 5 years.

PRESENT VALUEIn 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 $ 127.63, where the interest rates is 5% annually.

Finding the present value

niFvnP )1(0

ni

FvnP

)1(0

FV5= $ 127.63; i= 5%

It means that if you are offered an income at end of year 5 of $ 127.63, you will accept this offer if maximum investment is $ 100

100)05.01(

63.1270

5

P

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 $1

1.0400

1.0816

FVA 3.1216

From the FVA line you know that each $1invested at the end of every year during 3 years, it would be $ 3.1216

End of year Compounded period

1 2 year= 1.0816

2 1 year= 1.0400

3 0 year= 1

total 3.1216

PRESENT VALUE OF ANNUITY (PVA)

(i=4%)

0 1 2 3

1 1 1

1)04.01(9615.0

2)04.01(9246.0

3)04.01(8890.0

2.7751

We have an information that the sum of interest factor of equal serial cash flow of $ 1 during 3 years is 2.7751

The Application of PVAOne 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

Payment Interest Principal repayment

Remaining Balance

1 1,000 374.11 60 314.11 685.89

2 685.89 374.11 41.15 332.96 352.93

3 352.93 374.11 21.18 352.93 0.00

1,122.33 122.33 $1,000,000

PINJAMAN Rp 150000000BUNGA9% PER TAHUNANGSURAN 4 TAHUN DALAM ANUITASANGSURAN ANNUITAS Rp46.300.299,314

TH PINJAMAN AWAL BUNGA ANGSURAN POKOKSISA PINJAMAN

AKHIR

1 Rp150.000.000 Rp13.500.000 Rp32.800.299,314 Rp117.199.700,686

2 Rp117.199.700,686 Rp10.547.973 Rp35.752.326,252 Rp81.447.374,434

3 Rp81.447.374,434 Rp7.330.264 Rp38.970.035,615 Rp42.477.338,820

4 Rp42.477.338,820 Rp3.822.960 Rp42.477.338,820 Rp0,000