Corporate Finance

48
Corporate Finance

The term within brackets,

r

rn−+ 1)1(

is called the Future Value Interest Factor of an Annuity or FVIFA.

It is the future value of an annuity of Re 1 for various values of r and n. To make our life simple, the value
of FVIFA for various r and n are presented in the form of a Table (Table A-2 at the end of this book). A section
of the table is shown in Exhibit 2.3. The FVIFA corresponding to, say, 6 percent; and 3 years is 3.184.
Assuming an interest rate of 13 percent, the amount to be invested every year in the given example is:

250000 = A × FVIFA (13 percent, 5)

A= 250000/6480 = Rs 38580

Exhibit 2.3 Future value interest factor of an annuity

Interest rate r (percent)
Year (n)56789

1 1.000 1.000 1.000 1.000 1.000

2 2.050 2.060 2.070 2.080 2.090

3 3.152 3.184 3.215 3.246 3.278

4 4.310 4.375 4.440 4.506 4.573

5 5.526 5.637 5.751 5.867 5.985

Present Value of an Annuity

The present value of an annuity ‘A’ receivable at the end of each year for a period of ‘n’ years at an interest
rate of ‘r’ is given by:

PVAn = A × n

n

rr

r

) 1(

) 1( – 1

+

+

(4)

The term in the bracket

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+

+

n

n

rr

r

) 1(

) 1( – 1

is called Present Value Interest Factor of an Annuity or PVIFA. It

is the present value of an annuity of Re 1 for the given values of r and n. The values of PVIFA (K, n) for
various combinations of r and n are given in Table A-4 at the end of the book. A section of the same is shown
in Exhibit 2.4.

Exhibit 2.4 Present value interest factor of an annuity

Interest rate r (percent)
Year (n)6 7 8 9

1 0.943 0.935 0.926 0.909

2 1.833 0.873 0.857 0.826

3 2.673 0.816 0.794 0.751

4 3.465 0.763 0.735 0.688

The PVIFA for 8 percent and 2 years is 0.857. Note that PVIFA is not the reverse of FVIFA, although
PVIF is the reverse of FVIF. Also, the cash flows in all the cases occur at the end of the year.