# Future value

(FV).

If we invest money today (and roll up all the expected income) the future value receivable is the expected total value of our investment at its maturity.

If we borrow money today (and roll up all the interest payable) the future value payable is the total principal and interest repayable to the lender at the final maturity of the borrowing.

Example 1: One year at 10% per year

We hold \$100m today.

The rate of return on capital (r) is 10% per year.

The Future value in one year's time is:

= \$100m x 1.11

= \$110m.

More generally

FV = Present value x Compounding Factor (CF)

Where:

CF = (1 + r)n

r = return on capital or cost of capital per period

n = number of periods

Example 2: One year at 6%

If we hold \$10m today, and the return on capital (r) is 6% per year,

the Future value in one year's time is:

FV = \$10m x 1.061

= \$10.6m.

Example 3: One year at 6%, starting with \$9.43m

If we hold \$9.43m today, and the return on capital (r) is still 6% per year,

the Future value in one year's time is:

FV = \$9.43m x 1.061

= \$10m.

Example 4: Two years at 6%, starting with \$8.90m

Now we hold \$8.90m today, and the return on capital (r) is still 6% per year,

the Future value in two years time is:

FV = \$8.90m x 1.062

= \$10m.

Example 5: Two years at 6%, starting with \$10m

Now we hold \$10m today, and the return on capital (r) is still 6% per year,

the Future value in two years time is:

FV = \$10m x 1.062

= \$11.24m.