Question

An investment that costs $40,000 will produce annual cash flows of $12,000 for a period of 4 years. Given a desired rate of return of 10%, what will the investment generate?

Answer 1

30% return; 20% excess return over the desired rate of return

Step-by-step explanation:

The question "what will be investment generate" is not clear. As such, the answer below deals with the question as much as it could.

With an investment cost of $40,000 and annual cash flows of $12,000,

• the annual rate of return on the investment = 12,000/40,000 = 30%

• This rate of return exceeds the desired rate of return by = 30% - 10% = 20%.

In dollar terms, the excess return

= $12,000 - ($40,000 * 10%)

= $12,000 - $4,000

= $8,000.

The above solution assumes the annual cash flows comprises only the return on investment and that the principal investment will be repaid at the end of the investment period (4 years). It also assumes that the desired return on investment is an annual rate.

However, if the annual cash flows of $12,000 for 4 years comprises both the principal and interest repayment, and no return of capital will be made at the end of the tenor, then

total investment return over the 4 year period = 4 * 12,000 = $48,000

In dollar terms, the return on the investment = 48,000 - 40,000 = $8,000

In percentage terms, the return on investment

=
`(8,000)/(40,000)` = 20% (over 4 years).

The return on investment exceeds the desired rate of return (10%) by

= 20% - 10% = 10%.

(this solution assumed that the desired rate of return is not an annual rate, but a rate required over the lifetime of the investment, which is 4 years).