Question

14) Mitchell Investments has offered you an investment opportunity that throws out the following revenue stream: . $6000 at the end of each year for the first 5 years, plus $3000 at the end of each year from years 6 through 10, plus . $2000 at the end of each year from years 11 through 20. ed a 12% return? b) If the investment costs $30,000 today, what rate of return will you earn?

​​​​​​​

Answer 1

The picture above indicates the timeline for this given problem.

Let us divide the 3 phases as follows:

• R1 = From year 0 to year 5 (end of year 5)
• R2 = From year 6 to year 10 (end of year 10)
• R3 = From year 11 to year 20 (end of year 20)

Total number of periods in each phase is as follows:

• In R1, n = 5
• In R2, n = 5
• In R3, n = 10

(a)

To calculate the amount we will be paying today for these revenue streams, we will have to discount all these cash flows at the given rate, 12% for the given time periods. Also, all the cash flows occur at the end of time period, thus it is an ordinary annuity.

The Present Value of Annuity = Annuity* {(1/r) - [1/(r*(1+r)^n)]}

Present Value of R1 = $6,000* {(1/0.12) - [1/(0.12*(1+0.12)^5)]}

PV of R1 = $21,628.66

Present Value of R2 = $3,000* {(1/0.12) - [1/(0.12*(1+0.12)^5)]}

PV of R2 = $10,814.33

Present Value of R3 = $2,000* {(1/0.12) - [1/(0.12*(1+0.12)^10)]}

PV of R3 = $11,300.45

Thus, the amount you would be willing to pay for this investment, if required a 12% return would be $43,743.44 ( PV of R1 + PV of R2 + PV of R3)

(b)

At a cost of $30,000 today, we need to find the internal rate of return (IRR) to calculate the rate of return we would earn on the investment.

This can be calculated using the financial calculator, or using the Interpolation method

Using either ways, we shall get a return of 13.02%.