Question

You have a sum of $10,000 available for investments. You are offered two options:

Deposit the sum in a bank for 3 years, with an interest rate of 10% compounded annually. The bank is also prepared to take on any additional investments at the same rate at any time for the next 3 years.

Invest the $10,000 in a project with an annual return of $4200. The project life is 3 years.

Which is the preferred option? Explain your answer.

Note: This question highlights one of the basic assumptions used in economic evaluation techniques.

Answer 1

You have a sum of $10,000 available for investments. You are offered two options:

Let’s calculate future value of both options by assuming same interest rate or required rate of return

Option 1:

Deposit the sum in a bank for 3 years, with an interest rate of 10% compounded annually.

The bank is also prepared to take on any additional investments at the same rate at any time for the next 3 years that means interest on investment are re-invested at same rate.

Future value of investment after 3 years,

FV = PV * (1+i) ^n

Where, FV is the future value =?

Present Value (PV) =$10000

i = I/Y = interest rate per year = 10%

And n is time period =3

Therefore,

FV = $10000 * (1+10%) ^3

= $13,310

Future value of option 1 is $13,310

Option2:

Invest the $10,000 in a project with an annual return of $4200. The project life is 3 years. You can deposit annual return in bank with an interest rate of 10% compounded annually.

Future value of option 2 after 3 years;

FV = $4,200* (1+10%) ^3 + $4,200 *(1+10%) ^2 * $4,200/ (1+10%) ^1

= $5,590.20 + $5,082.00 + $4,620.00

= $15,292.20

Future value of option 2 is $15,292.20

The preferred option is option 2 as the future value is more for that option.