Question

You are considering an investment that costs $2,000. It is expected to have a usefule life of three years. You are very confidnt about the revinues during the first two years ($1,000 in Year 1 and $1,200 in Year 2), but you are very unsure about the revenue in year 3. If you hope to make at least 10% rate of return in your investment, what is the minimun revenue in year 3 that would make this possible?

Answer 1

The minimum revenue in year 3 is $132

Step-by-step explanation:

The minimum revenue in year can be ascertained at the point where the initial investment equals the present value of all future cash flows:

$2000=$1000*(1+10%)^-1+$1200*(1+10%)^-2+X*(1+10%)^-3

Note that X is the revenue in year 3

$2000= $909.09+$ 991.74 +X*0.7513

$2000-$909.09-$991.74=X*0.7513

99.17 =X*0.7513

X=99.17/0.7513

X=$132

Hence the minimum revenue expected in year 3 is $132 which means that the company is left at a position where no gain or loss is made on the initial investment of $2000.

If it is envisaged that revenue in year 3 would be less than $132 , the project would be not investing because it would be put the business at a disadvantageous position on loss on investment

Answer 2

The minimum revenue in year 3 should be: $132.

Step-by-step explanation:

Denote X is the cashflow in year 3.

We have net present value of the project, to achieve 10% required rate of return should be:

- Initial investment + Present value of Year 1 Cashflow + Present value of Year 2 Cashflow + Present value of year 3 cash flow = -2,000 + 1,000/1.1 + 1,200/1.1^2 + X/1.1^3 = 0 <=> X/1.1^3 = 99.174 <=> X = $132.

So, to achieve at least 10% required rate of return, the revenue in year 3 should be at least $132.

Thus, the answer is $132.