Question

for engineering economics

(20) 4. A project has the cash flow shown below. How many real positive rates of return could there be? Year 0 1 2 3 4 Net Cash Flow (NCF): -$10,000 +$3,000 $5,000 +$5000 -$1,000

Answer 1

Solution: According to the rule of signs, which states that the number of changes in sign in the sequence of net cash flow, gives the real positive values of the rate of return.

Since there is a sign change from Year 0 to Year 1 that is the value changes from -$10,000 to + $3,000 and there is another sign change from Year 3 to Year 4 that is value changes from $ +$5,000 to -$1,0000

The real positive rate of returns possible are less than or equal to 2.

This can be shown as:

NPV= -10,000 + 3000/(1+r)¹ + 5000/(1+r)² + 5000/(1+r)³ -1000/(1+r)⁴= 0

The positive root of this equation is 0.0963 or the rate of return will be 9.63% for which the Net Present Value becomes 0.