Question

Question 9: Consider the following cash flow profile and assume MARR is 10%/year. 0 1 L End of Year Cash Flow -50 18 18 18 18 18 a. What does Descartes' rule of signs tell us about the IRR (s) of this project? b. What does the Norstrom's criterion tell us about the IRR (s) of this project? c. Determine the IRR for this project. Is this project economically attractive based on the IRR? d. Determine the ERR for this project. Is this project economically attractive based on the ERR?

Answer 1

A. As per Descartes rule the IRR of the project is one. That is the given project cash flow has only one sign change thus the IRR is only one.

B. Nordstrom criterion suggests that there is only single sign change in the cumulative cash flow therefore, there is a unique IRR.

C. The net present worth of the project is

$\large NPW = - 50 + 18(P/A,i\%,6)$

Assume rate to be 25%

$\large NPW = - 50 + 18(P/A,25\%,6)$

NPW = - 50 + 18 × 2.9514

NPW = 3.125632

Now assume rate to be 28%

$\large NPW = - 50 + 18(P/A,28\%,6)$

NPW = - 50 + 18 × 2.759379

NPW = - 0.331164

Now apply linear interpolation $\large IRR = 25 + (28 -25) \times \frac{3.125632}{3.125632 -(-0.331164)}$

IRR = 25 + 3 × 0.9041

IRR = 25 + 2.70

IRR = 27.70%

IRR is greater than MARR thus the project is beneficial.

D. First convert the cash inflow into future value

FW = 18(F/A,10%,6)

FW = 18 × 7.71561

FW = 138.88098

The present value of the cash outflow = $ 50

$\large 50(1+ ERR)^6 = 138.88098$

$\large \implies (1+ ERR)^6 = \frac{138.88098}{50}$

$\large \implies (1+ ERR)^6 = 2.7776196$

$\large \implies 1+ ERR= 2.7776196^{\frac{1}{6}}$

$\large \implies ERR= 1.18562 - 1$

$\large \implies ERR= 0.18562$

$\large \implies ERR= 18.56 \%$

The ERR is greater than MARR thus this project is beneficial.

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