Question

You have calculated the NPV and IRR for two investment projects based on the costs and cash flows, but you can only select the best one to choose between project A, and Project B. Based on the following data, which one will you select, and why?

Project A                     Project B

NPV: $10,000 $9,000

IRR: 9 % 12%

PART B:

If you invested in every stock listed on the New York Stock Exchange, would you be fully diversified? Would you have eliminated all of the risks? Explain.

You must provide any in-text citations as per the APA guide. Failure to comply with the APA standard will cause a reduction in your grade.

Answer 1

IRR indicates the rate of return achieved by the project. This can be used as a hurdle rate.This means any project having IRR less than the required rate of return should be rejected.

NPV indicates wealth created by the project for the shareholders. In this case Project A creates more wealth for the shareholders .Hence Project A should be selected though its IRR is lower than IRR of Project B.

PROJECT A

PART B

Diversified folios reduce the risk and also the ratio of Risk to reward.

If w1, w2 , w3 …wn are weight in the portfolio for assets 1, 2,3 ….n

Then,w1+w2+w3+……………………+wn=1

R1, R2,R3,…….Rn are the return of the assets 1, 2 , 3 ….n

S1, S2, S3……Sn are the standard deviation of the assets 1, 2, 3 …n

Portfolio Return=w1R1+w2R2+w3R3+…….+wnRn

Portfolio Variance=(w1^2)*(S1^2)+(w2^2)(S2^2)+………….(wn^2)*(Sn^2)+2w1w2*Cov(1,2)+2w1w3*Cov(1,3)+………+w(n-1)wn*Cov(n,(n-1)

Cov(1,2)=Covariance of returns of asset1 and asset2

Portfolio Standard Deviation =Square root of Portfolio variance

Risk of a stock is measured by standard deviation.

Hence reduction of standard deviation through diversification means reduction of risk.

We can take a simple example of two assets 1 and 2

Return of asset1=R1=15%

Return of asset2=R2=12%

Standard deviation of asset 1=S1=10%

Standard deviation of asset 2=S2=8%

Correlation of asset 1 and 2=Corr(1,2)=0.1

Covariance(1,2)=Corr(1,2)*S1*S2=0.1*10*8=8

Assume for simplicity, equal amount is invested in asset 1 and asset 2

Hence, w1=w2=0.5

Portfolio Return;

0.5*15+0.5*12=13.5%

Portfolio Variance=(0.5^2)*(10^2)+(0.5^2)*(8^2)+2*0.5*0.5*8=45

Portfolio Standard Deviation=Square root of Variance=(45^0.5)= 6.708204

We can see, the risk of portfolio as measured by Standard Deviation has reduced significantly to 6,7 whereas the assets in the portfolio had standard deviation of 10 and 8

Risk / Return ratio of the portfolio=6.7/13.5=0.496

Risk/Return ratio of asset1=10/15= 0.666667

Risk/Return ratio of asset2=8/12= 0.666667

Risk return ratio of the portfolio is lower

Diversification with more than 30 stocks gives diminishing returns.

If you invest in all stocks unsystematic risk will be reduced. But systematic risk or the market risk will not be eliminated.

Even after investing in all stocks, there will be systematic risk and uncertainty which cannot be eliminated