### Compute projects irr-npv and npi

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1) A firm is evaluating the following two mutually exclusive, but quite profitable, projects, projects. (ALL COMPUTIONSNEEDED FOR FULL CREDIT) (Assume cost of capital is 0.25)

Project

time I II

0 -\$10,000 -\$10,000

1 0 +\$23,026

2+ \$45,000 +\$10,000

A) Compute each project's IRR, NPV and NPI.

B) Use this example to show the inability of IRR to maximize shareholder's wealth.

C) Which project will accept and Why?

D) Later on it was found that there was a mistake in the problem. The cost of capital was not 25 but 52 percent. Will your answer to A, B, and C above will change? If yes, provide and explain all conclusions.

2) Consider a 10-year life project that will cost \$1000 today and will return \$200 for the first five years and \$300 for the next five years. If the cost of capital is 6%, what must be the cut-off payback period so that NPV and regular Pay-back period method will result in identical accept/reject decision? ( SHOW ALL THE COMPUTIONS).

3) The Tau company, with a present cost of capital of 14%, has the following cash flow:

t P Q

0-10,000 -12,000

1+5,506 +4,991

2+5,506+4,991

3 +5,506 +4,991

4 +5,506 +4,991

However management believes that during the next 4 years there will be change in business conditions that will result in the reinvestment rates and cost of capital shown in the following table:

t i t k t

1 16% 14%

2 18 10

319 10

420 10

Obtain 1) IRR, 2) NPV, 3) PI, 4)MNPV, 5) MIRR of each project. ( i = reinvestment rate, k = cost of capital). SHOW ALL COMPUTATIONS.

4) The following information about a project being considered are given:

Life of the project is 2 years.

Expected Cash Flows in Year 1 is \$250

Expected Cash Flows in Year2 is \$350

initial Investment is -\$300

CE Factors Year 1 is 0.93

CE Factors Year 2 is 0.86

Variance of Cash Flows in Year 1 is 100

Variance of Cash Flows in Year 2 is 144

Risk Free Rate in Year 1 is 0.06

Risk Free Rate in Year 2 is 0.05

Covariance between cash flow 1 and 2 is 42.20

Beta of the firm in Year 1 is 1.67

Beta of the firm in Year 2 is 1.30

The Expected Market rate of return in Year 1 is 0.11

The Expected Market rate of return in Year 2 is 0.10

Compute:

A) Obtain the NPV using the RADR approach

B) Obtain the NPV using the CE Approach

C) Obtain the variance of NPV assuming that cash flows are independent

D) Obtain the variance of NPV assuming that cash flows are perfectly positively correlated

E) Obtain the probability that NPV >= 0, under (C)

F) Obtain the probability that NPV >= 0, under (D)

G) Obtain the variance of NPV assuming the covariance structure given in the problem

H) Obtain the probability that NPV >= 0, under (G)

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