Question

Assume a world in which the assumptions of the capital asset pricing model (CAPM) hold. A company can invest in a project which costs today $5,000, in one year delivers $2,000 with certainty and in two years delivers -$1,000 with a probability of 25% and $8,000 with a probability of 75%. Suppose the annual risk free rate is 3%, the expected return on the market is 10% and the project’s market beta is 1.5. Should the company invest in the project or not? Explain why or why not

Answer #1

First of all lets find cost of equity

Cost of equity = Risk free rate of return + beta(Market return - Risk free rate of return)

=3% + 1.5(10%-3%)

=3%+1.5(7%)

=3%+10.5%

=13.5%

Now lets calculated expected cash flow in year 2

Cash flow | Probability | Cash flow x probability |

-1000 | 0.25 | -250 |

8000 | 0.75 | 6000 |

Expected cash flow | 5750 |

Thus expected cash flow in year 2 = 5750$

Now let's calculate NPV

Statement showing NPV

Year | Cash flow | PVIF @ 13.5% | PV |

A | B | C = A x B | |

1 | 2000 | 0.8811 | 1762.11 |

2 | 5750 | 0.7763 | 4463.51 |

Sum of PV of cash inflow | 6225.62 | ||

Less: Initial Investment | 5000.00 | ||

NPV | 1225.62 |

Thus NPV = 1225.62 $

Since NPV is positive , it will add value to the firm and hence investment must be made in the project

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