In: Finance

A firm has two mutually exclusive investment opportunities, Alpha and Beta. Returns on the projects are as follows: Project Alpha: returns $300 million after one year with probability 40% and $50 million after one year with probability 60%. Project Beta returns $180 million after one year for certain. Assume that all investors are risk-neutral so that present values can be calculated by discounting expected future cash flows at the risk-free interest rate of 5% per year. Also, assume that all tax rates are zero. If each of these projects requires an investment of $120 million and lenders were to agree to provide $120 million of financing today in exchange for a zero-coupon bond with a face value of $126 million maturing in one year, reflecting the 5% risk-free interest rate:

(a) Calculate the expected payoff after one year from each project for the firm and the equity holders.

(b) If management makes investment decisions that are in the best interest of equity holders, which project would they choose and what is the expected agency cost to the lenders?

**Solution 1) For project Alpha:**

Expected payoff | Probability | Probability weighted payoff | |

300 | 40% | =300*40% | 120 |

50 | 60% | = 60%*50 | 30 |

Thus, **expected payoff after 1 year = 120+30 =
150**

Investment = 120

Thus, the Net Present Value of the project is calculated as:

NPV = 150/(1+5%) - 120 =

Also, IRR can be calculated as 120 = 150/(1+5%)

**IRR = 150/120 - 1 = 25%**

**For project Beta:**

**Expected payoff after 1 year = 180**

Investment = 120

Thus, to calculate the internal rate of return (IRR):

120 = 180/(1+IRR)

IRR = 180/120 - 1

**IRR = 50%**

**Also, NPV = 180/(1+5%) - 120 = 51.42857**

**Solution 2)** Since NPV and IRR of the project
Beta is high, thus, Project Beta would be in the best interest of
the equity holders.

The agency cost of debt occurs when the wealth is transferred from the hands of the lenders to the shareholders. Thus, it may occur by transferring dividends before the interest payments.

The interest rate on debt raised from the lender is 5%

Expected payoff for the lender if Project Alpha is selected = 40%*5% = 2%

Expected payoff for the lender if Project Beta is selected = 100%*5% = 5%

Thus, the expected payoff for the lender is maximized by selecting Project Beta. Hence, there is no agency cost to debt in this case.

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