Lima Inc. can choose between two mutually exclusive projects, both costing 2,700

Question

Lima Inc. can choose between two mutually exclusive projects, both costing 2,700,000 and both having a one-year life.

Assume that all agents are risk neutral, and that the risk-free rate is 3%. The economic conditions in the upcoming year can be either good or bad. The first project has a low payoff volatility and the second project has a high payoff volatility. The payoff characteristics are as followed:

Situation Probability           Low Volatility Project Payoff                  High Volatility Project Payoff

BAD         0.6                        2,500,000                                                     1,400,000

GOOD      0.4                        3,750,000                                                     5,250,000

Assume that the company needs to fund 90% of the initial investment by issuing a zero coupon bind with maturity 1 year

a) What is the face value of the zero coupon bond if debt holders believe that the low volatility project will be undertaken?

Explanation / Answer

Answer FV is 2505154.64 Description Amount Remarks Cost of the project 2700000 Life in years 1 Risk free rate 3% Amount to be funded 2430000 (90%*2700000) Face Value of the zero coupon bond Let us assume it is x (This is to be found) Then interest on FV for 1 year x*3% 0.03x Equation 2430000+0.03x=x Concept of zero coupon bond is that after 1 year, the FV will be returned to the lenders. The requirement for borrowings was 2430000 which is nothing but the face value discounted by 3% over 1 year, in other words, the amount borrowed i.e. 2430000+interest @ 3% on the face value should equal the face value after 1 year. Solving for the value of x 2505154.64 Answer

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