Question

1. HAL Corporation is introducing a new artificial intelligence product.  There are three possible outcomes:  If the product is highly successful, the company will be worth $900 million, if moderately successful $500 million, if a complete failure $100 million.  Each outcome is equally likely.  The results will be known two years from today.  There are no taxes on income or capital gains.  
   1. If the risk-free rate of return is 10%, what is the maximum amount of risk-free debt HAL can issue?
   2. If HAL’s unlevered equity premium is 8%, what is the unlevered value of HAL today?
   3. What is HAL’s unlevered cost of capital?
   4. What is HAL’s cost of capital if it issues $82 million of debt? What is the cost of equity and debt, respectively?  Show your calculation.

Answer 1

a ) The lowest value generated by the project in 2 years = $100 million

maximum amount of risk free debt = 100/1.1^2 = $82.64 million

b) Unlevered equity premium = 8%

So, cost of unlevered equity = 10%+8% =18%

Expected value of the project after 2 years = 900*1/3+500*1/3+100*1/3 = $500 million

Unlevered value = 500/1.18^2 = $359.09 million

c) Unlevered cost of capital = Unlevered cost of equity = 18%

d)As there are no taxes value of firm will remain the same = $359.09 million

So, the cost of capital will be the same as the unlevered cost of capital = 18%

As $82 million can be issued at a riskfree rate , cost of debt =10%

Cost of levered equity = Cost of unlevered equity + (cost of unlevered equity -cost of debt)*D/E

= 18%+ (18%-10%)*82/(359.09-82)

=20.367%