Question

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 $250 billion, if moderately successful $100 billion, if a complete failure $10 billion. The probability of each outcome is as follows: highly successful: 40%, moderately successful: 40% and complete failure: 20%. The results will be known two years from today. There are no taxes on income or capital gains. Show your calculations. (10 pts) a. If the risk-free rate of return is 5% annually, what is the maximum amount of riskfree debt HAL can issue? b. If HAL’s unlevered equity premium is 18%, what is the unlevered value of HAL today? c. What is HAL’s unlevered cost of capital? d. HAL’s raises $4.622 billion by issuing debt. What is the cost of equity and debt, respectively? What is HAL’s WACC? e. Do your answers to a through d support MM I and II? Why or why not?

Answer 1

The question involves calculating the financial metrics for HAL Corporation under different scenarios with varying probabilities of success. The calculations include the maximum risk-free debt HAL can issue, the unlevered value of HAL today, the unlevered cost of capital, cost of equity, cost of debt, and HAL's WACC. Lastly, one evaluates whether these answers are consistent with the MM I and II theorems.

Step-by-step explanation:

The student's question involves calculations around the financial outlook for HAL Corporation which is introducing a new artificial intelligence product. To solve their question, we must consider the probabilities of different outcomes for the company's value and utilize financial concepts such as risk-free rate, equity premium, and unlevered cost of capital.

a. Maximum Amount of Risk-Free Debt HAL Can Issue

To calculate this, we discount the value of the company at the worst-case scenario ($10 billion) back to present value using the risk-free rate (5%). The formula for this is:

Present Value = Future Value / (1 + risk-free rate)^number of years

$10 billion / (1 + 0.05)^2 = $10 billion / 1.1025 = $9.0703 billion

This is the maximum amount of risk-free debt HAL can issue today.

b. Unlevered Value of HAL Today

The unlevered value of HAL is the present value of the company in all three scenarios, weighted by their probabilities. This is calculated as follows:

(Highly successful scenario's value * its probability) + (Moderately successful scenario's value * its probability) + (Complete failure scenario's value * its probability).

Discount these combined values back to present value using the risk-free rate.

c. HAL's Unlevered Cost of Capital

The unlevered cost of capital can be found as the yield that equates the present value of the expected future cash flows (from b) to the unlevered value of HAL today.

d. Cost of Equity and Debt, and HAL's WACC

After HAL raises $4.622 billion by issuing debt, we must calculate the cost of equity using the levered equity formula and the cost of debt using the yield on the issued bonds. Then, calculate HAL's weighted average cost of capital (WACC) by weighting the costs of equity and debt by their proportions in the total capital structure.

e. Support for MM I and II Theorems

To determine if the answers a through d support Modigliani and Miller Proposition I and II (MM I and II), we would analyze if the changes in HAL's leverage affect its overall cost of capital and the value, in accordance with MM theories.