Question

Rackin Pinion Corporation’s assets are currently worth $1,065. In one year, they will be worth either $1,000 or $1,340. The risk-free interest rate is 3.9 percent. Suppose the company has an outstanding debt with a face value of $1,000.

A) What is the value of equity?

B) What is the value of debt? The interest rate on debt?

C) Would the value of equity go up or down if the risk-free interest rate were 20 percent? What does your answer illustrate?

Answer 1

A) Value of assets represents the enterprise value of the business. Its at $1065 and debt has a face value of $1000. For the computation of equity value, the face value would be used, hence

Enterprise value = Equity value + Debt

1065 = Equity + 1000

Hence Equity value currently is $65

B) Market value of debt is usually determined based on the marginal borrowing rate for the company in consideration. Since the question does not have that information, and is largely vague in that area, it is not possible to answer this.

In absence of the details on the debt instruments and the marginal borrowing rate of teh company, we need to assume that the value of debt is equal to its face value or maturity obligation value

C) If risk free rate goes up, the required return on equity will increase as well (using the basic CAPM formula Risk free rate is added to the product of Beta and market return premium to compute equity return requirement). This will result in a decline in equity value, everything else remaining the same.

The above simply illustrates that as the market starts expecting higher returns from risk free debt instruments, the required returns from risky forms of investments like equity also move in the same direction.

The question is generally vague.. a better answer is possible for B) and C) if the question can be properly framed and gaps can be filled.