Question

1. Nike has a project that will produce cash flows $200 next year if the economy is strong and $50 if the economy is weak. Suppose the corporate tax rate is 0. The economy will be strong with probability 50%. Nike issued both debt and equity to raise funds out of this project as much as possible. Specifically, Nike raised $60 by issuing debt with a face value $80. So, the creditors will receive $80 in total if the economy is strong but receive only $50 if the economy is bad because Nike defaults in this case. Nike also raised $50 by issuing equity as much as possible. The market risk premium is 7% and the risk-free rate is 5%. The entrepreneur of Nike has no equity shares in her firm. Now, suppose there is another shoes company, New Balance. This firm also has a project that will produce $200 next year if the economy is strong and $50 if the economy is weak. But the entrepreneur of New Balance wants to raise only $40 by issuing debt to avoid the chance of default. Assuming issued at risk-free rate and face value of $42 on the debt. She also plans to issue equity to raise funds as much as possible out of her project.

1. Suppose investor A is a single investor of Nike, who holds all the bonds and equities issued by Nike. Also, suppose investor B is a single investor of New Balance. The payoffs to these two investors will be the same?
2. If yes, how much can New Balance raise from equity holders? Does the total amount of funds that can be raised depend on the default risk of a firm?
3. What’s the expected return of equity for New Balance? What’s the equity beta?
4. What’s the cost of capital of New Balance?

Answer 1

Suppose investor A is a single investor of Nike, who holds all the bonds and equities issued by Nike. Also, suppose investor B is a single investor of New Balance. The payoffs to these two investors will be the same?

Yes, the payoffs to these two investors will be the same. They both are exposed to the same asset, same cash flows from the asset and same riskiness in the cash flows. Hence, the two investors will have the same payoff

If yes, how much can New Balance raise from equity holders? Does the total amount of funds that can be raised depend on the default risk of a firm?

In the absence of taxes, as per MM proposition, the value of the firm is independent of the capital structure.

Value of Nike = Debt + Equity = 60 + 50 = 110

Value of New Balance = 110 = 40 + Equity

Hence, equity that New Balance can raise = 110 - 40 = $ 70

Yes, the total amount of funds that can be raised does depend on the default risk of a firm. The default risk increases the cost of debt as well as equity thereby making capital expensive.

What’s the expected return of equity for New Balance? What’s the equity beta?

Equity = 70

Project cash flows = $200 next year if the economy is strong and $50 if the economy is weak.

Debt = $ 40

Residual Cash flows to equity holders = $200 - 40 = $ 160 next year if the economy is strong and $50 - 40 = $ 10 if the economy is weak

Probability of each outcome is 50%. Hence, expected cash flows by equity holder = 50% x 160 + 50% x 10 = $ 85

Hence, the expected return = 85 / 70 - 1 = 21.43%

Also the expected return = 21.43% = Risk free rate + beta x market risk premium = 5% + beta x 7%

Hence, beta = (21.43% - 5%) / 7% = 2.35

What’s the cost of capital of New Balance?

Proportion of debt = Wd = D / (D + E) = 40 / (40 + 70) = 0.3636

Proportion of equity = We = 1 - Wd = 1 - 0.3636 = 0.6364

Cost of debt = Kd = risk free rate = 5%

Cost of equity = Ke = 21.43% (Calculated earlier)

Cost of capital = Wd x Kd + We x Ke = 0.3636 x 5% + 0.6364 x 21.43% = 15.46%