I need help with this problem:
1. Hanster Inc. is a levered firm with publicly traded shares. The company has 250 million shares outstanding with a share price of $16 and an estimated equity beta of 1.50. The company has market value based outstanding debt of about $400 million in its capital structure. It plans to continuously refinance the debt and keep it at the same level. That is, it will not change its capital structure going forward. The market cost of the debt is 5% and this is expected to stay so long as the firm maintains its target capital structure. Given the portfolio of assets currently managed by the firm, a stream of perpetual EBIT in the amount of $953.3333 million per annum is expected. The corporate income tax rate (Tc) is 40 percent. Risk free rate is 2% and the expected return on the market portfolio is 10%. It is easy to see that the value of Hanster Inc. is $4,400 million which is the sum of debt and equity, both in market values. Using this as your guideline, please verify that Hanster Inc is indeed worth $4,400 million using both the APV method and the WACC method.
To verify the value of Hanster Inc. using both the APV (Adjusted Present Value) method and the WACC (Weighted Average Cost of Capital) method, we'll need to follow these steps:
1. APV Method:
- Calculate the value of the tax shield (TS) associated with the debt.
- Tax Shield (TS) = Debt * Tax rate
- TS = $400 million * 40% = $160 million
- Calculate the unlevered value of the firm (VU).
- VU = Value of the assets = Perpetual EBIT / Risk-free rate
- VU = $953.3333 million / 2% = $47,666.665 million
- Calculate the value of equity (VE) using the equation:
- VE = VU + TS
- VE = $47,666.665 million + $160 million = $47,826.665 million
- Verify that Hanster Inc. is worth $4,400 million:
- Total value (V) = VE + Debt = $47,826.665 million + $400 million = $48,226.665 million
- Since $48,226.665 million is not equal to $4,400 million, the APV method does not confirm the given value.
2. WACC Method:
- Calculate the cost of equity (Ke) using the Capital Asset Pricing Model (CAPM):
- Ke = Risk-free rate + Beta * (Expected return on the market - Risk-free rate)
- Ke = 2% + 1.50 * (10% - 2%) = 2% + 1.50 * 8% = 2% + 12% = 14%
- Calculate the weighted average cost of capital (WACC):
- WACC = (Equity / Total value) * Ke + (Debt / Total value) * Cost of debt
- WACC = ($47,826.665 million / ($47,826.665 million + $400 million)) * 14% + ($400 million / ($47,826.665 million + $400 million)) * 5%
- WACC = 99.16% * 14% + 0.84% * 5% = 13.86%
- Calculate the value of the firm (V) using the equation:
- V = Perpetual EBIT / WACC
- V = $953.3333 million / 13.86% ≈ $6,876.789 million
- Verify that Hanster Inc. is worth $4,400 million:
- Total value (V) = V = $6,876.789 million
- Since $6,876.789 million is not equal to $4,400 million, the WACC method does not confirm the given value.
In both the APV and WACC methods, we have found that the calculated values for Hanster Inc. do not match the given value of $4,400 million. Hence, the calculated values indicate that Hanster Inc. is not worth $4,400 million based on these methods.