Math Problem Statement

(The following information applies to questions 1 through 6.) Consider Rhye, amid-size pharmaceutical company. Rhye’s equity has a book value of $2.8 billion and a market value of $19.4 billion. Rhye’s debt, on the other hand, has a book value of $500 million and a market value of $600 million; the debt’s annual interest rate and yield to maturity are 6% and 5%, respectively. Currently, Rhye has a beta of 1.2 and faces a corporate tax rate of 35%. Also currently, the yield to maturity on 10-year U.S. Treasury Notes is 2.5%. The market risk premium remains around its historical average of 5.5%.

Solution

Based on the information provided about Rhye, we can compute several financial metrics that might be useful for answering various questions related to corporate finance. Let’s start by organizing the dataBased on the information provided about Rhye, we can compute several financial metrics that might be useful for answering various questions related to corporate finance. Let’s start by organizing the

Given Data:

  • Book Value of Equity (BVE): $2.8 billion
  • Market Value of Equity (MVE): $19.4 billion
  • Book Value of Debt (BVD): $500 million
  • Market Value of Debt (MVD): $600 million
  • Interest Rate on Debt: 6%
  • Yield to Maturity (Debt): 5%
  • Beta (β): 1.2
  • Corporate Tax Rate (T): 35%
  • Yield to Maturity on 10-year Treasury Notes (Risk-Free Rate, rfr_f): 2.5%
  • Market Risk Premium (MRP): 5.5%

Key Formulae:

  1. Weighted Average Cost of Capital (WACC): WACC=(EV)re+(DV)rd(1T)WACC = \left(\frac{E}{V}\right) \cdot r_e + \left(\frac{D}{V}\right) \cdot r_d \cdot (1 - T) Where:

    • EE = Market Value of Equity
    • DD = Market Value of Debt
    • VV = Total Value (E + D)
    • rer_e = Cost of Equity (using CAPM)
    • rdr_d = Yield to Maturity (Cost of Debt)
    • TT = Corporate Tax Rate
  2. Cost of Equity (Using CAPM): re=rf+βMRPr_e = r_f + \beta \cdot \text{MRP} Where:

    • rfr_f = Risk-Free Rate (2.5%)
    • β\beta = Beta (1.2)
    • MRP = Market Risk Premium (5.5%)
  3. Capital Structure: EV=Market Value of EquityTotal Market ValueandDV=Market Value of DebtTotal Market Value\frac{E}{V} = \frac{\text{Market Value of Equity}}{\text{Total Market Value}} \quad \text{and} \quad \frac{D}{V} = \frac{\text{Market Value of Debt}}{\text{Total Market Value}}

With this data and formulae, you can answer multiple questions related to Rhye's cost of capital, its leverage, and other corporate finance metrics.

Would you like to calculate the WACC, cost of equity, or any other metric based on the provided information? Let me know!

Here are 5 related questions:

  1. What is the cost of equity for Rhye using the CAPM model?
  2. How do you calculate the weighted average cost of capital (WACC) for Rhye?
  3. What impact does the corporate tax rate have on the WACC?
  4. How do Rhye's book and market values of debt and equity compare in terms of financial health?
  5. Why is the yield to maturity used as the cost of debt in WACC calculations?

Tip: When analyzing WACC, keep in mind that a company's debt can lower its overall cost of capital due to the tax shield on interest payments.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Cost of Capital
Weighted Average Cost of Capital (WACC)
Capital Asset Pricing Model (CAPM)

Formulas

WACC = (E/V) * r_e + (D/V) * r_d * (1 - T)
r_e = r_f + β * MRP
E/V = Market Value of Equity / (Market Value of Equity + Market Value of Debt)
D/V = Market Value of Debt / (Market Value of Equity + Market Value of Debt)

Theorems

Capital Asset Pricing Model (CAPM)
Weighted Average Cost of Capital (WACC)

Suitable Grade Level

College/University Level (Corporate Finance)