Related To Checkpoint 91 Floating Rate Loans The Bensington

Related To Checkpoint 91 Floating Rate Loans The Bensington G

Analyze a series of financial problems related to floating-rate loans, bond valuation, and stock valuation, including calculations of interest rates, present values, and stock prices based on given data and market conditions.

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Financial decision-making requires a comprehensive understanding of various valuation methods, interest rate calculations, and market dynamics. The questions provided address fundamental concepts in finance, including floating-rate loans, bond valuation, and stock valuation, which are critical for both corporate finance management and investment analysis.

Floating-Rate Loans: Interest Rate Calculations

The Bensington Glass Company has entered into a floating-rate loan agreement linked to LIBOR, which varies weekly. The loan's rate is set as LIBOR plus 0.27%, with caps and floors on the annual interest rate. To calculate weekly interest rates from week 2 through 10, we start with the given LIBOR rates:

  • Week 1: 1.94%
  • Week 2: 1.59%
  • Week 3: 1.55%
  • Week 4: 1.32%
  • Week 5: 1.59%
  • Week 6: 1.66%
  • Week 7: 1.69%
  • Week 8: 1.94%
  • Week 9: 1.88%
  • Week 10: 1.88%

To determine the interest rate for each week, we add 0.27% to each LIBOR rate, ensuring the resultant interest rate stays within the specified maximum of 2.24% and minimum of 1.72%. For week 2, the calculation is as follows:

Interest Rate Week 2 = LIBOR Week 2 + 0.27% = 1.59% + 0.27% = 1.86%

Since 1.86% is between 1.72% and 2.24%, it is the applicable interest rate for week 2.

Similarly, the interest rates for weeks 3 through 10 are computed:

  • Week 3: 1.55% + 0.27% = 1.82%
  • Week 4: 1.32% + 0.27% = 1.59%
  • Week 5: 1.59% + 0.27% = 1.86%
  • Week 6: 1.66% + 0.27% = 1.93%
  • Week 7: 1.69% + 0.27% = 1.96%
  • Week 8: 1.94% + 0.27% = 2.21%
  • Week 9: 1.88% + 0.27% = 2.15%
  • Week 10: 1.88% + 0.27% = 2.15%

All these calculated interest rates fall within the stipulated annual cap and floor, ensuring compliance and accurate calculation of the floating rates for each week.

Bond Valuation: Present Value Calculation

The second problem involves calculating the value of a bond with a 17-year maturity, a $1,000 par value, a 15% annual coupon rate, and a market yield of 14%. The bond's cash flows consist of annual coupon payments and face value repayment at maturity.

The annual coupon payment is:

Coupon = 15% of $1,000 = $150

The present value of the bond (PV) is the sum of the present value of future coupon payments and the present value of the $1,000 face value, discounted at the market yield of 14%:

PV = (C × [1 - (1 + r)^-n]/r) + (FV / (1 + r)^n)

Where:

  • C = $150
  • r = 14% = 0.14
  • n = 17 years
  • FV = $1,000

Calculating each component:

PV of coupons = $150 × [1 - (1 + 0.14)^-17] / 0.14 ≈ $150 × 7.263 = $1,089.45

PV of face value = $1,000 / (1 + 0.14)^17 ≈ $1,000 / 7.843 ≈ $127.52

Thus, the bond's total value is approximately:

PV ≈ $1,089.45 + $127.52 ≈ $1,217.00

This valuation indicates that the bond's market value, considering the given yield, is approximately $1,217.

Stock Valuation: Constant Growth Model

The third problem pertains to valuing a company's stock using the Gordon Growth Model, which assumes dividends grow at a constant rate.

Given:

  • Last year's dividend (D₀) = $4.43
  • Growth rate (g) = 5% = 0.05
  • Required rate of return (r) = 10% = 0.10

The formula for the stock's intrinsic value is:

V = D₁ / (r - g)

Where D₁ = D₀ × (1 + g) = $4.43 × 1.05 = $4.6515

Therefore:

V = $4.6515 / (0.10 - 0.05) = $4.6515 / 0.05 ≈ $93.03

The value of Header Motor, Inc.'s stock is approximately $93.03 based on these assumptions.

Stock Valuation with Dividend Growth and Required Rate of Return

The fourth question involves valuing a stock with a different starting dividend and growth rate. The constants are:

  • Last year's dividend (D₀) = $1.41
  • Growth rate (g) = 6.60% = 0.066
  • Required rate of return (r) = 8.70% = 0.087

The present value of the stock is computed similarly:

D₁ = D₀ × (1 + g) = $1.41 × 1.066 ≈ $1.504

Stock value V = D₁ / (r - g) = $1.504 / (0.087 - 0.066) = $1.504 / 0.021 ≈ $71.62

If the current market price is below this calculated value, the stock could be considered undervalued.

Relative Valuation Using P/E Ratio

The fifth task involves estimating stock price based on P/E multiples given earnings and expected growth.

Given:

  • Expected earnings (E₁) = $7
  • Retention ratio = 60% or 0.60
  • Return on equity (ROE) = 13% or 0.13
  • Required rate of return (k) = 13% or 0.13
  • PE multiple = 7.693 times earnings

The stock's intrinsic value using the P/E method is:

Price = Earnings × P/E multiple = $7 × 7.693 ≈ $53.85

Alternatively, applying the dividend model to confirm the valuation involves calculating dividends per share, expected growth, and discounting at the required rate, which yields a consistent price estimate.

These valuation approaches demonstrate the importance of multiple methodologies in assessing stock value accurately.

Conclusion

The analysis of floating-rate loans, bond valuation, and stock pricing highlights key financial principles essential in investment decision-making. Accurate calculations of interest rates using LIBOR, present value of bonds considering market yields, and stock valuation employing growth models provide vital insights for investors and financial managers. Familiarity with these methods enhances the capacity to make informed financial choices, gauge market conditions, and optimize portfolio performance.

References

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  • Brealey, R. A., Myers, S. C., & Allen, F. (2017). Principles of Corporate Finance. McGraw-Hill Education.
  • Fabozzi, F. J. (2015). Bond Markets, Analysis, and Strategies. Pearson.
  • Ross, S. A., Westerfield, R., & Jaffe, J. (2013). Corporate Finance. McGraw-Hill Education.
  • Levy, H. (2014). International Finance: Transactions, Policy, and Analysis. Routledge.
  • Gordon, M. J. (1962). The determinants of the value of a stock. The Review of Economics and Statistics, 44(2), 132-136.
  • McConnell, C. R., & Brue, S. L. (2014). Economics: Principles, Problems, and Policies. McGraw-Hill Education.
  • Hull, J. C. (2018). Options, Futures, and Other Derivatives. Pearson.
  • Shapiro, A. C. (2018). Multinational Financial Management. Wiley.
  • Penman, S. H. (2012). Financial Statement Analysis and Security Valuation. McGraw-Hill Education.

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