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Question 1determine The Following Based On The Data Provided For Thi

Question #1: Determine the following based on the data provided for this debt issue: Issued October 1, 2008, $500,000 face value, 5.5% annual coupon payable semiannual. Bond term: 15 years. Current market bond yield January 31, 2013: 4.5%. What is the bond’s market value on January 31, 2013? What is the return on the investment for the seller of the bond on January 31, 2013? What is the yield to maturity for the buyer of the bond on January 31, 2013?

Question #2: Part I: Maxwell Inc.'s stock has a 50% chance of producing a 25% return, a 30% chance of producing a 10% return, and a 20% chance of producing a -28% return. What is the firm's expected rate of return? Part II: Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to increase by 30%. In addition, expected inflation increases by 2.00%. What is the stock's new required rate of return? Initial beta 1.00 Initial required return (rs) 10.20% Market risk premium, RPM 6.00% Percentage increase in beta 30.00% Increase in inflation premium, IP 2.00%

Question #3: Part I: A stock is expected to pay a dividend of $0.75 at the end of the year. The required rate of return is rs = 10.5%, and the expected constant growth rate is g = 6.4%. What is the stock's current price? Part II: If D1 = $1.25, g (which is constant) = 5.5%, and P0 = $44, what is the stock’s expected total return for the coming year? Part III: Expected rate of return for your firm’s stock. As of today: Risk Free Rate (rf) = 3.0%, Market return (rm) = 11.0%. Find the current beta for the company you selected in our course and determine the Expected Rate of Return for this company.

Question #4: Sorensen Systems Inc. is expected to pay a $2.50 dividend at year end (D1 = $2.50), the dividend is expected to grow at a constant rate of 5.50% a year, and the common stock currently sells for $52.50 a share. The before-tax cost of debt is 7.50%, and the tax rate is 40%. The target capital structure consists of 45% debt and 55% common equity. What is the company’s WACC?

Paper For Above instruction

This paper aims to thoroughly analyze and compute various financial metrics based on the provided data, encompassing bond valuation, expected returns, required rates of return, and weighted average cost of capital (WACC). The focus will be on applying fundamental financial formulas, market concepts, and statistical methods to derive accurate answers to each specified question.

Question 1: Bond Valuation, Return, and Yield to Maturity

First, let's determine the market value of the bond as of January 31, 2013. The bond, issued on October 1, 2008, with a face value of $500,000, carries an annual coupon rate of 5.5% payable semiannually over a 15-year period. The market yield at January 31, 2013, is 4.5%. To find the bond's market value, the present value of its future cash flows (coupons and face value) must be discounted at the current market yield.

The semiannual coupon payment is calculated as:

Coupon Payment = Face Value × (Coupon Rate / 2) = $500,000 × 2.75% = $13,750

The number of remaining periods is:

Remaining Periods = 15 years × 2 = 30 periods

The semiannual market yield is:

Market yield per period = 4.5% / 2 = 2.25%

Using the Present Value of Annuity formula for coupons:

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

And for the face value:

PV of Face Value = Face Value / (1 + r)^n

Where:

• C = $13,750
• r = 0.0225
• n = 30

Calculating the present value:

PV of coupons = $13,750 × [1 - (1 + 0.0225)^-30] / 0.0225 ≈ $13,750 × 20.215 ≈ $278,756.25

PV of face value = $500,000 / (1 + 0.0225)^30 ≈ $500,000 / 1.847 ≈ $270,463.88

Thus, the bond's market value is approximately:

$278,756.25 + $270,463.88 ≈ $549,220.13

Next, the seller's return on investment as of January 31, 2013, depends on the bond's purchase price and the accrued interest. Assuming the bond was purchased at its current market value less any accrued interest, and considering the bond's semiannual coupons, the seller's return can be computed based on the change in market value plus received coupons over the holding period.

Furthermore, the yield to maturity (YTM) from the buyer's perspective aligns closely with the market yield (4.5%) at purchase, calculated using the bond valuation formula above, but solved for the yield. Since the bond is priced above face value, the YTM would be slightly below the coupon rate but close to the current market yield, approximately 4.5% annually.

Question 2: Expected Return and Required Rate of Return

Part I involves the calculation of the expected return based on probability-weighted outcomes:

Expected Return (ER) = (Probability1 × Return1) + (Probability2 × Return2) + (Probability3 × Return3)

Substituting the values:

• ER = 0.50 × 0.25 + 0.30 × 0.10 + 0.20 × (-0.28)

Calculating each component:

• 0.125 + 0.03 - 0.056 = 0.099 or 9.9%

Therefore, the expected rate of return for Maxwell Inc. is approximately 9.9%.

Part II examines the adjustment of Dana Industries' required rate of return considering a 30% increase in beta and a 2% rise in inflation premium. The initial required return using the Capital Asset Pricing Model (CAPM) is:

rs = rf + β × RPM

Initially, with β = 1.00 and rf estimated from market data:

Assuming rf includes the inflation premium, initial rf = risk-free rate + inflation premium. For simplicity, assume initial rf is approximated as 3.0% (risk-free rate), and the market risk premium (RPM) is 6.0%, leading to initial rs = 3.0 + 1.00 × 6.0 = 9.0%. However, given the initial rs is 10.20%, this indicates a slightly higher risk-free rate or other premiums incorporated.

With a 30% increase in beta:

New β = 1.00 × 1.30 = 1.30

The new required rate of return becomes:

rs_new = rf + (β_new × RPM) + inflation premium increase

Substituting the values:

rs_new = 10.20% + (0.30 × 6.00%) + 2.00% = 10.20% + 1.80% + 2.00% = 14.00%

This suggests that the stock’s new required rate of return, considering increased risk and inflation, is approximately 14.00%.

Question 3: Stock Valuation and Expected Returns

Part I involves calculating the current stock price using the Gordon Growth Model:

P0 = D1 / (rs - g)

Given D1 = $0.75, rs = 10.5%, g = 6.4%:

P0 = $0.75 / (0.105 - 0.064) = $0.75 / 0.041 = approximately $18.29

This current price suggests the fair value based on the dividend discount model.

Part II calculates the expected total return for the coming year with D1 = $1.25, g = 5.5%, and P0 = $44:

Expected Return = (D1 / P0) + g = ($1.25 / $44) + 0.055 ≈ 0.0284 + 0.055 = 8.34%

Thus, the expected total return for the upcoming year is approximately 8.34%.

Part III involves computing the current beta of a company's stock and the expected return. Using the Capital Asset Pricing Model:

rs = rf + β (rm - rf)

Rearranged to solve for beta:

β = (rs - rf) / (rm - rf)

Given rf = 3.0%, rm = 11.0%, and an assumed rs based on the company's characteristics—assuming rs is aligned with the market's average return, for example, 9.5%, then:

β = (9.5% - 3.0%) / (11.0% - 3.0%) = 6.5% / 8.0% ≈ 0.8125

Therefore, the company's stock has an approximate beta of 0.81, resulting in an expected return of:

rs = 3.0% + 0.81 × (11.0% - 3.0%) = 3.0% + 0.81 × 8.0% ≈ 3.0% + 6.48% = 9.48%

Question 4: WACC Calculation

The Weighted Average Cost of Capital (WACC) considers the proportion of debt and equity, their respective costs, and applicable taxes. Given a debt component of 45%, equity component of 55%, cost of debt before tax at 7.5%, and tax rate of 40%, the WACC is computed as:

WACC = (E/V) × Re + (D/V) × Rd × (1 - Tc)

Where:

• E/V = 0.55
• D/V = 0.45
• Re = cost of equity (using dividend growth model):
• Re = D1 / P0 + g = $2.50 / $52.50 + 0.055 ≈ 0.0476 + 0.055 ≈ 0.1026 or 10.26%
• Rd = 7.50%
• Tc = 40%

Calculating WACC:

WACC = 0.55 × 10.26% + 0.45 × 7.50% × (1 - 0.40)

WACC = 0.55 × 0.1026 + 0.45 × 0.075 × 0.60 ≈ 0.05643 + 0.02025 ≈ 0.07668 or 7.67%

Therefore, the company's WACC is approximately 7.67%.

Conclusion

Through detailed financial calculations, this analysis provided the bond market value, expected returns, required rate of return adjustments considering risk and inflation, stock valuation, and overall cost of capital. These metrics are essential for making informed investment and corporate finance decisions, highlighting the significance of accurate financial modeling in strategic planning and valuation.

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