Build A Model Solution Chapter 5 Student Ch 5-20

Build A Model Solution2112chapter 5 Student Ch 5-20 Build a Model

Rework Problem 5-19. Conroy Consulting Corporation (CCC) has been growing at a rate of 30% per year in recent years. This same growth rate is expected to last for another 2 years (g1 = g2 = 20%). a. If D0 = $2.50, rs = 12%, and gn = 7%, what is CCC's stock worth today? What are its expected dividend yield and capital gains yield at this time?

1. Find the price today. D0 = $2.50, rs = 12.0%, g0,1 = 30%. Short-run g1 for Year 1 only. g1,2 for Year 2 only. gL = 7% long-run g for Year 3 and all following years.

2. Calculate the expected dividend yield, which is equal to the next expected dividend divided by the current stock price.

3. Calculate the expected capital gains yield, which equals the total expected return minus the dividend yield.

To determine the stock price, first compute the dividends for subsequent years, discount the dividends and the terminal value to the present, and then derive dividend yield and capital gains yield. The terminal value P2 is calculated based on the long-term growth rate and the required return.

Assuming the growth rate shifts to a nonconstant period lasting 5 years, recalculate the stock price accordingly, discount dividends for 5 years, and compute the terminal value at year 5 using the long-term growth rate of 7%. The calculations for dividend yield and capital gains yield follow similar steps.

Once the nonconstant growth period ends, the dividend yield and capital gains yield stabilize at the same values as in the shorter period, reflecting the long-term growth assumptions.

Sample Paper For Above instruction

The valuation of a company's stock using the dividend discount model (DDM) hinges critically on expected future dividends and the growth rate of those dividends. Conroy Consulting Corporation (CCC) has experienced recent growth rates of approximately 30%. However, sustainable long-term growth is assumed to taper to a more modest 7%, consistent with industry averages or economic fundamentals. This paper aims to compute the intrinsic value of CCC’s stock considering a short-term high-growth phase followed by a stable, long-term growth phase. It will also detail the expected dividend yield and capital gains yield at the current valuation point.

Introduction

Valuing stocks with varying growth phases involves understanding the dividend discount model, particularly the Gordon Growth Model (GGM), and adjusting for periods of nonconstant growth. The primary task involves estimating the current stock price given the expected dividends, growth rates, and required rate of return. Additionally, the dividend yield, representing the portion of the stock's value paid out as dividends, and the capital gains yield, reflecting stock price appreciation, are essential for investor expectations and portfolio strategies.

Current Growth Environment and Data Inputs

Recent performance indicates a 30% annual growth rate in dividends and earnings for CCC. This high-growth period is projected to persist for the next two years, after which growth is expected to stabilize at a 7% long-term rate indefinitely. The initial dividend (D0) is $2.50, and the required rate of return (rs) is 12%. Using these inputs, the valuation approach involves forecasted dividends, discounting, and the application of terminal value calculations for the stable-growth phase.

Calculation of Stock Price with 2-Year High Growth

In the initial phase, dividends are expected to grow at 30% for Year 1 and Year 2:

  • D1 = D0 × (1 + g1) = $2.50 × 1.30 = $3.25
  • D2 = D1 × (1 + g2) = $3.25 × 1.30 = $4.225

At the end of Year 2, the stock's value (P2) can be estimated using the Gordon Growth Model, assuming a perpetual growth of 7% from Year 3 onwards:

P2 = D3 / (rs - gL), where D3 = D2 × (1 + gL) = $4.225 × 1.07 ≈ $4.523

Calculating P2:

P2 = $4.523 / (0.12 - 0.07) = $4.523 / 0.05 ≈ $90.46

This represents the present value at Year 2 of all dividends beyond Year 2.

Discounting D1, D2, and P2 back to today (Year 0):

  • PV of D1 = D1 / (1 + rs)^1 ≈ $3.25 / 1.12 ≈ $2.90
  • PV of D2 = D2 / (1 + rs)^2 ≈ $4.225 / 1.2544 ≈ $3.37
  • PV of P2 = P2 / (1 + rs)^2 ≈ $90.46 / 1.2544 ≈ $72.12

Adding these components yields the intrinsic stock price:

P0 = PV of D1 + PV of D2 + PV of P2 ≈ $2.90 + $3.37 + $72.12 ≈ $78.39

This is the estimated current value per share under high-growth assumptions for two years.

Dividend Yield and Capital Gains Yield

The expected dividend yield at present is D1 / P0:

Dividend yield ≈ $3.25 / $78.39 ≈ 4.15%

The total expected return is the required rate of 12%; thus, the capital gains yield is:

Capital gains yield = rs - dividend yield ≈ 12% - 4.15% ≈ 7.85%

This aligns with the long-term growth rate of 7%, confirming that stock appreciation compensates for the dividend yields.

Alternative Scenario: 5-Year Nonconstant Growth Period

If the high-growth period extends to 5 years with similar growth rates, the valuation adjustments involve computing dividends for each of those years, discounting them, and estimating the terminal value at Year 5 using the stable long-term growth rate:

  • D1 = $2.50 × 1.30 = $3.25
  • D2 = D1 × 1.30 = $4.225
  • D3 = D2 × 1.30 = $5.491
  • D4 = D3 × 1.30 ≈ $7.138
  • D5 = D4 × 1.30 ≈ $9.280

At the end of Year 5, the terminal value P5 is:

P5 = D6 / (rs - gL), where D6 = D5 × 1.07 ≈ $9.280 × 1.07 ≈ $9.94

P5 = $9.94 / 0.05 ≈ $198.80

Discounting all cash flows back to today provides an updated estimate of the stock value, generally higher due to the extended high-growth phase.

Similarly, the dividend yield and capital gains yield are derived from the computed P0, confirming their dependency primarily on the long-term growth assumptions.

Conclusion

Estimating a stock's intrinsic value involves complex assumptions about future growth, required returns, and dividend policies. The case of CCC demonstrates how a phased growth model affects valuation, yields, and expectations. Recognizing the acceleration and stabilization phases allows investors to gauge the present worth accurately and formulate informed investment decisions. Ultimately, the steady-state valuation reflects the sustainability of growth rates aligned with economic fundamentals, emphasizing the importance of long-term stability in dividend growth assumptions.

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