Analyzing Jillian’s Jewelry (JJ) Stock For A Possible ✓ Solved

You are analyzing Jillian’s Jewelry (JJ) stock for a possibl

You are analyzing Jillian’s Jewelry (JJ) stock for a possible purchase. JJ just paid a dividend of $2.25 yesterday. You expect the dividend to grow at the rate of 5% per year for the next 3 years, if you buy the stock; you plan to hold it for 3 years and then sell it. a. What dividends do you expect for JJ stock over the next 3 years? In other words, calculate D1, D2 and D3. Note that D0 = $2.25. b. JJ's stock has a required return of 13%, and so this is the rate you'll use to discount dividends. Find the present value of the dividend stream; that is, calculate the PV of D1, D2, and D3, and then sum these PVs. c. JJ stock should trade for $34.19 3 years from now (i.e., you expect = $34.19). Discounted at a 13% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $34.19. d. If you plan to buy the stock, hold it for 3 years, and then sell it for $34.19, what is the most you should pay for it? e. Use the constant growth model to calculate the present value of this stock. Assume that g = 5%, and it is constant. f. Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today? Explain your answer.

Paper For Above Instructions

Executive summary

This analysis computes the expected dividends for Jillian’s Jewelry (JJ) for the next three years, discounts those dividends and an expected terminal price to present value using a required return of 13%, compares the result with the constant-growth (Gordon) valuation, and explains whether holding period affects the stock's value today. Calculations follow standard dividend discount model (DDM) methodology (Gordon, 1962; Brealey, Myers, & Allen, 2019).

Given data and assumptions

  • D0 (most recent dividend paid) = $2.25
  • Dividend growth rate for next 3 years (g) = 5% per year
  • Required return (discount rate), r = 13%
  • Planned holding period = 3 years; expected selling price at year 3 = $34.19

Part (a) — Expected dividends: D1, D2, D3

With D0 = 2.25 and growth g = 5%, expected dividends are:

D1 = D0 × (1 + g) = 2.25 × 1.05 = $2.3625

D2 = D1 × (1 + g) = 2.3625 × 1.05 = $2.480625

D3 = D2 × (1 + g) = 2.480625 × 1.05 = $2.60465625

These figures are consistent with the standard discrete dividend-growth projection (Brealey et al., 2019).

Part (b) — Present value of the dividend stream

Discount each dividend at r = 13% to the present (time 0). Discount factors: 1/(1+r), 1/(1+r)^2, 1/(1+r)^3.

PV(D1) = 2.3625 / 1.13 = $2.0903 (rounded)

PV(D2) = 2.480625 / (1.13^2) = 2.480625 / 1.2769 = $1.9426 (rounded)

PV(D3) = 2.60465625 / (1.13^3) = 2.60465625 / 1.442897 = $1.8052 (rounded)

Sum of PVs of dividends over three years = 2.0903 + 1.9426 + 1.8052 = $5.8381 (rounded)

Part (c) — Present value of expected future stock price (terminal value)

Expected selling price in year 3 is given as $34.19. Discount it back to present at 13% for three years:

PV(Sale price) = 34.19 / (1.13^3) = 34.19 / 1.442897 = $23.7022 (rounded)

Part (d) — Most you should pay today (combined PV)

The most you should pay equals the PV of dividends you will receive during ownership plus the PV of the sale price at the planned exit date:

Maximum price today = PV(dividends D1–D3) + PV(sale price) = 5.8381 + 23.7022 = $29.5403 (rounded to $29.54)

Interpretation: If you can buy JJ today for $29.54 or less, the investment meets your 13% required return assuming the dividend and sale price forecasts hold. If the market price is higher, the expected return would be below 13% (Damodaran, 2012).

Part (e) — Constant growth model (Gordon growth) valuation

The constant growth (Gordon) model for a perpetuity growing at constant g states P0 = D1 / (r − g), valid when r > g (Gordon, 1962; Brigham & Ehrhardt, 2017).

Using D1 = $2.3625, r = 13% and g = 5%:

P0 = 2.3625 / (0.13 − 0.05) = 2.3625 / 0.08 = $29.53125 ≈ $29.53

Comparison: The DDM with a three-year explicit forecast plus a terminal sale that implicitly captures subsequent growth gave $29.54, essentially identical to the Gordon model result (minor rounding differences). This consistency occurs because the terminal price used ($34.19) is consistent with a perpetual 5% growth assumption applied at year 3.

Part (f) — Does holding period affect the value today?

Short answer: No. Under the efficient use of the dividend discount framework, the intrinsic value of the stock today (P0) is the present value of all expected future cash flows (dividends and sale proceeds) discounted at the required return. That PV is independent of the investor's personal horizon because any finite holding-period valuation must include the sale price (which itself equals the present value of remaining cash flows). In other words, whether you plan to hold for 2, 3, or 5 years, the present value of the same stream of expected future cash flows will be the same today if expectations and the discount rate are unchanged (Bodie, Kane, & Marcus, 2014; Berk & DeMarzo, 2019).

Illustration: If you plan to hold 2 years, you would value D1, D2 and the expected sale price at year 2 (which equals the PV at year 2 of dividends thereafter). Discounting those cash flows back to today gives the same P0 as discounting the full infinite series. Thus holding period affects realized returns and cash flow timing for the investor, but not the theoretical intrinsic value today provided forecasts and discount rates remain the same (Arnott & Bernstein, 2002).

Conclusion

Calculated expected dividends are D1 = $2.3625, D2 = $2.4806, and D3 = $2.6047. Discounting dividends and an expected year-3 sale price of $34.19 at 13% yields a present value of approximately $29.54. The Gordon constant-growth model with g = 5% yields a nearly identical P0 = $29.53. Finally, the stock’s intrinsic value today does not depend on an individual’s planned holding period; it depends on the present value of expected future cash flows under the adopted assumptions (Damodaran, 2012; Brealey et al., 2019).

References

  • Brealey, R. A., Myers, S. C., & Allen, F. (2019). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Berk, J., & DeMarzo, P. (2019). Corporate Finance (5th ed.). Pearson.
  • Brigham, E. F., & Ehrhardt, M. C. (2017). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley.
  • Gordon, M. J. (1962). The Investment, Financing, and Valuation of the Corporation. Review of Economics and Statistics, 44(1), 37–51.
  • CFA Institute. (2019). Equity Valuation: Concepts and Basic Tools. CFA Institute.
  • Higgins, R. C. (2012). Analysis for Financial Management (10th ed.). McGraw-Hill/Irwin.
  • Arnott, R. D., & Bernstein, P. L. (2002). What Risk Premium is 'Normal'?. Financial Analysts Journal, 58(2), 64–85.
  • Investopedia. (n.d.). Dividend Discount Model (DDM). Retrieved from https://www.investopedia.com/terms/d/dividenddiscountmodel.asp

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