Price and Total Return

Equity Return with No Dividends

The total return from holding an equity investment comes from two sources:

1. Cash dividends — discretionary payouts made to shareholders.
2. Price changes — the increase or decrease in the market value of each share over the holding period.

To measure performance, investors rely on current and past share prices, adjusting for events such as stock splits or reverse splits. Returns can be tracked over different time horizons—daily, weekly, or annual—depending on the analysis.

This framework focuses strictly on the mechanics of return calculation and does not account for the impact of taxation, which can alter realized investor outcomes.

For non-dividend-paying stocks, returns are based solely on price changes. Assuming that an equity issuer is subject to neither a restructuring nor a liquidation event over the holding period, for an investor who owns a share with a market price of \(P_t\) At time \(t\), and observes a per-share market price of \(P_{t+1}\) at time \(t+1\), the total realized equity rate of return. \(r_E\) over the period from \(t\) to \(t+1\) consists solely of price appreciation. This calculation is expressed as

$$ r_E=\frac {P_{(t+1)}-P_t}{P_t} $$

AUD45.00 per share and sells the stock for AUD52.00 per share at the end of the period. The holding period rate of return is 15.56%,

$$ r_E=\frac {(52.00-45.00)}{45.00}=0.1556=15.56\% $$

Equity Return with Dividends

Any cash dividends to which an investor is entitled must be included in the return calculation for a given holding period. For an investor who owns a share priced at \(P_t\) At time \(t\), it receives a regular cash dividend. \(D_{t+1}\), and observes a per-share market price of \(P_{t+1}\) At time \(t+1\), the equity security’s total rate of return \(r_E\) The holding period from \(t\) to \(t+1\) is calculated as

$$ r_E=\frac {P_{(t+1)}-P_t+D_{(t+1)}}{Pt} $$

Consider an investor who purchases a stock for CAD60.00 per share, receives a cash dividend of CAD2.50 per share at the end of the holding period, and sells the stock for CAD68.00 per share. The holding period rate of return is 17.50%, calculated as

$$ r_E=\frac {(68.00-60.00+2.50)}{60.0}=0.175=17.50\% $$

The difference between this return and the non-dividend case represents the dividend’s contribution to the total return. In this example, the price appreciation contributes 13.33% while the dividend contributes 4.17% to the total return of 17.50%. The dividend yield component of the return is calculated as the dividend divided by the initial price.

Equity Return with Reinvested Dividends

Although investors can allocate cash dividends in various ways, one common approach is to reinvest dividends, using the dividend proceeds to purchase additional shares of the same company. This practice effectively compounds returns by increasing the investor’s shareholding over time.

Because reinvestment is widely adopted, its impact is typically included in the calculation of holding-period returns. In such cases, dividends received during the investment horizon are assumed to be reinvested, thereby influencing the overall return measurement.

A shareholder who immediately reinvests a dividend \(D\) will purchase \(\frac {D}{P_{PD}}\) additional shares, where \({P_{PD}}\) is the prevailing market price on the dividend payment date. The calculation of holding period returns in the case where dividends are reinvested is
$$ r_E = \frac{\left[ P_{t+1} \times \left( 1 + \frac{D}{P_{PD}} \right) – P_t \right]}{P_t} $$

Consider an investor who buys a stock for GBP55.00 per share, receives a cash dividend of GBP2.20 halfway through the period, when the share price is GBP57.00, and observes an end-of-period share price of GBP60.00. To calculate the holding period return with reinvested dividends, we first determine that the investor purchases \(\frac {2.20}{57.00}\), or 0.0386, additional shares. Substituting this into the formula, we solve for a holding period rate of return of 13.05%, calculated as

$$ r_E = \frac{\left[ 60.00 \times \left( 1 + \frac{2.20}{57.00} \right) – 55.00 \right]}{55} = 0.1330 = 13.30\% $$

The reinvested dividend increases the investor’s ownership from one share at time t to 1.0386 shares at time t+1. The reinvestment of dividends gives rise to fractional share ownership, a situation in which an investor owns a fraction of a share with a similar proportional claim to distributions and net assets. Appreciating the fractional share purchased in this case increases the investor’s total return compared to receiving the dividend in cash. If the investor had taken the dividend in cash, the return would have been

$$ \frac {60.00-55.00+2.20}{55.00}=13.09\% $$

slightly lower than the reinvested dividend return.

Reinvesting dividends can significantly enhance the long-term performance of equity investments. By continually purchasing additional shares with dividend payouts, investors benefit from compounding, which magnifies overall returns over extended periods.

When comparing price-only returns (which reflect share price changes alone) to total returns (which include reinvested dividends), the difference becomes especially pronounced over long horizons. In mature markets with relatively high dividend yields, reinvested dividends often account for a significant share of total returns. In contrast, in many emerging markets, capital gains tend to drive performance more than dividend reinvestment, as companies often prioritize growth over regular payouts.

Equity Price Determination

The return from owning a stock over a given period can be broken down into two elements: cash dividends received and changes in the share price. Using these components, investors can assess the current value of an equity security relative to expected future outcomes.

In principle, the price of a stock at time t reflects the present value of all anticipated future cash flows, both dividend distributions and the expected selling price at the end of the holding period. For companies that do not pay dividends, today’s share price is simply the discounted value of the projected future price at the end of the investment horizon.

$$ P_t=\frac {E(P_{t+1})}{(1+r_e)} $$

The uncertainty of future stock prices ensures that investors are less able to predict future stock returns, so \(r_e\) may be interpreted as the appropriate periodic discount rate that shareholders apply to future cash flows and reflects the required return on equity.

For a firm that pays a cash dividend at time \(t+1\), the current share price \(P_t\) is equal to the sum of the present value of the expected dividend \(E(D_{t+1})\) plus the present value of the expected future price

$$ P_t=\frac {EP_{t+1}+E(D_{t+1})}{(1+r_e)} $$

Consider an investor who observes that an analyst has established a share price target for Sterling Chemicals AG of CHF85 in one year and considers 11% to be the appropriate annual discount rate. If the issuer pays no dividends, the current share price would be CHF 76.58, calculated as \(\frac {85}{1.11}\). If Sterling Chemicals AG announces a year-end dividend of CHF3.20 and the analyst maintains the same CHF85 year-end price target, the revised share price would be CHF79.46, calculated as \(\frac {(3.20 + 85) }{ 1.11}\). The difference in today’s share price between the no-dividend and dividend cases equals the present value of the CHF3.20 dividend, or CHF2.88.

For a more extended time horizon, if we consider the expected share price \(E(P_{t+n})\) At the end of an investment horizon of \(n\) periods, where a constant dividend \(D\) is paid at the end of each period, we can solve for \(P_t\) by discounting expected future cash flows at the annualized expected rate of return \(r_e\):

$$ P_t = \sum_{i=1}^{n} \frac{D}{(1+r_e)^i} + \frac{E(P_{t+n})}{(1+r_e)^n} $$

This formula allows us to compare the relative impact of expected dividends versus expected future share price appreciation. If an investor intends to hold a share with an expected constant dividend \(D\) indefinitely, the present value of future dividend cash flows will be the predominant factor in today’s share price. Conversely, if the firm is expected to pay no dividends over the investment horizon, the cash flows that contribute to net asset growth will be most important to today’s stock price. The present value of the terminal value estimate generally exceeds that of interim cash flows, unless the investment time horizon is very long or the discount rate is very high.

Example: Multi-Period Price Determination

Consider an analyst who has placed a four-year target price of JPY9,000 per share on a stock. The stock recently paid a JPY200 dividend, and this dividend is expected to grow at 5% annually over the next four years. The analyst believes that a 9% discount rate is appropriate for the stock. The current price of this stock is calculated by discounting the dividend stream of JPY210, JPY220.50, JPY231.53, and JPY243.10 plus the terminal price of JPY9,000 in Year 4. The present value of the dividends is JPY735.23, and the present value of the terminal price is JPY6,373.77, producing a current price of JPY7,109.00. This calculation demonstrates that approximately 10.3% of the current stock price is attributable to expected future dividends. In comparison, approximately 89.7% is attributable to the expected future share price, illustrating the relative importance of terminal value in equity valuation over a four-year horizon. The terminal value dominates the valuation because the 9% discount rate applied over four years does not significantly reduce the value of distant cash flows relative to the near-term dividend stream.

Question:

An analyst has placed a three-year target price of NZD150.00 per share on a stock. The stock recently paid a NZD 4.00 dividend, and this dividend is expected to grow at 6% annually over the next three years. The analyst believes that a 10% discount rate is appropriate for the stock. Which one of the following is closest to the current price of this stock?

1. NZD117.72
2. NZD119.64
3. NZD121.93

Solution

The correct answer is B.

The correct valuation incorporates the growing dividend stream over the three-year forecast period. The resulting cash flow stream consists of dividends of NZD4.24, NZD4.49, and NZD4.76 in Years 1 through 3, respectively, plus the Year 3 price of NZD150.00. The current price is calculated by discounting each of these cash flows at the 10% required rate of return. The present value of the dividends is NZD10.90, and the present value of the terminal price is NZD112.70, producing a total of NZD119.64.

A is incorrect. The result of NZD117.72 occurs when the analyst incorrectly fails to grow the dividends in the first year, using NZD4.00 instead of NZD4.24. This underestimates the current price because it does not properly account for dividend growth in the first year. The dividend is expected to grow at 6%, so the first year dividend should be NZD4.24, not NZD4.00.

C is incorrect. The result of NZD121.93 occurs when the analyst incorrectly uses a 5% discount rate instead of the correct 10% rate. This overestimates the current price because the lower discount rate would make future cash flows appear more valuable. Using a 10% discount rate is appropriate because the analyst specified that rate for the stock.