Common Timing and Input Errors in Dividend Discount Models

Why Timing and Input Checks Matter

A dividend discount valuation can use the right general model and still produce the wrong price. The most common causes are small-looking inconsistencies: using the dividend just paid where the next dividend is required, valuing cash flows from a different date than the stated price date, or comparing a growth rate with a required return measured on a different basis. In a multistage model, a further error is to calculate a terminal value at a future date but treat it as though it were already worth that amount today.

These errors matter because a dividend discount model values future payments at a particular valuation date. Before calculating, write down when each dividend is paid, when the valuation occurs, and the period and compounding basis for each rate. The checks in this tutorial are aligned with the SOA VEE Accounting and Finance syllabus.

Definition: Let $P_t$ be the stock value immediately after any dividend paid at time $t$, and let $D_t$ be the dividend paid at time $t$. Let $k$ be the required effective annual return and $g$ the effective annual dividend growth rate. When a stock has just paid $D_0$, its next dividend is $D_1=D_0(1+g)$. These symbols refer to annual periods unless a different period is stated explicitly.

The Current Dividend Is Not the Next Dividend

The Gordon growth model values a stock whose dividends are expected to grow at a constant rate indefinitely. Its assumptions include a valuation immediately after $D_0$ has been paid, a constant annual growth rate $g$ beginning with $D_1$, a constant annual required return $k$, and $k>g$. Dividends are assumed to be paid once per year at year-end.

Formula: Under those assumptions, the value immediately after the current dividend is

P_0=\frac{D_1}{k-g}=\frac{D_0(1+g)}{k-g}, \qquad k>g.

The numerator is the next dividend, not the dividend that has already been paid.

A short derivation makes the timing explicit. At time 0, the first payment is $D_1$ at time 1, the second is $D_1(1+g)$ at time 2, and the pattern continues. Discounting those payments at the effective annual return $k$ gives a geometric series:

P_0=\frac{D_1}{1+k}+\frac{D_1(1+g)}{(1+k)^2} +\frac{D_1(1+g)^2}{(1+k)^3}+\cdots.

The first term is $D_1/(1+k)$. Each later term is the preceding term multiplied by $(1+g)/(1+k)$. Since $k>g$, this ratio is less than 1 and the infinite geometric series converges. Its sum is

P_0= \frac{D_1/(1+k)}{1-(1+g)/(1+k)} =\frac{D_1}{k-g}.

The formula does not apply as a finite positive value when $k\leq g$; the infinite series does not converge under those conditions. It also does not directly apply when growth is not constant, dividends have irregular timing, or the valuation date differs from the point just after $D_0$. Those situations require a model that matches the cash-flow pattern and date.

Worked Example: Using the Next Dividend

A hypothetical company has just paid an annual dividend of $2.00 per share. Dividends are forecast to grow at an effective annual rate of 4.0% indefinitely, and investors require an effective annual return of 10.0%. Find the value immediately after the dividend payment.

Method. This is a constant-growth valuation at time 0, immediately after $D_0$ is paid. The rates use the same annual period, and $10.0\%>4.0\%$, so the Gordon formula applies.

Step 1: Forecast the next dividend.

D_1=D_0(1+g)=\$2.00(1.04)=\$2.08.

Step 2: Calculate the return-growth spread.

$$ k-g=0.10-0.04=0.06. $$

Step 3: Calculate the value.

P_0=\frac{\$2.08}{0.06}=\$34.6666\ldots=\$34.67.

The value is $34.67 per share, rounded to the nearest cent. Check: the first dividend is $2.08, not $2.00, because the $2.00 payment has already occurred. Using $D_0/(k-g)$ would give $33.33 and understate the value by $1.33. That is the common current-versus-next dividend mistake.

Match the Rate Periods and Compounding Basis

The dividend growth rate and required return must describe comparable periods. For annual dividends and annual growth, use an effective annual required return. A quoted nominal rate convertible monthly is not itself an effective annual return: it must first be converted. In general, if a nominal annual rate $i^{(m)}$ is convertible $m$ times per year, its effective annual equivalent is

i_{\text{eff}}=\left(1+\frac{i^{(m)}}{m}\right)^m-1.

This conversion assumes the nominal rate is compounded $m$ times each year and that the dividend and growth forecasts are annual. Do not subtract an annual effective growth rate from a nominal rate per year convertible monthly. The two inputs do not represent the same annual accumulation basis.

Worked Example: Converting a Nominal Return Before Valuing

A hypothetical stock has just paid an annual dividend of $2.00. Dividends grow at an effective annual rate of 2.5% indefinitely. The required return is quoted as 8.0% nominal per year, convertible monthly. Find the value immediately after the payment.

Method. Convert the quoted return to an effective annual rate, then apply the Gordon formula using annual dividends. Assume the stated growth continues indefinitely and the effective annual return exceeds growth.

Step 1: Convert the return. The monthly rate is $0.08/12=0.0066666667$. Thus:

k=\left(1+\frac{0.08}{12}\right)^{12}-1 =0.0829995068 \approx 8.3000\%.

Step 2: Forecast the next annual dividend.

D_1=\$2.00(1.025)=\$2.05.

Step 3: Check the condition and calculate. The effective annual return, about 8.3000%, exceeds the annual growth rate of 2.5%. The denominator is $0.0829995068-0.025=0.0579995068$, so

P_0=\frac{\$2.05}{0.0579995068} =\$35.3451\ldots=\$35.35.

The value is $35.35 per share, rounded to the nearest cent. The check is both conceptual and numerical: the return was converted before comparison, and the dividend used in the numerator is $2.05. Directly subtracting 2.5% from the nominal 8.0% rate would give an incorrect denominator and value.

Keep Every Cash Flow on the Valuation Timeline

A stock value is always a value at a specified date. In a multistage model, dividends during the explicit forecast period are discounted individually to the valuation date. A terminal value summarizes dividends after the forecast period, but it is calculated at the date immediately before those continuing dividends begin. It must then be discounted back to the valuation date.

Timing rule: If the forecast period ends at time $N$, and the first dividend in the stable-growth period is $D_{N+1}$, then the terminal value at time $N$ is $P_N=D_{N+1}/(k-g)$, provided $k>g$. For a value at time 0, discount $P_N$ by $(1+k)^N$, in addition to discounting the explicit dividends.

The timing follows from what the terminal value represents: $P_N$ is already the value at time $N$ of payments beginning at time $N+1$. It is not a payment made at time 0. Omitting its discount factor moves future value to the present without accounting for the required return over the intervening years.

Worked Example: Discounting a Terminal Value to Today

A hypothetical stock is valued at time 0, immediately after any dividend at that date. Its forecast dividends are $D_1=\$1.00$, $D_2=\$1.10$, and $D_3=\$1.21$. Beginning with $D_4$, dividends grow at 5.0% per year indefinitely. The required return is 10.0% effective annually. Find $P_0$.

Method. Discount the three forecast dividends to time 0, calculate the stable-growth terminal value at time 3, and discount that terminal value to time 0. All payments and rates are annual, and $10.0\%>5.0\%$.

Step 1: Forecast the first stable-growth dividend.

D_4=D_3(1+g)=\$1.21(1.05)=\$1.2705.

Step 2: Calculate the terminal value at time 3. It uses $D_4$, because the value is immediately after $D_3$ and before $D_4$ is paid.

P_3=\frac{D_4}{k-g} =\frac{\$1.2705}{0.10-0.05} =\$25.41.

Step 3: Discount all time-1, time-2, and time-3 amounts to time 0.

\begin{aligned} P_0 &=\frac{D_1}{1.10}+\frac{D_2}{(1.10)^2} +\frac{D_3+P_3}{(1.10)^3}\\ &=\frac{\$1.00}{1.10}+\frac{\$1.10}{1.21} +\frac{\$1.21+\$25.41}{1.331}\\ &=\$0.9090909+\$0.9090909+\$20.0000000\\ &=\$21.8181818. \end{aligned}

Therefore, $P_0=\textbf{\$21.82}$, rounded to the nearest cent. The check is that $D_3$ and $P_3$ are both time-3 amounts, so they share the same discount factor. Treating $P_3=\$25.41$ as though it were already a time-0 value would omit three years of discounting and substantially overstate the stock value.

Worked Example: Aligning a Forecast Date With Today’s Value

A hypothetical stock is valued at time 0. It is expected to pay $D_1=\$1.50$ at time 1 and $D_2=\$2.00$ at time 2. Immediately after paying $D_2$, its dividends are expected to remain at $2.00 annually forever. The required return is 10.0% effective annually. Find its time-0 value.

Method. First find the value at time 2 of dividends paid after that date. Then discount that value, along with the two forecast dividends, to time 0. The stock pays no dividend at time 0, and the constant $2.00 dividends after time 2 imply $g=0\%$; $k=10.0\%>0\%$.

Step 1: Calculate the value at time 2. Because $D_2$ has just been paid at that date, the next dividend is $D_3=\$2.00$.

P_2=\frac{D_3}{k-g}=\frac{\$2.00}{0.10-0}=\$20.00.

Step 2: Discount the time-1 dividend to time 0.

\frac{D_1}{1.10}=\frac{\$1.50}{1.10}=\$1.3636364.

Step 3: Discount the time-2 dividend and time-2 value to time 0. Both amounts are at time 2.

\frac{D_2+P_2}{(1.10)^2} =\frac{\$2.00+\$20.00}{1.21} =\$18.1818182.

Step 4: Add the present values.

P_0=\$1.3636364+\$18.1818182 =\$19.5454546=\$19.55.

The time-0 value is $19.55 per share, rounded to the nearest cent. The common date mismatch is to report $P_2=\$20.00$ as today’s value, even though it is the value two years from today and excludes dividends paid at times 1 and 2. Here, those dividends and the value of later dividends are all accounted for at their proper dates.

A Practical Audit Before Accepting a Valuation

A short, ordered review catches most timing and input errors. Do not start by checking arithmetic alone; first verify that the formula describes the forecast and the stated valuation date.

Mark the valuation date.
Specify whether the value is just before or just after a dividend payment. Label each forecast dividend by its payment date.

Identify the dividend in the numerator.
For a Gordon value immediately after $D_0$, use $D_1$. For a terminal value at time $N$, use the first dividend after time $N$, namely $D_{N+1}$.

Put the rates on one basis.
Confirm that growth and required return cover the same period and are expressed using compatible effective rates. Convert a nominal convertible rate when necessary.

Check the model condition.
For a constant-growth infinite stream, verify $k>g$, constant growth, and a valuation date consistent with the formula.

Discount future values.
Discount every explicit dividend and every terminal value from its own date to the requested valuation date. A terminal value is not automatically a time-0 value.

A useful final reasonableness check is to state what each amount represents: “This dividend is paid at time 1,” or “this terminal value is at time 3.” If the timeline cannot be described clearly, the calculation is not yet ready to be trusted. These checks are especially useful when forecasts combine changing dividends with a stable-growth period, because the correct formula depends on both the cash-flow pattern and its dates.

Check Your Understanding

For each hypothetical stock, use the stated valuation date and rate basis. Round dollar values to the nearest cent.

A stock has just paid an annual dividend of $1.80. Dividends grow at an effective annual rate of 5.0% forever, and the required effective annual return is 11.0%. Find the value immediately after the payment. (Answer: $31.50)
A stock has just paid an annual dividend of $1.20. Dividends grow at an effective annual rate of 2.0% forever. Its required return is 6.0% nominal per year, convertible quarterly. Convert the return to an effective annual rate and find the value immediately after the dividend. (Answer: $29.59)
A stock’s forecast dividends are $D_1=\$0.80$, $D_2=\$0.90$, and $D_3=\$1.00$. From $D_4$ onward, dividends grow at 4.0% annually. The required effective annual return is 9.0%. Find the value at time 0, showing the terminal value date. (Answer: $18.33)
A stock will pay $1.50 at time 1 and $2.00 at time 2. Immediately after the time-2 payment, it pays $2.00 annually forever. The effective annual required return is 10.0%. Find its value at time 0, including the time-2 value of later dividends. (Answer: $19.55)
A stock has just paid $D_0=\$3.00$, and the next dividend is forecast to be $3.15. Dividends then grow at 5.0% annually forever; the required effective annual return is 9.0%. State whether the Gordon model condition holds and find $P_0$. (Answer: The condition holds; $P_0=\$78.75$)

What You'll Learn