BBA 7th Sem | Investment Analysis | Chapter 6 | Equity Valuation | Practice Question Solution

🎾 Tennis Racket Company

Advanced Stock Valuation Analysis with Interactive Models

📋 Problem Statement

Bharomal Tennis Racket Manufacturing Company is a little-known producer of Tennis Rackets. The earnings and dividend growth prospects of the company are disputed by financial analysts:

• Ms. Upadhyaya is forecasting 10 percent growth in dividends indefinitely
• Mr. Lama is predicting 20 percent growth in dividends, but only for the next two years, after which the growth rate is expected to decline to 5 percent for the indefinite future

Rs. 30

Current Dividend per Share

15%

Required Rate of Return

We need to find:

1. The value of company's stock according to Ms. Upadhyaya
2. The value of company's stock according to Mr. Lama
3. If the stock sells for Rs. 316.5 per share, what is the implied perpetual dividend growth rate?
4. What is the implied P/E ratio on next year's earnings, based on this perpetual dividend growth assumption and assuming a 30 percent payout ratio?

🔍 Solution

📊 Given Information

Current dividend per share: \(D_0 = \text{Rs. } 30\)

Required rate of return: \(k = 15\% = 0.15\)

1️⃣ Valuation according to Ms. Upadhyaya

Ms. Upadhyaya forecasts constant growth: \(g = 10\% = 0.10\)

We use the Gordon Growth Model (Constant Growth DDM):

\[P_0 = \frac{D_1}{k - g}\]

First, calculate next year's dividend:

\[D_1 = D_0 \times (1 + g) = 30 \times (1 + 0.10) = 30 \times 1.10 = \text{Rs. } 33\]

Now apply the formula:

\[P_0 = \frac{33}{0.15 - 0.10} = \frac{33}{0.05} = \text{Rs. } 660\]

🎯 Value according to Ms. Upadhyaya: Rs. 660

2️⃣ Valuation according to Mr. Lama

Mr. Lama predicts a two-stage growth model:

• Stage 1: \(g_1 = 20\% = 0.20\) for 2 years
• Stage 2: \(g_2 = 5\% = 0.05\) indefinitely

We calculate the present value of dividends for the first two years and the terminal value at the end of year 2.

Step 1: Calculate dividends for the high-growth period

\[D_1 = D_0 \times (1 + g_1) = 30 \times 1.20 = \text{Rs. } 36\] \[D_2 = D_1 \times (1 + g_1) = 36 \times 1.20 = \text{Rs. } 43.2\]

Step 2: Calculate terminal value at the end of year 2

At the end of year 2, the stock enters stable growth at 5%.

First, calculate the dividend for year 3:

\[D_3 = D_2 \times (1 + g_2) = 43.2 \times 1.05 = \text{Rs. } 45.36\]

Then apply the Gordon Growth Model for the terminal value:

\[P_2 = \frac{D_3}{k - g_2} = \frac{45.36}{0.15 - 0.05} = \frac{45.36}{0.10} = \text{Rs. } 453.6\]

Step 3: Discount all cash flows to present value

The total cash flows are:

• \(D_1 = \text{Rs. } 36\) at time 1
• \(D_2 = \text{Rs. } 43.2\) at time 2
• \(P_2 = \text{Rs. } 453.6\) at time 2

\[P_0 = \frac{D_1}{(1+k)} + \frac{D_2 + P_2}{(1+k)^2}\]

\[P_0 = \frac{36}{1.15} + \frac{43.2 + 453.6}{(1.15)^2}\] \[P_0 = \frac{36}{1.15} + \frac{496.8}{1.3225}\] \[P_0 = 31.3043 + 375.6510 = \text{Rs. } 406.96\]

🎯 Value according to Mr. Lama: Rs. 406.96

3️⃣ Implied perpetual growth rate if current price is Rs. 316.5

Assume the stock is fairly priced at \(P_0 = 316.5\)

Using the constant growth model, we solve for \(g\):

\[P_0 = \frac{D_0 \times (1 + g)}{k - g}\]

Substituting the known values:

\[316.5 = \frac{30 \times (1 + g)}{0.15 - g}\]

Cross-multiplying and solving:

\[316.5 \times (0.15 - g) = 30 \times (1 + g)\] \[47.475 - 316.5g = 30 + 30g\] \[47.475 - 30 = 316.5g + 30g\] \[17.475 = 346.5g\] \[g = \frac{17.475}{346.5} = 0.05043 = 5.043\%\]

🎯 Implied perpetual growth rate: 5.043%

4️⃣ Implied P/E ratio based on perpetual growth

We need to find the forward P/E ratio (based on next year's earnings)

Given information:

• Dividend payout ratio = 30% = 0.30
• So, \(D_1 = E_1 \times 0.30\), where \(E_1\) is next year's earnings

From the constant growth model:

\[P_0 = \frac{D_1}{k - g} = \frac{E_1 \times 0.30}{k - g}\]

Rearranging to find the P/E ratio:

\[\frac{P_0}{E_1} = \frac{0.30}{k - g}\]

Substituting our values:

• \(k = 0.15\)
• \(g = 0.05043\)

\[\text{P/E} = \frac{0.30}{0.15 - 0.05043} = \frac{0.30}{0.09957} = 3.012\]

🎯 Implied forward P/E ratio: 3.012

🧮 Interactive Stock Valuation Calculator

Experiment with different parameters to see how they affect stock valuation:

Current Dividend (D₀):

Required Rate of Return (k):

Growth Rate (g):

📈 Calculation Result

Next Year's Dividend (D₁):

Current Stock Price (P₀):

Formula Used: \(P_0 = \frac{D_1}{k - g}\)