Math Problem Statement

TUGAS 6 MATERI 6 PENILAIAN SAHAM: Evaluating stock values using Dividend Discount Model (DDM), Price-Earnings (P/E) ratio, and understanding how retention ratio affects growth and stock value.

Solution

Let's go over the contents of the uploaded image, which is an assignment (TUGAS 6) titled "Materi 6 Penilaian Saham" (Stock Valuation) for the subject of Financial Management (Manajemen Keuangan).

Here’s a breakdown of the questions:


SOAL I

You are asked to evaluate a stock that paid a $2 dividend last year. It is expected to continue paying cash dividends every year indefinitely. Each year, the dividend is expected to grow at a rate of 10%. Based on the evaluation of the stock risk, the required return (rate of return) for investors is 15%. The question asks for the current value of the stock.


SOAL II

Assume the following:

  • The required return for investors is 13.5%.
  • The expected earnings at the end of this year (E1) are $6.00.
  • The retention ratio is 50%.
  • The return on equity (ROE) is 15%.
  • A similar stock is selling at a price-earnings (P/E) ratio of 16.667 times earnings per share.

You are asked to:

a. Determine the expected growth rate for dividends.
b. Determine the P/E ratio using the provided formula (10–5a).
c. Calculate the stock price using the P/E valuation method.
d. Determine the stock price using the dividend discount model.
e. Analyze how the P/E ratio and stock price would change if the company increased the retention ratio to 60%, keeping everything else constant.
f. Discuss what you have learned about the relationship between retention ratio and P/E ratio.


SOAL 3

The Pioneer stock is sold at $33 in the market and pays an annual dividend of $3.60. If the required return by investors is 10%, determine whether the stock is a good buy (calculate the stock value for the investor). Should the investor buy the stock?


Would you like help with a specific question or explanation for solving any part of the assignment? Feel free to ask for detailed solutions!

Here are some relative questions for further exploration:

  1. How do we calculate stock value using the Dividend Discount Model (DDM)?
  2. What factors influence a company’s Price-to-Earnings (P/E) ratio?
  3. How does the retention ratio affect a company’s growth rate and stock value?
  4. Why is the required rate of return important in stock valuation?
  5. What are the differences between P/E valuation and Dividend Discount Model valuation?

Tip: Understanding the relationship between dividend growth and required return is essential for estimating stock prices using models like the DDM.

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Math Problem Analysis

Mathematical Concepts

Stock Valuation
Dividend Growth
Price-Earnings (P/E) Ratio
Return on Equity (ROE)
Retention Ratio
Discount Rate

Formulas

Dividend Discount Model (DDM): P = D1 / (r - g)
P/E Ratio: P/E = Price / Earnings
Growth Rate (g) = Retention Ratio * ROE

Theorems

Dividend Discount Model (DDM)
Price-Earnings Ratio Valuation

Suitable Grade Level

Undergraduate Finance / MBA Level