The 

HNHHNH 

Corporation will pay a constant dividend of 

$ 2.00$2.00 

per​ share, per​ year, in perpetuity. Assume all investors pay a 

15 %15% 

tax on dividends and that there is no capital gains tax. The cost of capital for investing in 

HNHHNH 

stock is 

10 %10%.

**a.** What is the price of a share of 

HNHHNH 

​stock?

**b.** Assume that management makes a surprise announcement that 

HNHHNH 

will no longer pay dividends but will use the cash to repurchase stock instead. What is the price of a share of 

HNHHNH 

stock​ now?

Question content area bottom

Part 1

**a.** What is the price of a share of 

HNHHNH 

​stock?

The price of a share of 

HNHHNH 

stock is 

​$enter your response here.

  ​(Round to the nearest​ cent.)

Part 2

**b.** Assume that management makes a surprise announcement that 

HNHHNH 

will no longer pay dividends but will use the cash to repurchase stock instead. What is the price of a share of 

HNHHNH 

stock​ now?

The price of a share of 

HNHHNH 

stock is 

​$enter your response here.

  ​(Round to the nearest​ cent.)

### Part 1: Price of a Share of HNHHNH Stock with Dividends

The formula to calculate the price of a stock paying a constant dividend in perpetuity is given by the dividend discount model (DDM) for a perpetuity:

\[
P_0 = \frac{D}{r}
\]

Where:
- $ P_0 $ is the price of the stock
- $ D $ is the dividend per share
- $ r $ is the cost of capital (or required rate of return)

In this case:
- The annual dividend $ D = 2.00 $ dollars per share.
- The cost of capital $ r = 10\% = 0.10 $.
- Investors pay a 15% tax on dividends, so the effective dividend after tax is $ 2.00 \times (1 - 0.15) = 1.70 $.

Now, applying the formula:

\[
P_0 = \frac{1.70}{0.10} = 17.00
\]

Thus, the price of a share of HNHHNH stock is **$17.00**.

---

### Part 2: Price of a Share of HNHHNH Stock with Stock Repurchases

If the company stops paying dividends and instead uses the cash for stock repurchases, the price of the stock should remain the same. This is based on the idea that both dividends and stock repurchases are ways to return value to shareholders, and in a perfect market with no taxes (or only the same dividend tax applies here), they are equivalent in terms of value.

Therefore, the price of the stock remains:

\[
\text{New Price} = \text{Old Price} = 17.00
\]

---

### Final Answers:
- **(a)** The price of a share of HNHHNH stock is **$17.00**.
- **(b)** After the announcement of stock repurchases, the price remains **$17.00**.

Would you like further clarification or details?  

Here are five related questions for deeper understanding:
1. How does the dividend discount model (DDM) change if the dividends grow over time?
2. How would a change in the cost of capital affect the stock price?
3. What is the effect of a higher tax rate on dividends on the stock price?
4. How do stock repurchases impact earnings per share (EPS)?
5. What happens if a company decides to alternate between dividends and stock repurchases?

**Tip**: When stock prices are calculated under perpetual dividends, always consider any taxes that affect the investor's return, as this can change the actual value of the dividends received.

The HNHHNH Corporation will pay a constant dividend of $2.00 per share, per year, in perpetuity. Assume all investors pay a 15% tax on dividends and that there is no capital gains tax. The cost of capital for investing in HNHHNH stock is 10%. a) What is the price of a share of HNHHNH stock? b) Assume that management makes a surprise announcement that HNHHNH will no longer pay dividends but will use the cash to repurchase stock instead. What is the price of a share of HNHHNH stock now?

Calculate the price of HNHHNH stock using the dividend discount model with a $2.00 per share dividend, 10% cost of capital, and a 15% tax on dividends. Explore the price impact of a stock repurchase announcement. Suitable for college-level finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation