The 

HNHHNH 

Corporation will pay a constant dividend of 

$ 2.75$2.75 

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 

13 %13%.

**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.)

Let's tackle part (a) first:

We are given that HNHHNH Corporation pays a constant dividend of **$2.75** per share annually, and this dividend is in perpetuity (meaning it will be paid forever). The cost of capital (required rate of return) for the stock is **13%**. However, investors pay a **15%** tax on dividends, so we need to adjust the dividend for taxes before calculating the stock price.

### Step 1: Adjust the dividend for the tax rate

The after-tax dividend is calculated as follows:
\[
\text{After-tax dividend} = \text{Dividend} \times (1 - \text{Tax rate})
\]
\[
\text{After-tax dividend} = 2.75 \times (1 - 0.15) = 2.75 \times 0.85 = 2.3375
\]

### Step 2: Use the perpetuity formula to calculate the stock price

The price of the stock can be calculated using the formula for the present value of a perpetuity:
\[
P = \frac{D}{r}
\]
where:
- $ P $ is the price of the stock,
- $ D $ is the after-tax dividend (\$2.3375),
- $ r $ is the required rate of return (13% or 0.13).

Substitute the values:
\[
P = \frac{2.3375}{0.13} = 17.9808
\]

Thus, the price of a share of HNHHNH stock is approximately **$17.98**.

---

### Part (b): Stock Repurchase Announcement

Now, let's consider the impact of the announcement that HNHHNH will no longer pay dividends but will use the cash to repurchase stock.

In this case, the total return for investors comes entirely from stock price appreciation. Since there is no capital gains tax, the effective return for investors will still be 13%, and the value of the stock should remain the same as before the announcement. Hence, the price of a share should still be **$17.98**.

This is because the firm is still providing value to shareholders by repurchasing shares instead of paying dividends, and investors will expect the same overall return on their investment, even if it's in the form of stock price appreciation rather than dividends.

---

### Summary:
**a.** The price of a share of HNHHNH stock is approximately **$17.98**.

**b.** After the announcement that HNHHNH will repurchase stock instead of paying dividends, the price of a share of stock will remain approximately **$17.98**.

---

Do you need any additional details or have any further questions?

Here are 5 related questions to explore:
1. How would the stock price change if the dividend tax increased to 25%?
2. What happens to the stock price if the required rate of return changes?
3. How does stock repurchasing affect the number of shares outstanding?
4. Can a company's dividend policy affect investor perception and stock price?
5. How does capital gains tax impact an investor's decision between dividends and stock buybacks?

**Tip:** When dividends are taxed but capital gains are not, stock repurchases can be more tax-efficient for investors than dividend payments.

The HNHHNH Corporation will pay a constant dividend of $2.75 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 13%. 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?

Learn how to calculate the price of HNHHNH Corporation stock using the dividend discount model and how stock repurchase announcements affect stock prices. This example covers the perpetuity formula and tax adjustments, suitable for finance students.

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