Math Problem Statement

​,

​Inc., is an​ all-equity firm with assets worth

$ 50.00$50.00

billion and

23.80523.805

billion shares outstanding.

RallyRally

plans to borrow

$ 12.50$12.50

billion and use funds to repurchase shares.

RallyRally​'s

corporate tax rate is

21 %21%​,

and

RallyRally

plans to keep its outstanding debt equal to

$ 12.50$12.50

billion permanently.

a. Without the increase in​ leverage, what would be

RallyRally​'s

share​ price?

b. Suppose

RallyRally

offers

$ 2.06$2.06

per share to repurchase its shares. Would shareholders sell for this​ price?

c. Suppose

RallyRally

offers

$ 2.43$2.43

per​ share, and shareholders tender their shares at this price. What will be

RallyRally​'s

share price after the​ repurchase?

d. What is the lowest price

RallyRally

can offer and have shareholders tender their​ shares? What will be its stock price after the share repurchase in that​ case?

Question content area bottom

Part 1

a. Without the increase in​ leverage, what would be

RallyRally​'s

share​ price?

Without the increase in​ leverage,

RallyRally​'s

share price is

​$enter your response here.

​ (Round to the nearest​ cent.)

Solution

Part 1: Share Price Without Leverage

a. To find the share price without the increase in leverage, we can simply divide the value of the firm's assets by the number of shares outstanding.

  • Value of assets = $50 billion
  • Number of shares outstanding = 23.805 billion

The formula for the share price is:

Share Price=Value of AssetsNumber of Shares Outstanding\text{Share Price} = \frac{\text{Value of Assets}}{\text{Number of Shares Outstanding}}

Let's calculate that:

Share Price=5023.805=2.10 (rounded to nearest cent)\text{Share Price} = \frac{50}{23.805} = 2.10 \text{ (rounded to nearest cent)}

So, without the increase in leverage, Rally's share price is $2.10.


Would you like me to continue with part b? Let me know if you want more details on any of the steps above.

5 Follow-up Questions:

  1. What impact does leverage have on share price in general?
  2. How does repurchasing shares typically affect a company’s financial metrics?
  3. What are the benefits of maintaining permanent debt?
  4. How does the corporate tax rate influence debt and equity decisions?
  5. What might happen to stock prices if the repurchase offer is too low?

Tip:

A share repurchase can sometimes signal to investors that the company believes its stock is undervalued, which may result in a stock price increase after the repurchase.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Stock Repurchase
Debt-Equity Valuation
Leverage

Formulas

Share Price = Value of Assets / Number of Shares Outstanding
Debt Impact on Share Price
Share Repurchase Valuation Formula

Theorems

Modigliani-Miller Theorem
Debt Valuation Theorem

Suitable Grade Level

Undergraduate (Finance and Economics)