Fundamentals of Corporate Finance
Fundamentals of Corporate Finance
11th Edition
ISBN: 9780077861704
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 8, Problem 14QP

Stock Valuation [LO1] Bayou Okra Farms just paid a dividend of $2.65 on its stock. The growth rate in dividends is expected to be a constant 4.5 percent per year indefinitely. Investors require a return of 15 percent for the first three years, a return of 13 percent for the next three years, and a return of 11 percent thereafter. What is the current share price?

Expert Solution & Answer
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Summary Introduction

To determine: The current price of the share.

Introduction:

Stock price is a price of a share on the number of saleable stock of a company.

Answer to Problem 14QP

The current share price is $37.21.

Explanation of Solution

Given information:

BO Company has currently paid dividends of $2.65. The constant growth rate of dividends is 4.5%. The investor’s required rate of return for the first three years is 15%, for the next three years is 13%, and a return of 11% for subsequent years.

Formulae:

Formula to calculate the stock price of Year 6:

P6=Do×(1+g)n(Rg)

Where,

P6 refers to the price of stock in 6 years

Do refers to the dividend paid presently

R refers to the required return on the stock

g refers to the constant growth rate

n refers to the number of years

Note: The dividend value of Year 7 is computed to determine the price of stock in Year 6.

Formula to calculate the stock price of Year 3:

P3=D1(1+g)4(1+R)1+D2(1+g)5(1+R)2+D3(1+g)6(1+R)3+P6(1+R)3

Where,

P3 refers to the price of the stock in Year 3

D1…Dn refers to the next period expected dividend per share

R refers to the required rate of return on its stock

g refers to the constant growth rate

Note: At the time when the required return changes frequently, then the stock price in Year 3 is the present value of the dividends in Year 4, Year 5, and Year 6 plus the present value of stock of Year 3.

Formula to calculate the current price of the share:

Po=D1(1+g)(1+R)1+D2(1+g)2(1+R)2+D3(1+g)3(1+R)3+P6(1+R)3

Where,

Po refers to the present price of stock

D1…Dn refers to the next period expected dividend per share

R refers to the required return on the stock

g refers to the constant growth rate

Compute the stock price of Year 6:

P6=Do×(1+g)n(Rg)=$2.65×(1+4.5100)7(111004.5100)

=$2.65×(1.045)7(0.110.045)=$2.65×1.360860.065=$2.65×20.93630=$55.48

Hence, the stock price of Year 6 is $55.48.

Compute the stock price of Year 3:

P3=D1(1+g)4(1+R)1+D2(1+g)4(1+R)2+D3(1+g)6(1+R)3+P6(1+R)3=$2.65(1+4.5100)4(1+13100)1+$2.65(1+4.5100)5(1+13100)2+$2.65(1+4.5100)6(1+13100)3+$55.48(1+13100)3=$2.65(1.045)41.13+$2.65(1.045)5(1.13)2+$2.65(1.045)6(1.13)3+$55.48(1.13)3

=$2.65×1.192511.13+($2.65×1.24618)1.2769+($2.65×1.30226)1.44289+$55.481.44289=$3.16015+$3.302371.2769+$3.450981.44289+$55.481.44289=$3.16015+$2.58624+$2.39171+$38.45060=$46.58

Hence, the stock price of Year 6 is $46.58.

Compute the current price of the share:

Po=D1(1+g)1(1+R)1+D2(1+g)2(1+R)2+D3(1+g)3(1+R)3+P6(1+R)3=$2.65×(1+4.5100)1(1+15100)1+$2.65×(1+4.5100)2(1+15100)2+$2.65×(1+4.5100)3(1+15100)3+$46.58(1+15100)3=$2.65×(1.045)1(1+0.15)1+$2.65×(1.045)2(1+0.15)2+$2.65×(1.045)3(1+0.15)3+$46.58(1+0.15)3=$2.769251.15+($2.65×1.09202)(1.15)2+($2.65×1.14116)(1.15)3+$46.58(1.15)3

=$2.40804+$2.893851.3225+$3.024071.52087+$46.581.52087=$2.40804+$2.18816+$1.98838+$30.62720=$37.21178

Hence, the current price of the share is $37.21.

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Chapter 8 Solutions

Fundamentals of Corporate Finance

Ch. 8 - An 8 percent preferred stock sells for 54 a share....Ch. 8 - Prob. 8.3CTFCh. 8 - Stock Valuation [LO1] Why does the value of a...Ch. 8 - Stock Valuation [LO1] A substantial percentage of...Ch. 8 - Stock Valuation [LO1] A substantial percentage of...Ch. 8 - Dividend Growth Model [LO1] Under what two...Ch. 8 - Common versus Preferred Stock [LO1] Suppose a...Ch. 8 - Prob. 6CRCTCh. 8 - Growth Rate [LO1] In the context of the dividend...Ch. 8 - Prob. 8CRCTCh. 8 - Prob. 9CRCTCh. 8 - Prob. 10CRCTCh. 8 - Prob. 11CRCTCh. 8 - Two-Stage Dividend Growth Model [LO1] One of the...Ch. 8 - Prob. 13CRCTCh. 8 - Price Ratio Valuation [LO2] What are the...Ch. 8 - Stock Values [LO1] The JacksonTimberlake Wardrobe...Ch. 8 - Stock Values [LO1] The next dividend payment by...Ch. 8 - Stock Values [LO1] For the company in the previous...Ch. 8 - Stock Values [LO1] Caan Corporation will pay a...Ch. 8 - Stock Valuation [LO1] Tell Me Why Co. is expected...Ch. 8 - Stock Valuation [LO1] Suppose you know that a...Ch. 8 - Stock Valuation [LO1] Estes Park Corp. pays a...Ch. 8 - Valuing Preferred Stock [LO1] Moraine, Inc., has...Ch. 8 - Prob. 9QPCh. 8 - Prob. 10QPCh. 8 - Prob. 11QPCh. 8 - Prob. 12QPCh. 8 - Stock Valuation and PS [LO2] TwitterMe, Inc., is a...Ch. 8 - Stock Valuation [LO1] Bayou Okra Farms just paid a...Ch. 8 - Prob. 15QPCh. 8 - Nonconstant Dividends [LO1] Maloney, Inc., has an...Ch. 8 - Nonconstant Dividends [LO1] Lohn Corporation is...Ch. 8 - Supernormal Growth [LO1] Synovec Co. is growing...Ch. 8 - Prob. 19QPCh. 8 - Prob. 20QPCh. 8 - Prob. 21QPCh. 8 - Valuing Preferred Stock [LO1] E-Eyes.com just...Ch. 8 - Prob. 23QPCh. 8 - Two-Stage Dividend Growth Model [LO1] A7X Corp....Ch. 8 - Two-Stage Dividend Growth Model [LO1] Navel County...Ch. 8 - Stock Valuation and PE [LO2] Summers Corp....Ch. 8 - Stock Valuation and PE [LO2] You have found the...Ch. 8 - Stock Valuation and PE [LO2] In the previous...Ch. 8 - Stock Valuation and PE [LO2] YGTB, Inc., currently...Ch. 8 - PE and Terminal Stock Price [LO2] In practice, a...Ch. 8 - Stock Valuation and PE [LO2] Fly Away, Inc., has...Ch. 8 - Prob. 32QPCh. 8 - Stock Valuation [LO1] Most corporations pay...Ch. 8 - Nonconstant Growth [LO1] Storico Co. just paid a...Ch. 8 - Nonconstant Growth [LO1] This ones a little...Ch. 8 - Constant Dividend Growth Model [LO1] Assume a...Ch. 8 - Two-Stage Dividend Growth [LO1] Regarding the...Ch. 8 - Prob. 38QPCh. 8 - Prob. 1MCh. 8 - Prob. 2MCh. 8 - What is the industry average priceearnings ratio?...Ch. 8 - Prob. 4MCh. 8 - Assume the companys growth rate slows to the...Ch. 8 - Prob. 6M
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