Chapter 9, Problem 18P

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Chapter
Section

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

# NONCONSTANT GROWTH STOCK VALUATION Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This same growth rate is expected to last for another 2 years, then decline to gn =6%. a. If D0 = $1.60 and rs = 10%, what is TIC’s stock worth today? What are its expected dividend, and capital gains yields at this time, that is, during Year 1? b. Now assume that ITC’s period of supernormal growth is to last for 5 years rather than 2 years. Flow would this affect the price, dividend yield, and capital gains yield? Answer in words only. c. What will TTC’s dividend and capital gains yields be once its period of supernormal growth ends? (Hint: These values will be the same regardless of whether you examine the case of 2 or 5 years of supernormal growth; the calculations are very easy.) d. Explain why investors are interested in the changing relationship between dividend and capital gains yields over time. a. Summary Introduction To identify: The stock value, expected dividend and capital gain. Introduction: Corporate Value Model: The model that evaluates a firm on the basis of its future operations and the results of those operations is called corporate valuation model. It is a useful tool to analyze a firm’s stock for investment purposes. Explanation Formula to calculate the present value of share, P0=Div1(1+r)1+Div2(1+r)2+...+Divn+Horizonvalue(1+r)n Where, • P0 is the stock value. • Div1 is the dividend for the first year. • Div2 is the dividend for the second year. • Divn is the dividend for the third year. • n is the number of years. • r is the interest rate. Substitute$1.92 for Div1 , $2.30 for Div2 , and$60.95 for stock value.

P0=$1.92(1+0.10)1+$2.30(1+0.10)2+$60.95(1+0.10)2=$1.921.10+$2.301.21+$60.951.21=$1.75+$1.90+$50.37=$54.022

The stock value is $54.022. Compute the expected dividend yield. The dividend for the first year is$1.92. (Calculated in working note)

The stock value is $54.022. (Calculated above) Formula to calculate the expected dividend yield, Expecteddividendyield=Div1P0 Where, • P0 is the stock value. • Div1 is the dividend for the first year. Substitute$1.92 for Div1 and $54.022 for P0 Expecteddividendyield=$1.92$54.022=0.036 The expected dividend yield is 0.036 or 3.6%. Compute the capital gain yield. In order to compute the capital gain yield, price at the first year needs to calculate. The rate of return is 10% or 0.10. (Given) The dividend of the second year is$2.30. (Calculated in working note)

The stock value of the second year is \$60.95. (Calculated in working note)

Formula to calculate the stock value of the first year,

P1=(Div2+P2)(1+r)

Where,

• P1 is the stock value of first year

b.

Summary Introduction

To identify: The affect of reduction in maturity period on price, dividend yield and capital gain yield.

c.

Summary Introduction

To identify: The capital gain yield and dividend yield.

d.

Summary Introduction

To explain: The reason to take the interest of investors in the dividend and capital gain yield change relationship.

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