Chapter 7-Problem 3 Consider Borden’s 83/4 percent bonds ...



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Chapter 7-Problem 3 Consider Borden’s 83/4 percent bonds that mature on April 15, 2016. Assume that the interest on these bonds is paid and compounded annually. Determine the value of a $1,000 denomination Borden bond as of April 15, 2004, to an investor who holds the bond until maturity and whose required rate of return is a. 7 percent b. 9 percent c. 11 percent

a. Po = Σ I/(1 + kd)t + M/(1 + kd)n

t=1

I = .0875 X 1000 = $87.50 kd = 0.07

M = $1000 n = 12 years (2012 - 2004)

12

Po = Σ 87.50/(1 + 0.07)t + 1000/(1 + 0.07)12

t=1

= 87.50(PVIFA.07,12) + 1000 (PVIF.07,12)

= 87.50(7.943) + 1000 (0.444) = $1139 (tables and calculator)

b. I = $87.50 kd = .09 M = $1000 n = 12

12

Po = Σ 87.50/(1 + .09)t + 1000/(1 + 0.09)12

t=1

= 87.50 (PVIFA0.09,12) + 1000(PVIF0.09,12)

= 87.50(7.161) + 1000 (0.356) = $983 (Tables)

$982 (Calculator)

c. I = $87.50 kd = .11 M = $1000 n = 12

12

Po = Σ 87.50/(1 + 0.11)t + 1000/(1 + 0.11)12

t=1

= 87.50 (PVIFA0.11,12) + 1000(PVIF0.11,12)

= 87.50(6.492) + 1000 (0.286) = $854 (tables and calculator)

d. I = .0875(1000)/2 = $43.75 M = $1000

kd = 0.08/2 = 0.04; n = 12 X 2 = 24

24

Po = Σ 43.75/(1 + 0.04)t + 1000/(1 + 0.04)24

t=1

= 43.75(PVIFA0.04,24) + 1000(PVIF0.04,24)

= 43.75(15.247) + 1000(0.390) = $1057 (tables and calculator)

Chapter 7-P 7 Consider the Leverage Unlimited, Inc., zero coupon bonds of 2008. Th e bonds were issued in 1990 for $100. Determine the yield to maturity (to the nearest 1/10 of 1 percent) if the a. Issue price in 1990. (Note: To avoid a fractional year holding period, assume that the issue and maturity dates are at the midpoint—July 1—of the respective years.) b. Market price as of July 1, 2004, of $750. c. Explain why the returns calculated in Parts a and b are different.

a. Po = M/(1 + kd)n

= M(PVIFkd,n)

n = 18 (2008 - 1990); Po = $100; M = $1000

$100 = $1000(PVIFkd,18)

(PVIFkd,18) = 0.100

From Table II, this present value interest factor in the 18-year row is between the values for 13% (0.111) and 14% (0.095). Calculator solution is

kd = 13.65 %.

b. Po = $750; n = 4 (2008 - 2004)

$750 = $1000(PVIFkd,4)

(PVIFkd,4) = 0.750

kd = 7.46% (by calculator)

c. Over the period from 1985 to 1999, the general level of interest rates declined, causing bond prices to rise and yields to fall.

Chapter 7-Problem 12** Consider again the American Telephone & Telegraph 81/8 percent debentures that mature on July 15, 2024 (see problem 6). Determine the yield to call if the bonds are called on July 15, 2010 at $1,016.55.

I = $81.25; n = 6 (2010-2004); P0 = $1,025; Call price = $1,016.55

kd = 7.81% (calculator)

Chapter 7-Problem 19 Zheng Enterprises, a multinational drug company specializing in Chinese medicines, issued $100 million of 15 percent coupon rate bonds in January 2005. Th e bonds had an initial maturity of 30 years. Th e bonds were sold at par and were callable in fi ve years at 110 (i.e., 110 percent of par value). It is now January 2010, and interest rates have declined such that bonds of equivalent remaining maturity now sell to yield 11 percent. How much would you be willing to pay for one of these bonds today? Why?

Maximum value:

P0 = $150(PVIFA.11,25) + $1000(PVIF.11,25)

= $1337

Value at call = $1,1000

You would pay $1,100 or perhaps a slight premium over that amount, but nowhere near $1,337, due to the imminent risk of a call of the bonds.

Chapter 8-Problem 2 The common stock of General Land Development Company (GLDC) is expected to pay a dividend of $1.25 next year and currently sells for $25. Assume that the fi rm’s future dividend payments are expected to grow at a constant rate for the foreseeable future. Determine the implied growth rate of GLDC’s dividends (and earnings), assuming that the required rate of return of investors is 12 percent.

Po = $25 D1 = $1.25 ke = .12

ke = D1/Po + g

.12 = 1.25/25 + g

g = .07 (or 7%)

Chapter 8-Problem 4 Cascade Mining Company expects its earnings and dividends to increase by 7 percent per year over the next six years and then to remain relatively constant thereaft er. Th e firm currently (that is, as of year 0) pays a dividend of $5 per share. Determine the value of a share of Cascade stock to an investor with a 12 percent required rate of return.

Σ[Do(1 + g1)t/(1 + ke)t]; Do = $5.00; g1 = .07; ke = .12

t=1

Present Value

Year Dividend Interest Factor Present Value

t Dt = 5.00(1 + .07)t PVIF.12,t Dt x PVIF.12,t

1 5.00(1 + .07)1 = .893 $ 4.778

$5.35

2 5.00(1 + .07)2 = .797 4.563

5.725

3 5.00(1 + .07)3 = .712 4.361

6.125

4 5.00(1 + .07)4 = .636 4.168

6.554

5 5.00(1 + .07)5 = .567 3.976

7.013

6 5.00(1 + .07)6 = .507 3.805

7.504

PV (First 6-Years' Dividends) $25.651

Value of Stock at End of Year 6:

P6 = D7/(ke - g2) g2 = .00

D7 = D6(1 + g2) = 7.504(1 + .00) = $7.504

P6 = 7.504/(.12 - .00) = $62.533

Present Value of P6:

PV(P6) = P6/(1 + ke)6 = 62.533/(1 + .12)6 = 62.533 x PVIF.12,6

= 62.533 X .507 = $31.704

Value of Common Stock (Po):

Po = PV (First 6-Years' Dividends) + PV(P6)

Chapter 8-Problem 6 Simtek currently pays a $2.50 dividend (D0) per share. Next year’s dividend is expected to be $3 per share. Aft er next year, dividends are expected to increase at a 9 percent annual rate for three years and a 6 percent annual rate thereafter. a. What is the current value of a share of Simtek stock to an investor who requires a 15 percent return on his or her investment? b. If the dividend in year 1 is expected to be $3 and the growth rate over the following three years is expected to be only 7 percent and then 6 percent thereafter, what will the new stock price be?

a. 4

Po = D1/(1 + ke) + Σ [D1(1 + g1)t-1/(1 + ke)t]

t=2

+ [D5/(ke - g2)]/[(1 + ke)4]

ke = .15 Do = $2.50 D1 = $3.00 g1 = .09 g2 = .06

Present Value of First Year Dividend

PV(D1) = 3.00/(1 + .15) = 3.00(PVIF.15,1)

= 3.00(.870) = $2.610

Present Value of Next 3-Years' Dividends

Year Dividend P.V. Interest Factor Present Value

t Dt = 3.00(1 + .09) t-1 PVIF.15,t Dt x PVIF.15,t

2 3.00(1 + .09)1 = .756 $2.472

$3.270

3 3.00(1 + .09)2 = .658 2.345

$3.564

4 3.00(1 + .09)3 = .572 2.222

$3.885

PV(Next 3-Years' Dividends) $7.039

Value of Stock at End of Year 4

D5 = D4(1 + g2) = 3.885(1 + .06) = $4.118

P4 = D5/(ke - g2) = 4.118/(.15 - .06) = $45.756

Present Value of P4

PV(P4) = P4/(1 + ke)4 = P4 x PVIF.15,4

= 45.756 x .572 = $26.172

Value of Common Stock:

Po = PV(D1) + PV(Next 3-Years' Dividends) + PV(P4)

= $2.610 + $7.039 + $26.172 = $35.82 (tables)

b. ke = .15 Do = $2.50 D1 = $3.00 g1 = .07 g2 = .06

Present Value of First Year Dividend

PV(D1) = $2.610 (same as part (a))

Present Value of Next 3-Years' Dividends

Year Dividend P.V. Interest Factor Present Value

t Dt=3.00(1 + .07)t-1 PVIF.15,t Dt x PVIF.15,t

2 3.00(1 + .07)1 = .756 $2.427

$3.210

3 3.00(1 + .07)2 = .658 2.260

$3.435

4 3.00(1 + .07)3 = .572 2.102

$3.675

PV(Next 3-Years' Dividends) $6.789

Value of Stock at End of Year 4

D5 = 3.675(1 + .06) = $3.896

P4 = 3.896/(.15 - .06) = $43.289

Present Value of P4

PV(P4) = 43.289 x .572 = $24.761

Value of Common Stock:

Po = $2.610 + $6.789 + $24.761 = $34.16 (tables)

Chapter 8-Problem 8 The Seneca Maintenance Company currently (that is, as of year 0) pays a common stock dividend of $1.50 per share. Dividends are expected to grow at a rate of 11 percent per year for the next four years and then to continue growing thereafter at a rate of 5 percent per year. What is the current value of a share of Seneca common stock to an investor who requires a 14 percent rate of return?

Present Value of First 4-Year's Dividends:

4

Σ [Do(1 + g1)t/(1 + ke)t]; Do = $1.50; g1 = .11; ke = .14

t=1

Present Value

Year Dividend Interest Factor Present Value

t Dt = 1.50(1 + .11)t PVIF.14,t Dt x PVIF.14,t

1 1.50(1 + .11)1 = .877 1.460

$1.6650

2 1.50(1 + .11)2 = .769 1.421

$1.8482

3 1.50(1 + .11)3 = .675 1.385

$2.0514

4 1.50(1 + .11)4 = .592 1.348

$2.2771

PV (First 4-Years' Dividends) $5.614

Value of Stock at End of Year 4:

P4 = D5/(ke - g2) g2 = .05

D5 = D4(1 + g2) = 2.2771(1 + .05) = $2.391

P4 = 2.391/(.14 - .05) = $26.567

Present Value of P4:

PV(P4) = P4/(1 + ke)4 = $26.567/(1 + .14)4

= $26.567(PVIF.14,4) = $26.567 x 0.592 = $15.728

Value of Common Stock (Po):

Po = PV(First 4-Years' Dividends) + PV(P4)

= $5.614 + $15.728 = $21.34 (tables)

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