Fin 5219
Bonds and Stocks Homework
1. The bonds issued by Jensen & Son bears an 8% coupon, payable semiannually. The
bond matures in 8 years and has a $1,000 face value. Currently, the bond sells at par.
What is the yield to maturity?
A bond will only sell at par when its coupon payment equals its yield to maturity.
8%
2. The MerryWeather Firm wants to raise $10 million to expand its business. To
accomplish this, it plans to sell 30-year, $1,000 face value zero-coupon bonds. The bonds
will be priced to yield 8%. What is the minimum number of bonds it must sell to raise the
$10 million it needs?
The price of each bond will be 1000 / 1.0830 = 99.38
MerryWeather needs 10,000,000
Therefore MerryWeather needs to sell 100,624 bonds: 10,000,000/ 99.38
3. A corporate bond with a face value of $1,000 matures in 4 years and has an 8%
coupon paid at the end of each year. The current price of the bond is $901. What is the
yield to maturity for this bond?
N
=4
I/Y = ?
PV = -901
PMT = 80
FV = 1,000
I/Y = 11.2%
4. Weisbro and Sons common stock sells for $19 a share and pays an annual dividend
that increases by 5% annually. The market rate of return on this stock is 9%. What is the
amount of the last dividend paid by Weisbro and Sons?
19= Div1 / (.09-.05)
Div1 = 19 * (.04) = 0.76
However this is the next dividend not the last one
Div1 = Div0 * (1 + g)
0.76 = Div0 * (1.05)
Div0 = 0.76 / 1.05 = 0.72
5. Can’t Hold Me Back, Inc. is preparing to pay its first dividends. It is going to pay
$1.00, $2.50, and $5.00 a share over the next three years, respectively. After that, the
company has stated that the annual dividend will be $1.25 per share indefinitely. What is
this stock worth to you per share if you demand a 5% rate of return?
First, we can get the value of the stock, when it is
acting like a perpetuity (D4 and beyond)
1.25 / .05 = 25.00 This is a year 3 value, as the first payment is in year 4
Discount back the three specified dividends and the year 3 value of the perpetuity
1 / 1.05 + 2.50 / 1.052 + 5 / 1.053 + 25.00 / 1.053
29.14
6. Now or Later, Inc. recently paid $1.10 as an annual dividend. Future dividends are
projected at $1.14, $1.18, $1.22, and $1.25 over the next four years, respectively. After
that, the dividend is expected to increase by 3% annually. What is one share of this stock
worth to you if you require an 8% rate of return on similar investments?
First, we can get the value of the stock, when it is acting like perpetuity
(Div4 and beyond: treat the 1.25 as the first perpetuity payment)
1.25 / (.08-.03) = 25 @ year 3
Then discount back the 5 cash flows
1.14 / 1.08 + 1.18 / 1.082 + 1.22 / 1.083 + 25 / 1.083
22.88
7. Mother and Daughter Enterprises is a relatively new firm that appears to be on the
road to great success. The company paid its first annual dividend yesterday in the amount
of $0.28 a share. The company plans to double each annual dividend payment for the
next three years. After that time, it is planning on paying a constant $1.50 per share
indefinitely. What is one share of this stock worth today if the market rate of return on
similar securities is 9.5%?
Part 1: The Growing Annuity
(A) PV0 = 0.56/(0.095-1) * {1-(2/1.095)3} = 3.15
Part 2 is the Growing Perpetuity
1.5 / .095 = 15.79 @ year 3
(B) PV0 = 15.79/(1.0953) = 12.03
The price of the stock today is 15.18
8. BC ‘n D just paid its annual dividend of $0.60 a share. The projected dividends for
the next five years are $0.30, $0.50, $0.75, $1.00, and $1.20, respectively. After that time,
the dividends will be held constant at $1.40. What is this stock worth today at a 4%
discount rate?
First, we can get the value of the stock, when it is
acting like a perpetuity (Div6 and beyond)
1.4 / .04 = 35.00 @ year 5
Then discount back the six cash flows
0.3 / 1.04 + 0.5 / 1. 042 + 0.75 / 1. 043 + 1 / 1. 044 + 1.2 / 1. .045 + 35.00 / 1. 045
32.03
9. The Felix Corp. projects to pay a dividend of $0.75 next year and then have it grow
at 12% for the following 3 years before growing at 8% indefinitely thereafter. The equity
has a required return of 11% in the market. The price of the stock should be ____.
Year 1
0.75
Year 2
0.75*1.12
Year 3
0.75*1.122
Year 4
0.75*1.123
Part 1 is the Growing Annuity
PV0 = 0.75/(0.11-0.12) * {1-(1.12/1.11)4} = 2.74
Part 2 is the Growing Perpetuity
Div5 = 0.75 * 1.123 * 1.08 = 1.14
PV4 = 1.14/(0.11-0.08) = 38
Part 3 Bring it back to time 0
PV0 = 38/(1.114) = 25.03
Part 4 Add them together
PV = 25.03 + 2.74 = $27.77
Year 5
0.75*1.123*1.08
10. Doctors-On-Call, a newly formed medical group, just paid a dividend of $0.50. The
company’s dividend is expected to grow at 20% for the next 5 years and at 4% thereafter.
What is the value of the stock if the appropriate discount rate is 12%?
Year 0
0.5
Year 1
0.5*1.2
Year 2
0.5*1.22
Year3
Year 4
3
0.5*1.2 0.5*1.24
Year 5
0.5*1.25
Part 1 is the Growing Annuity
PV0 = (0.5*1.2)/(0.12-0. 2) * {1-(1.2/1.12)5} = 3.089547
Part 2 is the Growing Perpetuity
Div6 = 0. 5 * 1.25 * 1.04 = 1.293926
PV5 = 1.293926/(0.12-0.04) = 16.17408
Part 3 Bring it back to time 0
PV0 = 16.17408/(1.125) = 9.17761
Part 4 Add them together
PV = 3.089547+ 9.17761 = 12.27
Year 6
0.5*1.25*1.04