Fin 3322
Bonds and Stocks Homework
1.
The bonds issued by Jensen & Son bear a 6% 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?
I bond will only sell at pay when it’s coupon payment equals it’s yield to maturity.
6%
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 6%. 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 / 1.06^30 = 174.11
10,000,000 / 174.11 = 57,434.95
Therefore, MerryWeather needs to sell 57,435 bonds
3.
A corporate bond with a face value of $1,000 matures in 4 years and has a 8%
coupon paid at the end of each year. The current price of the bond is $932.
What is the yield to maturity for this bond?
N
I/Y
PV
PMT
FV
=4
=?
= -932
= 80
= 1,000
I/Y = 10.15%
4.
Weisbro and Sons common stock sells for $21 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?
21= Div / (.09-.05)
Div = 21 * (.04) = 0.84
However this is the next dividend not the last one
Div1 = Div0 * (1 + g)
0.84 = Div0 * (1.05)
Div0 = 0.84 / 1.05 = 0.80
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
7% rate of return?
First, we can get the value of the stock, when it is
acting like a perpetuity (year 4 and beyond)
1.25 / .07 = 17.86 @ year 3
Then discount back the four cash flows
1 / 1.07 + 2.50 / 1.07^2 + 5 / 1.07^3 + 17.86 / 1.07^3
21.78
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 2% 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 a perpetuity (year 5 and beyond)
(1.25*1.02) / (.08-.02) = 21.25 @ year 4
Then discount back the 5 cash flows
1.14 / 1.08 + 1.18 / 1.08^2 + 1.22 / 1.08^3 + 1.25 / 1.08^4 + 21.25 / 1.08^4
19.57
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 $.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 11.5%?
Part 1 is the Growing Annuity
(A) PV0 = 0.56/(0.115-1) * {1-(2/1.115)3} = 3.02
Part 2 is the Growing Perpetuity
1.5 / .115 = 13.04 @ year 3
(B) PV0 = 13.04/(1.1153) = 9.41
The price of the stock today is 12.43
8.
BC ‘n D just paid its annual dividend of $.60 a share. The projected dividends
for the next five years are $.30, $.50, $.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 6% discount rate?
First, we can get the value of the stock, when it is
acting like a perpetuity (year 6 and beyond)
1.4 / .06 = 23.33 @ year 5
Then discount back the six cash flows
.3 / 1.06 + .5 / 1. 06^2 + .75 / 1. 06^3 + 1 / 1. 06^4 + 1.2 / 1. .06^5 + 23.33 / 1. 06^5
20.48
9.
.
Year 0
The Felix Corp. projects to pay a dividend of $.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 10% in the market. The price of
the stock should be ____.
Year 1
0.75
Year 2
0.75*1.12
Year3
0.75*1.122
Part 1 is the Growing Annuity
PV0 = 0.75/(0.1-0.12) * {1-(1.12/1.1)4} = 2.802559
Part 2 is the Growing Perpetuity
Div5 = 0.75 * 1.123 * 1.08 = 1.137992
PV4 = 1.14/(0.1-0.8) = 57
Part 3 Bring it back to time 0
PV0 = 57/(1.14) = 38.93
Part 4 Add them together
PV = 38.93 + 2.08 = 41.73
Year 4
0.75*1.123
Year 5
0.75*1.123*1.08
10. Doctors-On-Call, a newly formed medical group, just paid a dividend of $.50.
The company’s dividend is expected to grow at a 20% rate for the next 5 years
and at a 3% rate thereafter. What is the value of the stock if the appropriate
discount rate is 12%?
Year 0 Year 1
0.5
0.5*1.2
Year 2
0.5*1.22
Year3
Year 4
0.5*1.23 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 * 1.03 = 1.281485
PV5 = 1.28/(0.12-0.03) = 14.23872
Part 3 Bring it back to time 0
PV0 = 14.24/(1.125) = 8.08
Part 4 Add them together
PV = 3.09 + 8.08 = 11.17
Year 6
0.5*1.25*1.03