Time Value Formulas
Future Value (lump sum):
FVn = PV(1+r)n where PV is the current value
Present Value (lump sum):
PV = FVn/(1+r)n
Present Value for a series of payments (C1, C2, C3, etc):
PV
C1
C2
C3
CN
.
2
3
(1 r1 ) (1 r2 )
(1 r3 )
(1 rN ) N
Perpetu
Valuation Problem Solution
1. a. Beta for the Health Division = 1.15. Cost of Equity = 7% + 1.15 * 5.5% = 13.33%. Cost of Capital
= 13.33% * 0.80 + (7.5% * 0.6) * 0.2 = 11.56%.
b. The table below contains the FCF calculations.
Depreciation
EBIT
EBIT(1-T)
Solutions to Time Value Problems
There is some notation that I want to point out. Rather than write out the formula for an annuity
1
1
the book, and I, will use some shorthand notation. Atr% =
t is the present value of
r r (1 + r )
a $1 annuity discoun
Solutions to Stock and Bond Problems
1. Since the coupons are going to be reduced by half they will be $50 for the next three years.
The final payment will be the remaining unpaid coupons of $150, plus the last coupon of
$100 plus the face value of $1,000
Solutions to Additional Problems Capital Structure
1.
a. Annual tax savings from debt = $ 40 million * .09 * .35 = $ 1.26
b. PV of Savings assuming savings are permanent = $ 40 million .35 = $ 14.00
c. PV of Savings assuming savings occur for 10 years = $
CHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS
PROBLEM SETS
1.
There is little hedging or speculative demand for cement futures, since cement prices
are fairly stable and predictable. The trading activity necessary to support the futures
market w
CHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT
CHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT
PROBLEM SETS
1.
In formulating a hedge position, a stocks beta and a bonds duration are used
similarly to determine the expected percentage gain or loss in the
Finance 30233, Fall 2011
S. Mann
Sample problem - Colgate Straddle deltas solution.
A straddle consists of buying a call and buying a put with the same strike price. Use the
information below to construct a straddle using Colgate January 2012 options, wit
Finance 30233, Fall 2011
Name_Solution_
S. Mann
Sample Problem Create Payoff diagrams - solution
Examine the following payoff diagram and call prices:
Option
Call
Cal
Call
Call
Strike
45
50
55
60
Price
12.00
8.00
4.25
2.00
45
50
5
0
55
60
ST
a) What posit
Finance 30233, Fall 2011
S. Mann
Name_Solution_
Sample Problem forward contract valuation
Your firm has existing forward contracts with ESSO Oil to purchase 1 million barrels of oil for
delivery at the end of March, May, and July 2011 (total forward purch
Finance 30233, Fall 2011
S. Mann
Name_Solution_
Sample problem forward pricing
PLQ, Inc. stock is currently priced at $420 per share. It pays a $25 dividend to shareholders of
record in six months. Use the following discount rate information for 3,6, 9 an
Finance 30233, Fall 2011
S. Mann
Sample problem One Period Binomials - Solution.
1. A stock price is currently $50. It is known that at the end of two months it will be either $53 or
$48. The price per dollar of a two-month T-bill is B(0,2 months)= 0.99.
Finance 30233, Fall 2011
Name_Solution_
S. Mann
Sample Problem Payoff diagrams - solution
Draw the payoff diagrams for the following positions:
a)
Long 2 calls with strike of 50
Short 1 put with strike of 50
Position Payoff
slope = +2
5
0
-5
slope = +1
45
Finance 30233, Fall 2011
Name_Solution_
S. Mann
Sample problem structured currency note.
Structured Note. Assume that the current peso exchange rate is $1 to 10 pesos.
You are considering the purchase of a one-year note with the following redemption
value
Finance 30233
Fall 2010
S. Mann
Name_Solution_
Sample Problem 1. Solution
Show your work to receive full credit.
Assume the following:
Asset/portfolio
Expected return
Standard deviation
Riskless rate
5%
0
Risky portfolio A
10 %
20 %
Risky portfolio B
20 %
Finance 30233
Fall 2010
Associate Professor S. Mann
Name_Solution_
Sample Problem 2. Solution
Show your work to receive full credit.
Consider the following, and assume the CAPM holds.
Asset
beta
standard deviation
Riskless asset, yielding 3%
Delta Company
Finance 30233, Fall 2010
S. Mann
Name_Solution_
Sample problem 3: APT
1. Assume that there is one priced risk factor for assets (This assumption would be true
for the CAPM, as well as a single factor APT). Consider the following betas and
expected returns
Finance 30233 , Fall 2010
The Neeley School, TCU
S. Mann
Name_Solution_
Sample Problem Four. Solution
Show your work to receive full credit.
Assume the following:
Riskless borrowing & lending rate is 5%.
E[R]
Asset A
Asset B
Asset C
(std deviation)
10%
1
Finance 30233. Fall 2010
Neeley School of Business
Texas Christian University
S. Mann
Sample problems #5: Yields
Name_Solution_
1. Yield Curves.
You observe the following zero-coupon bond yields (all default-free).
a) Find in the price per $100 Face value
Finance 30233. Fall 2010
Neeley School of Business
Texas Christian University
S. Mann
Name_Solution_
Sample problems #6: forward rates , bond pricing: solution
For all parts, use the following information:
B(0,1)
= 0.95
B(0,2)
= 0.90
B(0,3)
= 0.86
B(0,4)
Finance 30233, Fall 2010
S. Mann
Name_solution_
Sample problem for final_01 solution.
The Bogus bank has the following market value asset/liability structure:
Assets
$10,000,000
Asset duration (modified)
8.0
Liabilities
9,000,000
Liability duration (modif
Finance 30233, Fall 2010
S. Mann
Name_Solution_
Sample problem for final #2
PLQ, Inc. stock is currently priced at $420 per share. It pays a $25 dividend to shareholders of
record in six months. Use the following discount rate information for 3,6, 9 and 1
Finance 30233, Fall 2010
S. Mann
Sample problem for final #3.
Name_Solution_
Structured Note. Assume that the current peso exchange rate is $1 to 10 pesos.
You are considering the purchase of a one-year note with the following redemption
value formula:
Re
Finance 30233, Fall 2010
S. Mann
Name_Solution_
Sample Problem for Final #4: Solution
Your firm has existing forward contracts with ESSO Oil to purchase 1 million barrels of oil for
delivery at the end of March, May, and July 2011 (total forward purchase
Finance 30233, Fall 2010
Advanced Investments
S. Mann
Name_Solution_
Sample problem for final: # 5.
Billy Hill manages a $100 million equity portfolio for Silverman Bags, Inc.
His equity portfolio has an average Beta of 1.50.
During the past year, returns
Finance 30233, Fall 2010
Advanced Investments, S. Mann
Sample problem for final: # 6.
Name_Solution_
Billy Hill manages a $100 million equity portfolio for Silverman Bags, Inc.
His equity portfolio has an average Beta of 1.50.
Billy also has maintained a
Finance 30233, Fall 2010
Advanced Investments
S. Mann
Name_Solution_
Sample problem for final: # 7: solution.
Christine Callaghan manages a $100 million bond portfolio for a pension fund. At the
beginning of the year, the modified duration of her portfoli
Finance 30233, Fall 2010
M.J. Neeley School of Business, TCU
S. Mann
Self-quiz Monday, November 08, 2010
Name_
Examine the following information regarding options written on MMM stock. At the
time of the quotes below, MMM stock traded at $90.
Put
Market
S