FIN 418 A1 – INSTRUCTIONS FOR CASE REPORT

 

Due at 3:00 p.m. on Wednesday, November 26, 2014. Hand in the report at the

assignment drop-off box located outside the General Office on the third floor of the

School of Business building. Late submissions will not be accepted. Also, electronic

submissions will not be accepted.

 

Attach a covering page to the front of your report giving your name, course number, and

section number (A1).

 

Work on the case report may be done individually or in pairs. If you decide to work in

pairs, both names must appear on the final report. The instructor will assign the same

mark to both members of a pair.

 

Instructions:

1. Hand in paper copies of Excel worksheets showing your analysis. Put these in an appendix. Don’t shrink the worksheets to such a small size that they are difficult

to read. You could hide some of the data to reduce the bulk of your report.

2. The report should be at most five pages (that is, five typewritten pages double spaced), plus Excel worksheets. (The Excel worksheets are over and above the

five typewritten pages.)

3. State clearly any assumptions that you make. 4. Answer the questions in turn. Write down each question number followed by

your answer.

5. Strive for a professional looking submission.

On November 8, 2000, Corning, INC. (Corning) announced it would issue $2.7 billion in

zero-coupon convertible debentures priced at $741.923 per $1,000 principal amount.

Concurrent with the offering, Corning also conducted a separate public offering of 30

million shares of its common stock at $71.25 per share.

 

Julianna Coopers, an investment analyst at the Paradigm Group of mutual funds, has been

tasked with assessing the new issue of convertibles. She must recommend whether or not

Paradigm’s Convertible Securities Fund should invest in the issue. Her recommendation

would be guided by:

 Her independent valuation analysis.

 The volatility of Corning stock.

 The sustainability of Corning’s current high stock market valuations and the outlook for the firm.

 

Questions:

 

1. [1] “The initial public offering (IPO) price yielded 2% per annum to maturity,

compounded semiannually.” Show the required calculation that demonstrates that the 2%

figure is correct.

 

 

 

2. [4] Observe the entries for Corning in Exhibit 5. Show the calculation of the

following:

 Conversion price per share.

 Conversion premium per share. (In the class note, we call this the market conversion premium ratio.)

 Income spread per bond (This is equivalent to what is called (in the class note) the favourable income differential per share times the conversion ratio.)

 Premium payback period.

3. [2] What do the conversion premium per share and premium payback period reported

in Exhibit 5 for Corning tell Ms. Coopers?

 

4. [2] In Exhibit 5, the conversion premium per share is close to zero for some of the

convertible bonds listed and larger for others. What is the reason for this?

 

5. [4] What is the straight value of the issue per $1,000 face value? To answer this

question, use Exhibits 6 – 8. Identify clearly your choice of discount rate and give a

reason for this choice. What is one important difference between the bonds listed in

Exhibit 8 and the Corning issue?

 

6. [1] Why does Ms. Coopers say that the strike price of the conversion option is $89.062

per share?

 

7. [2] What are the sources of potential dilution? Why is this important?

 

8. Value the Corning issue using the model given in the class note on Convertible Bonds.

Note: You may find it easiest to work with a binomial tree of the following shape. Then

formulas can easily be dragged across and down.

 

 

 

 

 

(a) [2] Note that the swap rate for a 15-year maturity is the average of the bid and offer

fixed rates that banks are willing to swap for six-month LIBOR in a 15-year interest-rate

swap agreement. Estimate the swap rate for a 15-year maturity as follows: linearly

interpolate between the 10-year and 30-year Treasury yields given in Exhibit 12 to

estimate the 15-year Treasury yield. To this add 50 basis points. Note that the rate

derived is expressed as an annual rate compounded semi-annually. Convert this rate to

an equivalent annual continuously compounded rate.

 

(b) [2] Calculate the dividend yield of Corning’s stock by dividing the annual dividend

(Exhibit 9) by the current stock price. Convert this effective annual rate to an equivalent

annual continuously compounded rate.

 

 

 

(c) [2] In a table, list the call price for all six-month intervals between November 8, 2005

(when the bond is first callable by Corning) and November 8, 2015. Exhibit 1 describes

the call (or redemption) price as the IPO price plus the accrued original issue discount

through the redemption date. Note: On each call date, calculate the call price as follows:

$741.93 ($1, 000 $741.93) 30

t     

  , where “t” denotes the number of half-years since

the bond was issued. This implies that the call price is $1,000 (per $1,000 face value)

when the bond matures in 15 years.

 

(d) [20] As a base case, assign the following parameter values:

 Use a 30-step model with a time step of 0.5 years.

 Let the risk-free rate in the model equal the swap rate calculated in (a).

 Assign to volatility a value of 75%.

 Assign to q the dividend yield calculated in (b).

 Assign to  , the default intensity, a value of zero.

Calculate the following:

 The value of the bond (per $1,000 face value) assuming that none of the options (conversion, call, or put) are present.

 The value of the bond (per $1,000 face value) with the embedded conversion option only. What is the implied value of the conversion option?

 The value of the bond (per $1,000 face value) with the embedded call option only. What is the implied value of the call option?

 The value of the bond (per $1,000 face value) with the embedded put options only. What is the implied value of the put options?

 The value of the bond (per $1,000 face value) with all embedded options, conversion, call, and put. What is the implied value of all the options

available in combination?

 

Summarize your results in a table.

 

Is the value of the embedded conversion, call, and put options in combination equal to the

sum of their individual values on the assumption that that other options are not present?

 

Note:

 The straight value of the bond (with no embedded options) according to this model will not agree with what you have calculated in question 5 since in this

model, under the base case, we are assuming a zero probability of default whereas

the discount rate we use in question 5 takes default risk into account. When

answering the above questions about the implied values of the options, compare

the value of the bond with the specified options given by the model to the straight

value given by the model.

 The case does not give us the prices at which the bond can be put by the bondholder on November 8, 2005 and November 8, 2010. Assume that on each

of these dates, the put price equals the call price (calculated in 8(c)).

 

 

 With all options present (conversion, call, and put), calculate the value of the

bond as follows: 4 1 2 3

max( , max(min( , ), ))Q Q Q Q , where 1

Q is the value of the

bond if not called, put, or converted; 2

Q is the call price; 3

Q is the conversion

value; and 4

Q is the put price.

 

(e) [2] Under the base case, is conversion forced at any node? Explain.

 

(f) [4] Refer to Exhibit 11 and the call option expiring in November with a strike price of

$70.00 and the put option expiring in May with a strike price of $70.00. For each option,

calculate the volatility implied by the Black-Scholes model, the premium listed, the New

York close stock price of $68.50, the dividend yield calculated in (b) expressed as an

annual continuously compounded rate, and a risk-free rate of 6.4% per annum

compounded continuously. Measure time to maturity by the reported number of days to

maturity divided by 252, the number of trading days in a year.

 

(g) [5] Recalculate the value of the bond (per $1,000 face value) with the embedded

conversion, call, and put options making alternative assumptions with respect to

volatility. Provide some justification for the range of values assumed for volatility.

Consider the validity of estimating expected volatility using historical volatilities.

Develop your own view with respect to whether Corning will perform like the past month

or will be less/more volatile. Refer to Exhibit 10. Summarize your results in a table.

 

(h) [2] What are two important limitations of the analysis that has been conducted?

 

9. [10] Should Ms. Coopers recommend that Paradigm’s Convertible Securities Fund

invest in the issue? Does your analysis imply that the bond issue is overvalued or

undervalued? Why? Discuss these issues in a few paragraphs, referring to your analysis

and what you judge to be important considerations with respect to the sustainability of

Corning’s current high stock market valuations, the outlook for the firm, and any other

factors you judge to be important.

Sheet1

Problem 9-1

What is the price of a Treasury STRIPS with a face value of $100 that matures in 5 years and has a yield to maturity of 9.0 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “$” sign in your response.)

Answer

Example

Price = $100 / (1 + .035/2)2(10) =

Sheet2

Problem 9-2
A Treasury STRIPS matures in 8 years and has a yield to maturity of 5.4 percent. Assume the par value is $100,000.
a.	What is the price of the STRIPS? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “$” sign in your response.)
Price	$
b.	What is the quoted price? (Do not round intermediate calculations. Round your answer to 3 decimal places.)
Quoted price
Example
a.
Price = $100,000 / (1 + .054/2)2(8.5) =
b.
Quoted price = $63,577.36 / $1,000 =

Sheet3

Problem 9-3
A Treasury STRIPS is quoted at 67.181 and has 7 years until maturity. What is the yield to maturity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
YTM	%
Example
YTM = 2 × [(100 / 81.265)1/(2 × 8) − 1] = .0261 or 2.61%

Sheet4

roblem 9-4
What is the yield to maturity on a Treasury STRIPS with 6 years to maturity and a quoted price of 81.247?(Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
YTM	%
Example
YTM = 2 × [(100 / 65.492)1/(2 ×7) − 1] = .0614 or 6.14%

Sheet5

Problem 9-11
A Treasury bill with 136 days to maturity is quoted at 96.012. What is the bank discount yield, the bond equivalent yield, and the effective annual return? (Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places. Omit the “%” sign in your response.)
Discount yield	%
Bond equivalent yield	%
Effective annual return	%
Example
98.921 = 100 × [1 − (82/360) × DY); discount yield = .04737 or 4.737%
bond equivalent yield = [365(.04737)]/[360 − (82)(.04737)] = .04855 or 4.855%
EAR = [1 + .04855/(365/82)]365/82 − 1 = .04947 or 4.947%

Sheet6

Problem 9-12
A Treasury bill purchased in December 2015 has 123 days until maturity and a bank discount yield of 2.38 percent. Assume a $100 face value.
a.	What is the price of the bill as a percentage of face value? (Do not round intermediate calculations. Enter your answer as a percent rounded to 3 decimal places. Omit the “%” sign in your response.)
Price	%
b.	What is the bond equivalent yield? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
Bond equivalent yield	%
Example
1.0593 = [1 + (APR)(90/365)]365/90 ; APR = bond equivalent yield = 5.802%
discount yield = [360(.05802)]/[365 + (90)(.05802)] = 5.642%

Sheet7

Problem 9-13
The treasurer of a large corporation wants to invest $16 million in excess short-term cash in a particular money market investment. The prospectus quotes the instrument at a true yield of 6.64 percent; that is, the EAR for this investment is 6.64 percent. However, the treasurer wants to know the money market yield on this instrument to make it comparable to the T-bills and CDs she has already bought. If the term of the instrument is 80 days, what are the bond equivalent and discount yields on this investment? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
Bond equivalent yield	%
Discount yield	%
Example
1.0593 = [1 + (APR)(90/365)]365/90 ; APR = bond equivalent yield = 5.802%
discount yield = [360(.05802)]/[365 + (90)(.05802)] = 5.642%

Sheet8

Consider the following spot interest rates for maturities of one, two, three, and four years.

r1 = 3.7%    r2 = 4.2%     r3 = 4.9%     r4 = 5.7%

What are the following forward rates, where f1, k refers to a forward rate for the period beginning in one year and extending for k years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)

Example

f1,1 = (1.0492/1.043)1/1 − 1 = 5.50%

f1,2 = (1.0563/1.043)1/2 − 1 = 6.26%

f1,3 = (1.0644/1.043)1/3 − 1 = 7.11%

Sheet9

Problem 9-23
Consider the following spot interest rates for maturities of one, two, three, and four years.
r1 = 3.9%    r2 = 4.5%     r3 = 5.2%     r4 = 6.0%
Assuming a constant real interest rate of 2 percent, what are the approximate expected inflation rates for the next four years? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
I1	%
I2	%
I3	%
I4	%
EXAMPLE
f2,1 = 1.0563/1.0492 − 1 = 7.01%
f3,1 = 1.0644/1.0563 − 1 = 8.84%
I1 = r1 − 2%   = 4.30% − 2%   = 2.30%
I2 = f1,1 − 2% = 5.50% − 2%   = 3.50%
I3 = f2,1 − 2% = 7.01% − 2%   = 5.01%
I4 = f3,1 – 2% = 8.84% – 2%   = 6.84%

Sheet10

Problem 9-24
A Treasury bill that settles on May 18, 2012, pays $100,000 on August 21, 2012. Assuming a discount rate of 3.48 percent, what is the price and bond equivalent yield? Use Excel to answer this question. (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the “$” & “%” signs in your response.)
Price	$
Bond equivalent yield	%

Sheet11

Aloha Inc. has 8 percent coupon bonds on the market that have 11 years left to maturity. If the YTM on these bonds is 10.22 percent, what is the current bond price? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “$” sign in your response.)
Price	$

Sheet12

Problem 10-2
Rolling Company bonds have a coupon rate of 4.80 percent, 18 years to maturity, and a current price of $1,126. What is the YTM? The current yield? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
YTM	%
Current yield	%

Sheet13

bond has a coupon rate of 9.2 percent and 6 years until maturity. If the yield to maturity is 8.5 percent, what is the price of the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the “$” sign in your response.)
Price of the bond	$

Sheet14

Problem 10-5
A bond sells for $941.15 and has a coupon rate of 7.80 percent. If the bond has 21 years until maturity, what is the yield to maturity of the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
Yield to maturity	%

Sheet15

Problem 10-11
Ghost Rider Corporation has bonds on the market with 12 years to maturity, a YTM of 7.1 percent, and a current price of $932. What must the coupon rate be on the company’s bonds? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the “%” sign in your response.)
Coupon rate	%

Sheet16

LKD Co. has 12 percent coupon bonds with a YTM of 8.8 percent. The current yield on these bonds is 9.1 percent. How many years do these bonds have left until they mature? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Bonds mature