Chapter 8 - Master It!
Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a dedicated portfolio since the proceeds of the portfolio are dedicated to the future liability. In such a case, the portfolio is subject to reinvestment risk. Reinvestment risk occurs because the company will be reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed.
Suppose Ice Cubes, Inc. has the following liability due in five years. The company is going to buy bonds today in order to meet the future obligation. The liability and current YTM are below.
Amount of liability:	$ 100,000,000
Current YTM:	8%
a.	At the current YTM, what is the face value of the bonds the company has to purchase today in order to meet its future obligation? Assume that the bonds in the relevant range will have the same coupon rate as the current YTM and these bonds make semiannual coupon payments.
b.	Assume that the interest rates remain constant for the next five years. Thus, when the company reinvests the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in five years?
c.	Assume that immediately after the company purchases the bonds, interest rates either rise or fall by one percent. What is the value of the portfolio in five years under these circumstances?
One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same maturity as the liability, the company instead buys bonds with the same duration as the liability. If you think about the dedicated portfolio, if the interest rate falls, the future value of the reinvested coupon payments decreases. However, as interest rates fall, the price of the bond increases. These effects offset each other in an immunized portfolio.
Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is simply the weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a portfolio, you simply take the weight of each asset multiplied by its duration and then sum the results.
d.	What is the duration of the liability for Ice Cubes, Inc.?
e.	Suppose the two bonds shown below are the only bonds available to immunize the liability. What face amount of each bond will the company need to purchase to immunize the portfolio?
Bond A	Bond B
Settlement:	1/1/00	1/1/00
Maturity:	1/1/03	1/1/08
Coupon rate:	7.00%	8.00%
YTM:	7.50%	9.00%
Coupons per year:	2	2

Solution

Master It! Solution
a.	Value of liability today:
b, c.	Coupon payment:
Original YTM	YTM decrease	YTM increase
Reinvestment YTM:
Coupon rate:
Year	Six-month period	Coupon payment	Value of reinvested coupons at Year 5	Value of reinvested coupons at Year 5	Value of reinvested coupons at Year 5
1	1
2
2	3
4
3	5
6
4	7
8
5	9
10
Future value of coupons:
Par value received:
Total portfolio value:
d.	Since the liability is a lump sum in five years, the duration is equal to the maturity, or five years.
e.	Macaulay duration:
Bond A:
Bond B:
Bond weights:
Bond A:
Bond B:

Chapter 9

Ross, Westerfield, Jaffe, and Jordan's Spreadsheet Master

Corporate Finance, 11th edition

by Brad Jordan and Joe Smolira

Version 11.0

Chapter 9

In these spreadsheets, you will learn how to use the following Excel functions:

The following conventions are used in these spreadsheets:

1) Given data in blue

2) Calculations in red

NOTE: Some functions used in these spreadsheets may require that

the "Analysis ToolPak" or "Solver Add-In" be installed in Excel.

To install these, click on the File tab

then "Excel Options," "Add-Ins" and select

"Go." Check "Analysis ToolPak" and

"Solver Add-In," then click "OK."

ROUND

/xl/drawings/drawing2.xml#'Section%209.3'!A32

Concatenation

/xl/drawings/drawing2.xml#'Section%209.3'!A32

Web queries

/xl/drawings/drawing2.xml#'Section%209.5'!A27

Stock charts

/xl/drawings/drawing2.xml#'Section%209.5'!A92

Master It! (2)

Chapter 9 - Master It!
In practice, the use of the dividend discount model is refined from the method we presented in the textbook. Many analysts will estimate the dividend for the next 5 years and then estimate a perpetual growth rate at some point in the future, typically 10 years. Rather than have the dividend growth fall dramatically from the fast growth period to the perpetual growth period, linear interpolation is applied. That is, the dividend growth is projected to fall by an equal amount each year. For example, if the high growth period is 15 percent for the next 5 years and the dividends are expected to fall to a 5 percent perpetual growth rate 5 years later, the dividend growth rate would decline by 2 percent each year.
The Value Line Investment Survey provides information for investors. Below, you will find information for Boeing found in the 2012 edition of Value Line:
2011 dividend:	$ 2.90
5-year dividend growth rate:	9.5%
Although Value Line does not provide a perpetual growth rate or required return, we will assume they are:
Perpetual growth rate:	5.0%
Required return:	11.0%
a.	Assume that the perpetual growth rate begins 11 years from now and use linear interpolation between the high growth rate and perpetual growth rate. Construct a table that shows the dividend growth rate and dividend each year. What is the stock price at Year 10? What is the stock price today?
b.	How sensitive is the current stock price to changes in the perpetual growth rate? Graph the current stock price against the perpetual growth rate in 11 years to find out.
Instead of applying the constant dividend growth model to find the stock price in the future, analysts will often combine the dividend discount method with price ratio valuation, often with the PE ratio. Remember that the PE ratio is the price per share divided by the earnings per share. So, if we know what the PE ratio is, we can solve for the stock price. Suppose we also have the following information about Boeing:
Payout ratio:	30%
PE ratio at constant growth rate:	15
c.	Use the PE ratio to calculate the stock price when Boeing reaches a perpetual growth rate in dividends. Now find the value of the stock today finding the present value of the dividends during the supernormal growth rate and the price you calculated using the PE ratio.
d.	How sensitive is the current stock price to changes in PE ratio when the stock reaches the perpetual growth rate? Graph the current stock price against the PE ratio in 11 years to find out.

Solution (2)

Master It! Solution
a.	The dividend growth rates, dividends, and stock price are:
Year	1	2	3	4	5	6	7	8	9	10	11
Dividend growth:
Dividend:
Price at Year 11:
Price today:
b.	To graph the stock price for different growth rates, we need to calculate the price for various growth rates. Using a one-way data table, we get the following:
Growth rate	Stock price
0.0
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
c.	The earnings and price in year 11 will be:
Year 11 PE ratio:
Year 11 earnings:
Year 11 price:
So, the stock price today with this valuation method is:
Price today:
d.	Using a one-way data table, the stock price today at different PE ratios is:
PE ratio	Stock price
$ - 0
10.00
11.00
12.00
13.00
14.00
15.00
16.00
17.00
18.00
19.00
20.00