Slide #1: Lecture 15 – Rights Valuation
Welcome to Lecture 15: Rights Valuation.
A friendly preamble is appropriate here: It is assumed that you already know the
definitions of terms involved in this lecture, such as the meanings of rights, subscription
price, ex-rights, rights-on, net proceeds, and flotation cost. If you are unfamiliar with
these terms, or with the concept of a rights offering, please review the relevant areas in
your textbook.
Slide #2: Topics covered
So, the topics we will cover in this lecture are:
One, the definition of the variables involved in rights valuation.
Two, the formulas involved in rights valuation.
Three, we work through a numerical example.
And Four, as always, a practice question for you to work on after this lecture.
Slide #3: Definitions of Variables
The variables involved in valuing a right can be roughly divided into two groups: The
dollars-and- shares group, and the rights-valuation (or as I sometimes call it, ‘the
alphabet group’).
The dollars-and-shares group includes the dollar amount of funds raised from the rights
offer, the dollar or percentage flotation cost, the number of new shares generated from
the rights offer, and the number of old shares outstanding before the rights offer and on
the record date. Flotation cost is the fees that the company must pay to achieve the
rights offer, such as paying an investment dealer to take care of the issue.
The alphabet group consists of all the numbers that come with an alphabet
representation. These are
- Subscription price, as denoted by an S. Subscription price is the price that must
be paid by a shareholder for each new share from the rights offer.
- The number of rights needed to buy one new share, as denoted by an N.
- The theoretical value of one right, as represented by Ro.
- The rights-on share price, as represented by Mo. This is the share price before
the ex-rights date.
- The ex-rights share price, as represented by Me. This is the share price after the
ex-rights date.
- And last but not least, the ex-rights value of a right, as represented by Re. This
is the value of one right after the ex-rights date.
Slide #4: Relevant formulas
What are the formulas relevant for rights valuation? Conveniently enough, like the two
rough groups of variables, we can also divide the relevant formulas into two rough
groups: Those formulas related to the rights valuation and the alphabet variables, and
those formulas related to the calculation of flotation cost.
In the first group of formulas, we have the formula to calculate the subscription price,
which is equal to the dollar amount raised divided by the number of new shares issued
from the rights offer:
S = Funds raised / Number of new shares.
Notice that there are three variables in this formula: subscription price, funds raised, and
number of new shares. As long as we know the values for two of the variables, we can
find the value of the third. For example, if we know the values for subscription price and
the number of new shares, we can calculate the dollar amount raised in the rights
offering. This logic applies to all the formulas on this page here.
The second formula in this group is the one that helps us calculate N, the number of
rights needed to buy one new share. This is simply equal to the number of old shares
divided by the number of new shares:
N = #old shares / #new shares.
The third formula is to calculate the value of one right, Ro, which is equal to the rightson share price minus the subscription price (S), all divided by N plus one:
Ro = (Mo – S) / (N + 1).
The fourth formula is used to calculate the ex-rights share price, or Me, which is equal to
the rights-on share price (Ro) minus the value of a right (Ro):
Me = Mo – Ro.
The fifth formula in this group is the one for calculating the ex-rights value of a right, Re,
which is equal to the ex-rights share price (Me) minus the subscription price (S), all
divided by N:
Re = (Me – S) / N.
Those are the five formulas in group one.
In the second group of formulas, we have the dollar flotation cost, which is calculated as
the dollar amount of funds raised minus the net proceeds to the firm:
Dollar flotation cost = Funds raised – Net proceeds.
The second formula in this group calculates the percentage flotation cost, which is equal
to the dollar flotation cost divided by the dollar amount raised:
% flotation cost = Dollar flotation cost / Funds raised.
Slide #5: Numerical Example
And now, without further ado, let’s move on to our numerical example.
On November 1, 2011, XYZ Company announced a rights offering to sell 12 million
shares at a subscription price of $1.20 per share. The record date was November 10,
2011. The number of shares outstanding on the record date was 48 million. The shares
of the company were trading at a closing price of $3.00 per share on November 7, 2011,
three business days before the record date. The net proceeds to the company were
$13,392,000. Calculate the following:
a.
b.
c.
d.
e.
f.
g.
Number of rights needed to buy one new share, N
Value of a right, Ro
Ex-rights share price, Me
Ex-rights value of a right, Re
Amount of funds raised in the rights offer
Dollar flotation cost
Percentage flotation cost
Here, we have a company, XYZ, that has a rights offer to sell 12 million shares at a
subscription price of $1.20 per share. This gives us
# new shares = 12,000,000
S = $1.20
The next sentence gives us the record date and the ex-rights date. The number of
shares outstanding before the ex-rights date is 48 million, which gives us
# old shares = 48,000,000
The shares were trading at closing price of $3 per share three business days before the
record date, which gives us the rights-on share price,
Mo = 3
The net proceeds from the rights offer is $13,392,000. We are asked to find N, Ro, Me,
Re, and the dollar amount raised, dollar flotation cost, and percentage flotation cost.
Slide #6: Numerical example (cont.) - Calculations (a) and (b)
We first write down what we have:
Number of new shares = 12,000,000
Number of old shares = 48,000,000
Subscription price = S = $1.20
Rights-on share price = Mo = $3.00
Net proceeds = $13,392,000
For question (a), we are asked to calculate the number of rights needed to buy one new
share, which is denoted as N. Using the formula for N:
N = # old shares / # new shares = 48,000,000/12,000,000 = 4
For question (b), we are asked to find the value of one right, denoted as Ro. We use the
formula for Ro:
Ro = (Mo – S) / (N + 1) = (3 – 1.2) / (4 + 1) = $0.36
Slide #7: Numerical example (cont.) - Calculations (c) and (d)
For question (c), we are asked to calculate the ex-rights share price, which we can find
by using the formula:
Me = Mo – Ro = $3.00 - $0.36 = $2.64
For question (d), we calculate the ex-rights value of one right, using the formula:
Re = (Me – S) / N = (2.64 – 1.2) / 4 = $0.36
Slide #8: Numerical example (cont.) - Calculations (e), (f), and (g)
For question (e), we calculate the dollar amount raised in the rights offer, which can be
calculated as:
Funds raised = # new shares x S = 12,000,000 x $1.20 = $14,400,000
For question (f), we calculate the dollar flotation cost as:
Dollar Flotation cost = Funds raised – Net Proceeds = $14,400,000 - $13,392,000 =
$1,008,000
For question (g), we find the percentage flotation cost using the formula:
Percentage Flotation cost = Dollar flotation cost / Funds raised = 1,008,000 /
14,400,000 = 0.07 = 7%
That is, the fee that the company must pay to issue this rights-offer is 7%.
Slide #9: Practice question
Well, that was not too bad. So now, it’s your turn. Happiness is practicing!!! Try to see
if you can do the necessary calculations for rights valuation in this question.
A firm is looking to raise $10 million with a rights offering of 15 million new shares. The
firm hires an investment banker who will charge 5% on the gross proceeds of the rights
offer. Three days before the record date, the firm’s shares are priced at $2.50. The
number of shares outstanding on the record date is 50 million. Calculate the S, N, Ro,
Me, Re, and dollar amount of flotation cost.
Slide #10: Check answers
You are, as usual, provided with the check answers here.
Percentage flotation cost = Dollar flotation cost / Funds raised
=> Dollar flotation cost = Percentage flotation cost x Funds raised
=> Percentage flotation cost x Funds raised = Funds raised – Net proceeds
=> Net proceeds = Funds raised - (Percentage flotation cost x Funds raised)
=> Net proceeds = Funds raised x (1 – Percentage flotation cost)
=> Funds raised = Net proceeds / (1 – Percentage flotation cost)
Funds raised = $10,526,315.79
S = $0.70
N = 3.33333333
Ro = $0.41
Me = $2.09
Re = $0.42
Dollar flotation cost = 526,315.79
Slide #11: The end
And now, go forth and calculate. Here ends the lecture on rights valuation.