The Mathematics of Money

(Darren Dugan) #1

302


CHAPTER 6


SUMMARY


Topic Key Ideas, Formulas, and Techniques Examples


Calculating Dividends For
Each Shareholder, p. 252


  • The total dividend amount is divided by the
    number of shares to determine a dividend per
    share.

  • Multiply the shares owned by the dividend per
    share.


Jason and Dave’s dry
cleaning business is a
corporation with 100 shares.
Jason owns 51, Dave owns


  1. If the company declares a
    $35,000 dividend, how much
    will each receive? (Example
    6.1.2)


Calculating Dividend Yields,
p. 254


  • Determine the total dividends paid per share
    per year.

  • Divide this by the market value of each share.

  • If this is calculated by annualizing the current rate,
    it is the current yield; if the actual past 12 months’
    dividends are used it, is a trailing yield.


Zarofi re Systems pays a
quarterly dividend of $0.45
per share. The market price of
the stock is $49.75. Calculate
the current dividend yield.
(Example 6.1.4)

Calculating a Compound
Annual Growth Rate, p. 257


  • The CAGR formula:


i  (^)  FV___
PV
(^) 
1/n
 1
5 years ago I invested $8,400
in the stock of Sehr-Schlecht
Investment Corp. I sold the
stock today for $1,750. What
compound annual growth
rate does this represent?
(Example 6.1.8)
To tal Rate of Return, p. 257 • Return from an investment may include both
dividends and capital gains.



  • Total rate of return earned can be approximated
    by adding the CAGR from capital gains to an
    approximate average dividend yield.

  • If dividends are reinvested, this can be calculated
    by using the CAGR formula.


The dividend yield of Zarofi re
Systems has averaged 3^1 / 2 %
while you have owned it.
Capital gains from the stock
work out to a 21.90% CAGR.
What total rate of return have
you earned? (Example 6.1.9)
A $2,000 investment has
grown to $3,525.18 in
10 years with reinvested
dividends. Find the total rate
of return. (Example 6.1.10)

Volatility and Risk,
pp. 258–259


  • Investments in stocks carry risk of losing some
    or all of the amount invested.

  • Unlike compound interest, growth of stock
    investments does not occur at a steady pace.


See discussion at end of
Chapter 6.1.

Calculating Bond Coupons,
p. 264


  • The coupon rate is a percent of the par value.

  • Calculate the coupon amount using the simple
    interest formula.


A $1,000 par value bond has
an 8% coupon rate. Interest
is paid semiannually. What
payments will its owner
receive? (Example 6.2.1)

Current Yield of a Bond, p. 264 • Calculation of current yield is based on the
bond’s current market price.


  • Use the periodic coupon amount with the current
    market price in the simple interest formula.


A $1,000 par value bond with
an 8% coupon rate sells for
$1,094. Calculate the current
yield. (Example 6.2.3)

(Continued)
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