Formulas

Question 1

Current Yield (bond)

Answer 1

Current Yield = Annual interest ($)/ Bond’s market price

$1000 bond with 10% coupon selling for $900
Current yield= $100/$900= 11.11%

Question 2

Property’s intrinsic value

Answer 2

Property’s intrinsic value= net operating income (NOI)/ Cap rate

$40,800 NOI and cap rate 10%
$40,800/.10= $408,000

Question 3

Intrinsic value of CALL option

Answer 3

Intrinsic value of CALL= market price - exercise price

In the money: $60 MP, $50 EP
$60-$50=$10

Out of the money: $49 MP, $50 EP
$49-$50= ZERO

Question 4

Intrinsic value of PUT

Answer 4

Intrinsic value of PUT= exercise price - market price

In the money: $25 MP, $30 EP
$30-$25=$5

Out of the money: $35 MP, $30 EP
$30-$35= ZERO

Question 5

TEY (tax exempt yield)

Answer 5

TEY (tax exempt yield) = Taxable yield x (1- marginal tax rate)

15% marginal bracket, 7% coupon corporate bond or 5.5% muni bond?

TEY=7% x (1-0.15)= 5.95%

35% federal bracket, 7% state, 2% local. after-tax yield for T-bond with 6% coupon?

T-bonds are taxed only federally, so:
after-tax yield=6% x (1-0.35)

**muni bonds- no FED tax, but out-of-STATE taxed

Question 6

ROE (return on equity)

Answer 6

ROE (return on equity)= EPS/ Common equity
*common equity-> book value per share

EPS= earnings available for common

Book value $180,000
Shares outstanding 6,000,000
Dividends paid $1.5 per share
EPS $3.00
MP per share $50

ROE= $3.00/($180,000/6,000,000)= $30/share

Question 7

dividend payout ratio

Answer 7

dividend payout ratio= common dividends paid/ EPS
[earnings per share*]

Book value $180,000
Shares outstanding 6,000,000
Dividends paid $1.5 per share
EPS $3.00
MP per share $50

dividend payout ratio=1.50/3.00=50%

Question 8

margin call

Answer 8

margin call= [(1- initial margin %)/ (1-maintenance margin %)] x purchase price of stock

200 shares @ $150, minimum maintenance 25%, margin call?

margin call=(1-0.5)/(1-0.25) x 150= $100

Question 9

P/E ratio (price/earnings)

stock valuation when no dividend

Answer 9

P/E ratio= current market price/earnings

stock estimated earnings $3/share with P/E ratio of 15. valuation?

current market price= earnings x P/E ratio= $3 x 15= $45

Question 10

HPR (holding period return)

w/ and w/o margin, after-tax

Answer 10

HPR= total return/investment price

without margin:
MP(sale price) + (total) dividend - initial investment/ out of pocket

with margin:
sell price - (borrowed margin+ margin interest) - initial margin paid/ actual out of pocket

after-tax HPR:
(sale price+dividend-initial investment) x (1-LTCG brakcet (85% etc)) / out of pocket

Question 11

stock yield

Answer 11

stock yield = (dividend per share)/stock price per share

Book value $180,000
Shares outstanding 6,000,000
Dividends paid $1.5 per share
EPS $3.00
MP per share $50

stock yield=$1.50/$50= 3%

Question 12

maintenance call

Answer 12

100 @ $75 with 50% margin= $3750, maintenance 30%
stock drops to $40

maintenance call:
30% of CURRENT value ($40 x 100=$4000) required
=$1200
$4000-$3750=$250 (the equity you have left)

Maintenance call=$1200 - $250= $950

Question 13

YTC calculator

Answer 13

$1135 with 10% coupon maturing in 10 years but can be called in 5 years at $1100

same as YTM except use $1100 as FV and 5 years as N

Question 14

duration formula

Answer 14

percent price change in bond price (left side)

delta y is change in interest rate (don’t forget - sign if interest declined)

y is YTM

Question 15

conversion

Answer 15

convertible bond:
6% coupon, 8 yr maturity, convertible at $50/share, current common stock is $58, bond would sell for $1150, comparable debt 5.5%

Intrinsic value and conversion value?

Intrinsic (investment) value:
$1000 FV, $30 PMT, 8x2 N, 5.5/2 i, PV?($1032.01)

conversion:
CV=[par (not always $1000)/Conversion price] x MP of stock

($1000/ $50) x $58= $1160 (higher than what bond would sell for, so convert it!)

*the bond won’t sell for less than investment value or conversion value

Question 16

risk-adjusted return

Answer 16

divide realized return by beta

Question 17

dividend growth rate calc (DDM shortcut)

stock valuation when dividend paid

Answer 17

$2 dividend growing 6% for 3 years and then 8%, required rate of return is 10%

using the provided formula, use the SECOND number

• if first growth is LOWER, choose next LOWEST number
• if first is HIGHER, choose next HIGHER number

Question 18

Gross Profit Percentage (GPP) in installment sale

Answer 18

(gain from sale/sale price)=GPP

ex: basis $150,000, sold installment for $600,000, first payment $60,000

$450,000/$600,000= 75%
$60,000 x 75%=$45,000–> gain recognized first year

Question 19

intrinsic value of a bond

Answer 19

par $1000, matures in 12 years, 8% coupon ($80) semi-annually, comparable bonds yielding 10%. what’s the intrinsic value of this bond?

$1000 FV, 24 N, 40 PMT, 5 i, PV?(-$862.10)

Question 20

DDM (dividend discount model)

Answer 20

P= [D(1+g)]/(r-g)

can also be used when FCF (free cash flow) is available for dividends (replace dividend with fcf)

Question 21

EPS= ?

Answer 21

EPS= ROE (per share) x book value or net worth

Question 22

Expected return E(r)

Answer 22

E(r)=[D0(1+g)/sale price]+ g

Ex: $2.5 dividend
7% growth
Sell price $80

E(r)= [$2.50(1+.07)/$80] + .07= 10.34%