FINANCE OOF

If a stock has a 50% probability of having an expected return of 10% and a 50% probability of having an expected return of 20%, what is the overall expected return for this stock?

15%

E(R) formula

Variqance and standard deviation measure what?

The volatility of returns

A stock is expected to return 13 percent in an economic boom, 10 percent in a normal economy, and 3 percent in a recessionary economy. Which one of the following will lower the overall expected rate of return on this stock?

A decrease in the probability of an economic boom

Systemic risk (market risk)

Factors that affect a large number of assets
Think: changes in GDP, inflation

Unsystemic risk (asset-specific risk)

Factors, unique to a specific company, or a very limited number of assets
Think: labor strile, risk of hurricane

Minimum level of risk that cannot be diversified away?

Systematic portion

Systemic rule principle:

There is a reward for bearing risk

There is NO reward for bearing risk unnecessarily

The expected return (market required return) on an asset depends

ONLY on that asset’s systematic risk

Portfolio diversification eliminates:

Unsystemic risk

Mary owns a risky stock and anticipates earning 16.5 percent on her investment in that stock. Which one of the following best describes the 16.5 percent rate?

Expected return

Stock A comprises 28 percent of Susan's portfolio. Which one of the following terms applies to the 28 percent?

Portfolio weight

About how many stocks do you need in a portfolio for it to be considered well-diversified?

20 - 30

What do we want to understand about each stock in a portfolio?

How much each individual stock contributes to the portfolio’s overall riskiness — meaning the level of systematic (market) risk each stock carries.

What do you think is the beta of a U.S. Treasury bill?

0
Treasury bills are riak free

Beta < 1.0

Stock is less risky than average

Beta > 1.0

Stock is MORE risky than average

Standard deviation measures ___ risk, while beta measures ___ risk. 

Total

Systemati

Higher beta =

Higher expected return

What is a risk premium?

The excess return required from investing in a risky asset over the return required from a risk-free investment

What does CAPM let you determine if you know an asset’s beta?

If the systematic risk (beta) of an asset is known, CAPM can be used to determine its expected return

Risk free rate of return

Measures pure time value of money

Risk premium

Reward for bearing an average amount of systemic risk

Amount of systemic risk

Asset beta

Debbt does not have ownership interest

Equity has ownership interest

Debt has no voting rights

Equity has voting rights

Debt interest is tax deductible

Dividends for equity is not tax deductible

Debt: creditors have legal recourse if interest or principal payments are missed

Equity: Dividends are not a liability untill declared

Bank loans

1. More suitable for short-term needs

2. May be only option for smaller sized companies

3. Repayment includes interest and a portion of the principal amount

4. Not a tradable security

Corporate bonds

1. Relationship is with a group of investors

2. More suitable for longer-term investments

3. Requires a company to have been established with record of profits

4. Repayment is interest only until the maturity date

5. Interest rates tend to be lower than bank loans

Municipal securities

TAX EXEMPT

Debt of state and local governments

Treasury securities

Debt of the US federal government

What is par value (face value) of a bond?

The principal amount of a bond that is repaid at maturity.
(Assume $1,000 for corporate bonds.)

What is a coupon payment?

The stated interest payment made on a bond.

What is the coupon rate?

The annual coupon payment divided by the face value of the bond.

What is yield-to-maturity (YTM)?

The interest rate required in the market on a bond (also called the yield)

How is YTM quoted, and what is true at initial bond issuance?

YTM is quoted as an APR, and when a bond is first issued, the YTM usually equals the coupon rate.

A taxable bond has a yield of 8% and a municipal bond

has a yield of 6%. If you are in a 40% tax bracket,

which bond do you prefer?

B. Municipal bond

Aftertax return for taxable bond:

8%(1-.4) = 4.8%

What is a pure discount bond (zero or zero-coupon bond)?

A bond that makes no periodic interest payments (no coupons).

What is the coupon rate on a zero-coupon bond?

0% — because pure discount bonds pay no coupons.

Where does all the yield-to-maturity come from on a zero-coupon bond?

From the difference between the purchase price and the par value.

Can a zero-coupon bond sell for more than par value?

No — zeroes cannot sell above par.

What are examples of zero-coupon bonds?

Treasury Bills and U.S. Savings Bonds.

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 10 years to maturity, and a coupon rate of 8.7 percent paid annually. If the YTM is 10.7 percent, what is the current bond price in euros?

880.72

This is NOT asking for semiannual!
So use the TVM values as normal

Redan Corporation has bonds on the market with 13 years to maturity, a YTM of 9.9 percent, a par value of $1,000, and a current price of $950. The bonds make semiannual payments. What must the coupon rate be on the bonds?

9.20 %

CPT → PMT
Divide PMT / 1,000
× 2

Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 3.5 percent. What was your real return?

11.11%
r = (1 + R / 1 + h) - 1

You find a zero coupon bond with a par value of $10,000 and 23 years to maturity. The yield to maturity on this bond is 4.5 percent. Assume semiannual compounding periods. What is the price of the bond?

3,593.25

Elkus Company issued 17-year bonds one year ago at a coupon rate of 6.8 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 5.4 percent, what is the current price of the bond in dollars?

1,148.73

The rate of return an investor earns on a bond prior to adjusting for inflation is called the:

nominal rate

• Coupon rate = 5.6% annually → 2.8% each semiannual period

• Par value = $1,000

• Price = 97% of par = $970

• Payments = semiannual

• Original maturity = 25 years, but 2 years have passed, so 23 years remain

• Remaining periods = 23 × 2 = 46
  FIND YTM

CPT → I/Y
Multiply this answer by 2!

If Treasury bills are currently paying 6.5 percent and the inflation rate is 1.3 percent, what is the approximate and the exact real rate of interest?

Approx: 5.20%

Real: 5.13%

Gordon Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and selling for $961. At this price, the bonds yield 8.6 percent. What must the coupon rate be on the bonds?

8.15%

When a bond's yield to maturity is less than the bond's coupon rate, the bond:

is selling at a premium.

If interest rates RISE, then present values and bond prices

DECREASE

If interest rates DECREASE, then present values and bond prices

RISE

The current yield on a bond is equal to the annual interest divided by the:

current market price.

The Treasury yield curve plots the yields on Treasury notes and bonds relative to the __________blank of those securities.

Maturity

Which one of the following premiums is paid on a corporate bond due to its tax status?

Taxability premium

An upward-sloping term structure of interest rates indicates:

the nominal rate is increasing even though the real rate is constant as the time to maturity increases.

What condition must exist if a bond’s coupon rate is to equal both the bond’s current yield and its yield to maturity? Assume the market rate of interest for this bond is positive

The bond must be priced at par.

Which one of the following will increase the present value of a lump sum future amount to be received in 15 years?

A decrease in the interest rate.

The 5.3 percent bond of Dominic Cycle Parts has a face value of $1,000, a maturity of 12 years, semiannual interest payments, and a yield to maturity of 6.12 percent. What is the current market price of the bond?

93.01

One year ago, you purchased a $1,000 face value bond for a clean price of $980. The bond currently has seven years remaining until maturity, pays a coupon payment of $45 every six months, and has a yield to maturity of 6.87 percent. What is the percentage change in the bond price over the past year?

13.96%

A corporate bond pays 6.25 percent interest. How much would a municipal bond have to pay to be equivalent to this on an aftertax basis if you are in the 28 marginal percent tax bracket?

4.50%

Variance Logistics wants to issue 20-year, zero coupon bonds that yield 6.2 percent. What price should it charge for these bonds if the face value is $1,000? Assume semiannual compounding.

$249.89

A bond yielded a real rate of return of 3.87 percent for a time period when the inflation rate was 2.75 percent. What was the actual nominal rate of return?

6.73%

The capital gains yield equals which one of the following?

Dividend growth rate

Premium bond

YTM < Coupon Rate

Selling price > Face Value (par)

Ex: $1,015

Discount Bond

YTM > Coupon Rate

Selling Price < Face Value (par)

Ex: $935

Stocks have unlimited cash flows, unobservable required returns, and a potentially infinite term. So why invest?

▪ The proceeds when you sell the stock → the future sales price

▪ The future sales price → depends on earnings and the dividends received after that point

▪ Thus, the current stock price → ultimately the present value of all future dividends

Dividend: $2, Stock sale (future price): $14, Total cash flow in one year: $16

What are the expected cash flows for owning this stock for one year?

$13.33 or -13.33

N = 1

I/Y = 20

FV = 16

CPT → PV

If dividends are expected to be paid at the same

amount at regular intervals, this is a _____.

perpetuity.

Therefore:
Price of stock = D / R

ZERO GROWTH
Suppose a share of stock is expected to

pay a $0.50 dividend every quarter and the

required return is 10% with quarterly

compounding. What is the price?

$20

Constant dividend growth example:

D1 = D0 * (1 + g) ^1
D2 = D0 * (1 + g) ² 

D3 = D0 * (1 + g) ³

D0 = $2.00 and constant g = 6%
Whhat’s D3?

$2.3820

What’s the dividend growth model? Aka Gordon Growth

P0 = D0 (1 + g) / R - g

OR
P0 = D1 / R - g

Suppose Big D, Inc. just paid a dividend of $.50. It is

expected to increase its dividend by 2% per year. If the

market requires a return of 15% on assets of this risk,

how much should the stock be selling for?

$3.92

DIVIDEND GROWTH MODEL
Suppose Moore, Inc. is expected to pay a $2 dividend in

one year. If the dividend is expected to grow at 5% per year

and the required return is 20%, what is the price?

$13.33

Stock price sensitivity to dividend growth rate:

• As g increases, the denominator (R – g) becomes smaller

• When the denominator gets small → price explodes upward

Stock price sensitivity to required return:

• As R increases, the denominator (R – g) gets bigger

• Bigger denominator → stock price collapses

Cash dividend = 1
Dividend growth rate in year 1 = 20%
Dividend growth rate in year 2 = 15%
Constant dividend growth thereafter: 5%
R = 20%

What’s the price of the stock?

$8.67

The required return is made up of 

The dividend yield and the capital gains yield

Acme, Inc. stock is selling for $10.50. They just paid a

$1 dividend which is expected to grow at 5% per year.

What is the required return?

15%

What dividend rights do common shareholders have?

They share proportionally in any dividends declared by the company.

What liquidation rights do common shareholders have?

They share proportionally in any remaining assets during liquidation.

What is the preemptive right?

The right for existing shareholders to buy additional shares when new shares are issued, allowing them to maintain their proportional ownership.

When do dividends become a liability of the firm?

Dividends are not a liability until they are formally declared by the Board of Directors.

Can a firm go bankrupt for not declaring dividends?

No — a firm cannot go bankrupt for not declaring dividends.

Are dividends tax-deductible for the firm?

No — dividends are not tax-deductible for the firm.

How are dividends taxed for individuals?

Dividends are taxed as ordinary income for individuals.

Preferred stock:

Dividend priority over common stock
No voting right

The price of a stock at Year 4 (P4) can be expressed as:

P4 = D5 / (R-g)

Twitter Me, Inc. is a new company and currently has negative earnings. Its sales

are $1.35 million and there are 130,000 shares outstanding. If the benchmark

price-sales ratio is 4.8, what is you estimate of the appropriate stock price?

P = Benchmark PS ratio x Sales per share

Benchmark PS ratio = 4.8

Sales per share = $10.38 ($1.35M / 130,000)

P = 4.8 * $10.38

Ushuaia, Inc. currently has an EPS of $4.13, and the benchmark PE ratio

for the company is 15. Earnings are expected to grow at 5% per year.

What is your target price in year 1?

EPS 1 = EPS 0 x ( 1 + g )
$4.13 x ( 1.05)

= $4.34

P1 = PE Ratio * EPS115 × 4.34

=

$65.05

Pasha Entertainment, Inc. is expected to pay the following dividends over

the next four years: $6, $12, $17, and $3.25. Afterward, the company

pledges to maintain constant 5% growth rate in dividends, forever. If the

required return on the stock is 11%, what is the current share price?

$67.18

The X3 Company just paid a dividend of $2.80 per share on its stock. The dividends are expected to grow at a constant rate of 6.75 percent per year, indefinitely. Assume investors require a return of 12 percent on this stock.

What’s the price of the stock today? in 16 years?

Today = $56.93

16 years = $161.88

P16 = D0 ( 1 + g)^17 DIVIDED BY R - g

Sweet Treats pays a constant annual dividend of $2.54 a share and currently sells for $52.60 a share. What is the rate of return?

4.83

McCabe Corporation is expected to pay the following dividends over the next four years: $5.90, $16.90, $21.90, and $3.70. Afterward, the company pledges to maintain a constant 6 percent growth rate in dividends forever. If the required return on the stock is 10 percent, what is the current share price?

105.28

The next dividend payment by Guppy, Incorporated, will be $2.85 per share. The dividends are anticipated to maintain a growth rate of 5.00 percent forever. If the stock currently sells for $49.30 per share, what is the required return?

10.78

Sugar Cookies will pay an annual dividend of $1.23 a share next year. The firm expects to increase this dividend by 8 percent per year the following four years and then decrease the dividend growth to 2 percent annually thereafter. Which one of the following is the correct computation of the dividend for Year 7?

$1.23×1.08^4 × 1.02²

Rahm Corporation is growing quickly. Dividends are expected to grow at a rate of 30 percent for the next three years, with the growth rate falling off to a constant 7.5 percent, thereafter. If the required return is 13 percent and the company just paid a dividend of $2.55, what is the current share price?

$86.08