**You have learned about several different approaches for stock and company valuation including the Price-Earnings (or Price-EBITDA) Multiple Approach, which is a relative approach for stock valuation. After employing other approaches, you are now ready to apply the P-E multiple approach to valuing a publicly-held company in the EV sector with good growth potential that your company is considering to acquire. Your target company has been in business for several years since its IPO, but has not recorded a profit (or earnings) yet. As a newly-hired assistant to CFO, you are in charge of valuing your target company.**

**Discuss (a) what problems you might encounter in applying the P-E (or P-EBITDA) Multiple Approach to your target company; and (b) what alternative RELATIVE approach(es) you could use in place of the P-E (or P-EBITDA) Multiple Approach to value your target company. (Hints: Refer to my lecture video and class notes in Session II – Valuation of Stocks.)**

**Instructions:**

Please post your initial response by 23:59 EST Day 4 of the Week, and comments on the posts of at least four classmates by 23:59 EST Due Date.

Each Discussion Topic carries 10 points (6 points for own answers and 4 points for responses to classmates’ posts). **You must first post your own answers directly to the DT by Day 4 of the week before accessing other students’ answers. In addition, you****should post at least FOUR thoughtful and substantive responses to other classmates’ answers/comments by the due date in order to earn full 10 points for each DT.** A mere “Yes, I agree” or “No, I don’t agree” type of responses will not be given any credit.

Additional bonus credit may be given to at least TWO additional substantive responses to classmates’ posts at DIFFERENT DATES as they are valued and enrich our online learning.

Concluding comments on each Discussion Topic will be posted on the Discussion folder after due date.

Session II:

Valuation of Securities

1. Determination of Interest Rates

2. Valuation of Bonds

3. Valuation of Stocks

36

DETERMINATION OF INTEREST RATES

Learning Objectives:

Identify various factors that influence interest rates

Explain how norminal interest rates are determined

Explain and measure inflation premium, default risk premium, liquidity

premium, and maturity risk premium

Describe what the yield curve is and how its shape is determined

Explain the relationships between different yield curves and economic

conditions

——————————————————————————————————1.

Definition of Interest Rates

Cost of Money: Price paid to Borrowed Money

Reward for foregone current consumption

Determined by the supply of and the demand for investment capital.

2.

Factors That Influence Interest Rates

1)

Production opportunities: the rate of return producers expect to earn on

invested capital

2)

Time preference for consumption: consumers’/savers’ time preferences

for current vs. future consumption.

3)

Risk: the possibility that the borrower would be default.

4)

Expected inflation

5)

Federal Reserve policy

k

6)

Federal budget deficits

S

7)

Foreign trade balance

8)

Business activity

D

Components of Interest Rates

$

3.

k

k

where

=

=

k*

+

kRF

IP

+

+

DRP +

DRP +

k

k*

IP

kRF

DRP

LP

MRP

=

=

=

=

=

=

=

nominal interest rate on a given security

real risk-free interest rate

inflation premium

nominal risk-free interest rate

default risk premium

liquidity premium

maturity risk premium

37

LP

LP

+

+

MRP

MRP

4.

Term Structure of Interest Rates

1)

Definition: The relationship between yields and maturities of securities,

depicted by Yield Curve.

“normal” yield curve: upward-sloping

“inverted” yield curve: downward-sloping

2)

Term Structure Theory

Market segmentation theory

Liquidity preference theory

Expectations theory

Example) Determination of Interest Rates

Includes?

Type of

Security

Credit

Rating

Interest

Rate

IP DRP

LP MRP

Short-Term:

3-Month T-bill

“Risk-free”

7.44%

Yes

No

No

No

Long-Term:

30-year T-bond

“Risk-free”

8.86%

Yes

No

No

Yes

Corporate bond

AAA

9.41%

Yes

Corporate bond

AA

9.63%

Yes

Corporate bond

A

9.89%

Yes

Corporate bond

BBB

10.41%

Yes

Small

More

than AAA

More

than AA

More

than A

Depends

on

Yes

Corporation

Yes

Yes

Yes

Link for Treausry Yield Curve:

https://www.treasury.gov/resource-center/data-chart-center/interestrates/Pages/Historic-Yield-Data-Visualization.aspx

Reading – Grading Bonds on Inverted Curve (WSJ, 01/08/2007)

Reading – The Yield Curve Inverted (MarketWatch, 03/22/2019)

38

39

40

41

GENERAL VALUATION MODEL

General Valuation Model or Discounted Cash Flow (DCF) Model

𝑛

𝐶𝐹1

𝐶𝐹2

𝐶𝐹𝑛

𝐶𝐹𝑡

𝑉0 =

+

+

⋯

+

=

∑

(1 + 𝑘1 ) (1 + 𝑘2 )2

(1 + 𝑘𝑛 )𝑛

(1 + 𝑘𝑡 )𝑡

𝑡=1

The valuation of an asset requires:

(i)

An estimate of expected future cash flows: CFt

(ii) An estimate of discount rate (or required rate of return) for each CFt: kt

(iii) Each CF should be discounted and these PVs are then summed to find

the value of an asset.

Types of Cash Flows from Securities

a.

Bond

constant coupon interests:

Annuity

maturity value (= face value)

or selling price before maturity: Single sum

b.

Preferred Stock

constant preferred dividends:

Perpetuity

Common Stock

cash dividends:

selling price:

Perpetuity or Growing Perpetuity

Single sum

c.

42

VALUATION OF BONDS

Learning Objectives:

Explain basic terminologies and key features of bonds

Explain how bond prices are determined

Describe and calculate a bond’s yield to maturity (or total return), current yield,

and capital gains yield

Explain and measure interest rate risk for bonds with different maturities

——————————————————————————————————1.

Basic Terminology

Term

Notation

Unit

Note

Coupon interest rate

C

%

fixed

market interest rate

kd

%

varies

(= yield to maturity = cost of debt = return required by bondholders)

Coupon payment

I

$

C%*$1,000

Maturity

n

periods

Maturity, or par, value

M

$

$1,000

2.

Bond Valuation Model

Bond Value = PV of stream of interest payments + PV of maturity value

(PV of annuity)

(PV of a single sum)

𝑃0𝐵 =

𝐼

(1+𝑘𝑑 )

𝑃0𝐵 = ∑𝑛𝑡=1

+

𝐼

(1+𝑘𝑑 )

𝐼

(1+𝑘𝑑

)𝑡

2 + ⋯+

+

𝐼

𝑛 +

(1+𝑘𝑑 )

𝑀

(1+𝑘𝑑 )𝑛

𝑀

(1+𝑘𝑑 )𝑛

Annual coupon payment: P0 = I * PVIFAkd,n + M * PVIFkd,n

Semiannual coupon payment: P0 = I/2 * PVIFAkd/2,2n + M * PVIFkd/2,2n

For Financial Calculator:

INPUT

n or 2n

kd or kd/2

N

I/YR

PV

OUTPUT

?

43

I or I/2

1000

PMT

FV

3.

Bond Valuation Theorems

i)

Bond prices (P0) and market interest rates (kd) are inversely related.

ii)

premium

A bond will sell at

par

(6%)

when coupon rate (C)

discount

(4%)

>

= market rate (kd) (5%)

<
iii) Regardless of the type of a bond, the market value of a bond will approach
its par value as its maturity date approaches.
iv) The longer a bond's maturity, the larger the price change in response to a given
change in interest rates.
A longer-term bond has greater interest rate risk
than a shorter-term bond.
4.
Bond contract features which affect the cost of the bond
i)
Restrictive covenants in bond indentures
A provision that requires the issuer to meet certain stated conditions.
Makes the bond safer
offers a lower coupon.
ii)
Call provision
A provision that gives the issuer the right to call the bond for redemption
before maturity.
Firms will exercise this option when interest rates go down.
Issuer must pay call price plus call premium.
Makes the bond riskier
iii)
offers a higher coupon.
Sinking fund provision
A provision that requires the issuer to retire a portion of a bond issue each
year.
Failure to make a sinking fund payment constitutes technical default.
The firm may call a certain number of bonds for redemption OR it may
buy the required amount of bonds in the open market.
The firm will choose the less costly method.
Makes the bond safer
offers a lower coupon.
44
Example) Bond Valuation
On December 31, 2019, XYZ Company issued a 10-year bond with a 14
percent coupon, payable semiannually. The required rate of return, kd, on
this bond at that time of issue was 14 percent.
12/31/29
+$1,000.00 +$70.00
+$70.00
+$70.00
6/30/20
+$70.00
12/31/28
5
6/30/29
12/31/20
+$70.00
>

+$70.00

12/31/19

6

6/30/19

WSJ Quotation: XYZ 14s29

Value on 12/31/19

P0 = I/2(PVIFAkd/2, 2n) + M(PVIFkd/2, 2n )

= $70(PVIFA7%, 20) + $1,000(PVIF7%, 20)

= $70(10.5940) + $1,000(0.2584)

= $741.58 + $258.40 $1,000.00.

INPUT

20

7

N

I/YR

PV

OUTPUT

1000

45

70

1000

PMT

FV

Example) Bond Valuation: One Year Later

Now it’s 12/31/20 => Hence, XYZ bond is a 9-year bond:

If kd = 20%: P0 = $70(PVIFA10%,18) + $1,000(PVIF10%,18 )

= $70(8.2014) + $1,000(0.1799)

= $574.10 + $179.90 = $754.00.

Annual interest

Current yield =

$140

=

Price of bond

= 18.6%

$754

Total return = YTM = kd = 20% = Current yield + Capital gains yield

=> Capital gains yield = YTM – Current Yield = 20.0 % – 18.6%= 1.4%.

If kd = 14%: P0 = $70(PVIFA7%, 18) + $1,000(PVIF7%, 18)

= $70(10.0591) + $1,000(0.2959)

= $704.14 + $295.90 $1,000.00.

$140

Current yield =

= 14.0%

$1,000

If kd = 8%: P0 = $70(PVIFA4%,18) + $1,000(PVIF4%,18 )

= $70(12.6593) + $1,000(0.4936)

= $886.15 + $493.60 =$1,379.75

$140

Current yield =

= 10.1%

$1,379.75

=> Capital gains yield = 8% – 10.1% = -2.1% ? Capital loss?

Question: How can we check whether there is indeed a capital loss?

46

Example) Interest Rate Risk

Current Market

Current Market Value

Interest Rate (kd)

1-Year, 10% Bond

12-Year, 10% Bond

0%

$1,100.00

$2,200.00

5

1,047.62

1,443.16

10

1,000.00

1,000.00

15

956.52

728.97

20

916.67

556.08

Market Value of Bond, P0

($)

2,500

2,000

12-Year Bond

1,500

1,000

500

1-Year Bond

5

10

15

20

Market Interest Rate, kd(%)

47

VALUATION OF STOCK

Learning Objectives:

Describe how to value preferred stock and common stock

Explain the distinction between a stock’s market price and its intrinsic value

Apply the constant dividend growth model and the non-constant/supernormal

growth model to estimate stock prices

Apply the price-earnings multiple approach to estimate stock prices

——————————————————————————————————-

Preferred Stock Valuation

Application of PV of Perpetuities

𝑝𝑠

𝑃0 =

∞

∑

𝐷

𝐷

𝐷

=

===>

𝑘

=

𝑝𝑠

𝑝𝑠

𝑡

𝑘𝑝𝑠

𝑃0

𝑡=1 (1 + 𝑘𝑝𝑠 )

Example)

Ohio Edison preferred stock currently sells at $41.00 with an

annual dividend rate of 8.80% and a par value of $50. If you buy Ohio Edition

preferred stock today, what rate of return would you expect?

– Annual preferred stock dividends = 8.8% x $50 = $4.40

– P0 = $4.40/ kps = $41.00 => kps = $4.40/$41.00 = 10.7%

48

Common Stock Valuation

Intrinsic Value vs. Market Price of Common Stock

Outside investors, corporate insiders, and analysts use a variety of approaches to

estimate a stock’s intrinsic value (P0).

Stocks with a price below (above) its intrinsic value are undervalued (overvalued).

In equilibrium we assume that a stock’s price equals its intrinsic value.

Approaches for Estimating Intrinsic Value of Common Stock

Discounted dividend model

Price-Earnings (P/E) multiple approach

EVA approach

Corporate valuation model (Free cash flow model)

49

DISCOUNTED DIVIDEND MODEL

1.

Simple one-period and two-period stock valuation model

𝑃0𝑠 =

𝐷1 +𝑃1

(1+𝑘𝑠 )

where

; 𝑃0𝑠 =

𝐷1

(1+𝑘𝑠 )

+

𝐷2 +𝑃2

(1+𝑘𝑠 )2

Dt = cash dividend in time t;

Pt = stock price in time t

ks = return required by common stockholders

2. Extended multi-period stock valuation model

In a muti-period case:

𝑃0𝑠 =

𝐷1

(1+𝑘𝑠 )

+

𝐷2

(1+𝑘𝑠 )2

+ ⋯+

𝐷∞

(1+𝑘𝑠 )∞

= ∑∞

𝑡=1

𝐷𝑡

(1+𝑘𝑠 )𝑡

(Discounted Dividend Model)

i) Constant dividend (no growth in dividend)

Dt = Dt+1 = D for all t

𝑃0𝑠 = ∑∞

𝑡=1

𝐷𝑡

(1+𝑘𝑠 )𝑡

=

𝐷1

𝑘𝑠

Example) XYZ company has paid its annual dividend of $ 5.00 this year,

and expects to maintain the same dollar amount of dividends for the coming

years. If the stockholders require a 20% return, how much should the stock be

priced?

Then, P0 = $5/.20 = $25.00

ii) Constant dividend growth

Dt = D0(1+g)t and gt+1 = gt = g for all t

D1 = Do(1 + g)

D2 = D1(1 + g) = Do (1 + g)2

.

.

.

Dn = Dn-1(1 + g) = Do (1 + g)n

50

𝑃0𝑠 = ∑∞

𝑡=1

𝐷𝑡

(1+𝑘𝑠 )𝑡

=

𝐷1

𝑘𝑠 −𝑔

=

𝐷0 (1+𝑔)

𝑘𝑠 −𝑔

Constant Dividend Growth Model (CDGM) or Gordon’s Model

Notes:

i)

ii)

g = 0, g < 0
ks < g, ks = g, D0 = 0
=> YES, CDGM works.

=> NO, CDGM does not work.

Example) Owing to favorable market conditions, XYZ company now

expects to increase its earnings and thus dividends at the rate of 10% annual for

coming years. Assuming that other information stays the same (same

dividends this year and stockholders’ required return), how much should the

stock be priced?

𝑃0𝑠 =

𝐷1

𝑘𝑠 −𝑔

=

𝐷0 (1+𝑔)

=

𝑘𝑠 −𝑔

$5(1+.10)

(.20− .10)

= $55.00

iii) Non-constant (or Supernormal) dividend growth

0

1

2

–m

m+1

∞

|———|———|———————–|———-|———————>

non-constant

growth period

P0

constant (normal)

growth period

PV of dividends

during non-constant

growth period

=

𝑃0𝑠 = ∑𝑚

𝑡=1

𝑃0𝑠 = ∑𝑚

𝑡=1

𝑃0𝑠 = ∑𝑚

𝑡=1

𝑠

𝐷𝑡

𝑡 +

(1+𝑘𝑠 )

𝐷𝑡

(1+𝑘𝑠 )𝑡

𝐷𝑡

(1+𝑘𝑠 )

+

𝑡 +

𝐷

𝑘𝑠 −𝑔

1

(1+𝑘𝑠 )𝑚

1

+

𝑥 [𝑃𝑚𝑠 ]

𝐷

(1+𝑘𝑠 )𝑚

1

𝑥 [ 𝑚+1 + ⋯ +

(1+𝑘𝑠 )

𝐷

(1+𝑘𝑠 )

𝑚+1

]

𝑚𝑥 [

𝐷 (1+𝑔)

]

𝑘𝑠 −𝑔

𝑤ℎ𝑒𝑟𝑒 𝑃𝑚 = [ 𝑚+1 ] = [ 𝑚

51

PV of dividends

during constant

growth period

𝑘𝑠 −𝑔

𝐷∞

(1+𝑘𝑠 )∞

]

Example) Valuation of Stock with Nonconstant Divident Growth

(Information in blue is given for the problem.)

0

1

2

3

4———–> ∞

|—————|—————|————–m——— —-|————->

non-constant

growth period

constant (normal)

growth period

D0 =$2.00

gt ==>

g1=-10%

g2=+28%

g3=+13%

g4 = gn = +5%——>

Stockholders’ required rate of return, ks = 15%

—————————————————————————————————PV of dividends

during nonconstant

growth period

P0 =

𝑠

𝐷𝑡

𝑃𝑚

𝑠

𝑚

𝑃0 = ∑𝑡=1

+

(1+𝑘 )𝑡

(1+𝑘 )𝑚

𝑠

𝑠

+

PV of dividends

during constant

growth period

𝑤ℎ𝑒𝑟𝑒 𝑃𝑚𝑠 = [

𝐷𝑚+1

𝑘𝑠 −𝑔

𝐷 (1+𝑔)

]=[ 𝑚

𝑘𝑠 −𝑔

]

Step 1: Computing D1 through D3 during the nonconstant growth period

D1 = D0 (1+g1) = $2.00 x (1 – .1) = $1.80

D2 = D1 (1+g2) = $1.80 x (1 + .28) = $2.30

D3 = D2 (1+g3) = $2.30 x (1 + .13) = $2.60

Step 2: Computing D4 to find out P3 (that represents PV of dividends during the

constant growth period starting year 4)

D4 = D3 (1+g4) = $2.60 x (1 + .05) = $2.73

Then, P3 = D4/(ks – gn) = $2.73/(.15 – .05) = $27.30

Step 3: Combining all together,

𝑃0𝑠 =

$1.80

(1.15)

+

$2.30

(1.15)2

+

$2.60

(1.15)3

52

+(

1

$2.73

)3 [(.15−

1.15

.05)

] = $22.97

Question 1: Can the non-constant or super-normal dividend growth model be

applied to valuing stocks that currently pay no dividends?

Conceptually, there are at least two possible ways to apply the model to valuing

non-dividend paying stocks:

If one can estimate when and how much the firm will start paying dividends, as

well as their growth rate, etc. Then, one can proceed as in non-constant dividend

growth model.

If one can estimate some future market price of the firm’s stock and discount it

back to the present.

However, these ways are practically impossible to implement due to wide variations

of analysts forecasts on the estimates.

53

PRICE-EARNINGS (P/E) MULTIPLE APPROACH

1.

Factors that lead to a higher or lower P/E ratio or P-E multiple

– P/E multiple represents the price investors are willing to pay to get a dollar

of a firm’s earnings.

(Question: Why do some stocks sell at high P/E while others sell at low P/E?)

𝐷1

⁄𝐸

𝐷1

𝑠

1

𝑃

𝑃0 =

==> ⁄𝐸 =

𝑘 −𝑔

𝑘 −𝐵 𝑥 𝑅𝑂𝐸

𝑠

where

𝑠

E1 = earnings per share

B = retention (or plowback) ratio (= 1 – dividend payout ratio)

= 1- (D1/E1)

ROE = return on equity (return on investment)

=> g = growth rate of earnings and dividends = B x ROE

(e.g., B = 0.4; ROE = 15%; then earnings grow at the rate of 6%)

The model implies that:

P/E will go up if

E1 declines (temporary decline in earnings)

ks declines (lower risk, thus lower required return)

ROE increases (more valuable growth opportunities)

Question: Is a high P/E stock overpriced or a low P/E stock underpriced?

Question: How can we find a bargain stock using stock’s P/E multiple?

Reading – Bargain Growth Stocks (WSJ, 10/19/2006)

54

2.

Underlying rationale of P/E multiple approach

– P/E multiple represents the price investors are willing to pay to get a dollar

of a firm’s earnings.

– Hence, investors are willing to pay the same P/E multiple for companies

that are in a similar size and doing a similar business in the same industry.

– P/E multiple approach is one of a few relative approaches used by security

analysts as it uses proxy companies as benchmarking.

3.

Steps for P/E multiple approach

Step 1: Select proxy firms (at least two) and collect their data.

Note: Proxy firms are firms:

a)

doing a similar business in the same industry and

b)

with a similar size in terms of sales and/or total assets.

Step 2: Estimate proxy firms’ P/E multiples and measure their average.

Step 3: Multiply the average by expected (or this year’s) earnings to back out

an estimate of the firm’s stock price.

PriceY = EPSY x (Price/EPS)Proxy firms

where Y = your company;

EPS = earnings per share;

(Price/EPS) = average P/E multiple of proxy firms

Similar analysis can be applied to:

– Price to Sales (Revenue) multiple

– Price to Cash Flow multiple

– Market to book value multiple

55

Example) Stock Valuation Using P/E Multiple Approach

Information: (December 31, 20xx)

Y (My Company)

Jacobs Engr

Group

Stock symbol

JEC (NYSE)

Sales ($mil)

1,780.6

Price ($) = MVEPS

?

EPS ($)

1.80

P/E ratio

?

Dividend yield

0%

% Earned on total capital

12.5%

% Earned net worth

12.4%

Proxy Companies

Armstrong

Johns Manville

World

Corp.

ACK (NYSE)

JM (NYSE)

2,210

1,650

74

10

5.30

0.80

14.0

12.5

2.5%

1.6%

18.5%

13.0%

27.0%

18.5%

Source: Value Line Investment Survey, January 16, 20xx

Estimation:

P/E multiple approach using the average:P/E multiple of proxy companies:

PriceY = 1.80Y x (14.0 + 12.5)/2 = $23.85: Estimated stock price

P/E multiple approach using high and low P/E multiples of proxy companies:

PriceY = 1.80Y x 12.5 = $22.50: Estimated low-end stock price

PriceY = 1.80Y x 14.0 = $25.20: Estimated high-end stock price

===========================================================

Actual Stock Price of JEC on 12/31/20xx = $26 (High $32.6; Low $23.3)

===========================================================

Question 1: During late 1990s, security analysts encountered a difficulty in applying

the P/E multiple approach to many dot.com companies? What was the major issue?

Question 2: How was the application problem overcome?

56

The yield curve inverted — here are 5

things investors need to know

By William Watts

Published: Mar 25, 2019 1:55 p.m. ET

This article was originally published on March 22.

A closely watched measure of the yield curve briefly inverted Friday — with the yield on the 10-year

Treasury note falling below the yield on the 3-month T-bill — and rattled the stock market by underlining

investor worries over a potential recession.

Read: 5 key ways Wall Street and economists think about the yield curve

But while that particular measure is indeed a reliable recession indicator, investors may be pushing the

panic button prematurely. Here’s a look at what happened and what it might mean for financial markets.

See: Treasury yield curve inverts for first time since 2007, underlining recession worries

What’s the yield curve?

The yield curve is a line plotting out yields across maturities. Typically, it slopes upward, with investors

demanding more compensation to hold a note or bond for a longer period given the risk of inflation and

other uncertainties. An inverted curve can be a source of concern for a variety of reasons: short-term rates

could be running high because overly tight monetary policy is slowing the economy, or it could be that

investor worries about future economic growth are stoking demand for safe, long-term Treasurys, pushing

down long-term rates, note economists at the San Francisco Fed, who have led research into the

relationship between the curve and the economy.

They noted in an August research paper that, historically, the causation “may have well gone both ways”

and that “great caution is therefore warranted in interpreting the predictive evidence.”

What just happened?

The yield curve has been flattening for some time. On Friday, a global bond rally in the wake of weak

eurozone economic data pulled down yields. The 10-year Treasury note yield TMUBMUSD10Y, 1.85% fell as low as 2.42%, falling below the three-month T-bill yield at 2.455%. On Monday, the 10year yield stood at 2.395%, down more than 5 basis points, while the 3-month yield was down 0.8 basis

point at 2.447%.

Why does it matter?

The 3-month/10-year version that is the most reliable signal of future recession, according to researchers

at the San Francisco Fed. Inversions of that spread have preceded each of the past seven recessions,

including the 2007-2009 contraction, according to the Cleveland Fed. They say it’s offered only two false

positives — an inversion in late 1966 and a “very flat” curve in late 1998.

Is recession imminent?

A recession isn’t a certainty. Some economists have argued that the aftermath of quantitative easing

measures that saw global central banks snap up government bonds may have robbed inversions of their

reliability as a predictor. Since so many Treasurys are held by central banks, the yield can no longer be

seen as market-driven, economist Ryan Sweet of Moody’s Analytics, recently told MarketWatch’s Rex

Nutting.

Meanwhile, recessions in the past have typically came around a year after an inversion occurred. Data

from Bianco Research shows that the 3-month/10-year curve has inverted for 10 straight days six or more

times in the last 50 years, with a recession following, on average, 311 days later.

The price is based on these factors:

Academic level

Number of pages

Urgency

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more