Question: MSc Banking & International Finance MSc International Accounting & Finance - EXAM

09 Jan 2023,3:55 AM

SECTION A: Multiple Choice Questions

(25 marks – answer Questions 1 to 10)

Instructions:

- Please answer all 10 Multiple Choice Questions by selecting one answer from

the 5 options A., B., C., D., and E. given in each question. Answer E. means

that none of the choices, statement combinations, or solutions given in A., B.,

C., or D. are correct. It does not mean that none of the three or four statements

given are correct.

- Please write clearly your letter answer for the MCQs in one column, one

question each line in the following format.

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

- You do not have to show any intermediate work or explanation since no partial

credits are given for this section.

- You will score 2.5 marks for each correct answer, 0 for no answer or incorrect

answer.

Question 1

Which of the following statements is correct regarding valuation methods?

I. Multiple valuation is based on how the market currently values similar or

comparable firms (the “market approach”).

II. Multiple values for different firms should be the same if these firms have

the same value drivers and accounting policies.

III. Two firms that have the same EBITDA should have the same EBITDA

multiple.

IV. One assumption in using multiples of comparable firms is that the firms

in the peer group are of equivalent risks.

A. I and II only B. II and IV only C. I, II and IV only D. I, III and IV only

E. None of the choice combinations given in A., B., C., and D. are correct.

Question 2

Which of the following statements is correct regarding payout policy?

I. Modigliani and Miller states that in a world with perfect capital markets

the payout policy is irrelevant.

II. The payout practice in which firm offers to buy a specified number of

shares at a (specified) fixed price during a (specified) period of time is

called fixed price tender offer.

III. The signaling effect of dividends suggests that companies should start

paying dividends at any time.

IV. Stock price generally increases on the dividend payout date.

A. I and II only B. I and III only C. II and IV only

D. I, II, and IV only

E. None of the choice combinations given in A., B., C., and D. are correct.

Question 3

Which of the following statements is correct regarding capital budgeting practice?

I. Project A and project B are mutually exclusive. Project A’s IRR is 10%

while project B’s IRR is 8%. You should accept project A.

II. The cash flows that should be included in a capital budgeting analysis

are those that will only occur if the project is accepted.

III. The cannibalization cash flows as a result of taking a particular project

should be included in that project’s analysis.

IV. The payback rule ignores time value of money.

A. I and II only B. II and III only C. III and IV only

D. II, III, and IV only

E. None of the choice combinations given in A., B., C., and D. are correct.

Question 4

Which of the following statements is correct regarding corporate governance?

I. The market for used cars is an example of moral hazard.

II. A consequence of moral hazard is that the agent may take actions that

are harmful for the principal.

III. A board that consists of a majority of independent directors is an

example of good corporate governance practice.

A. I only B. II only C. III only

D. II and III only

E. None of the choice combinations given in A., B., C., and D. are correct.

Question 5

Which of the following statements must be correct regarding portfolio risk, return, and

beta?

I. There is a minimum level of risk that cannot be diversified away, and that

is the unsystematic (undiversifiable) portion.

II. The stock’s standard deviation of returns is a measure of systematic risk.

III. The optimal risk-return combination would be the point on the efficient

frontier that would be tangent to the lowest possible risk-return

indifference curve.

IV. The slope of the Capital Market Line is the market’s Sharpe ratio.

A. I only

B. I and II only C. I and III only D. II and IV only

E. None of the answers in A., B., C., and D. are correct.

Question 6

Which of the following statements must be correct regarding Capital Asset Pricing

Model (CAPM) and Factor Model?

I. The CAPM is used to determine a theoretically appropriate required rate

of return of an asset, if that asset is to be added to an already well-

diversified portfolio, given that asset's non-diversifiable risk.

II. The CAPM parameters can be estimated with highest confidence using

sophisticated statistical tools and the estimation power is high.

III. The factor models are derived from portfolio theory with the principle that

diversification can reduce risk.

A. I and II only B. I and III only C. II and III only D. I, II and III

E. None of the answers in A., B., C., and D. are correct.

Question 7

Which of the following statements is correct about mergers and acquisitions?

I. In most developed markets, stock prices of the target and the acquirer

always increase at the deal announcement.

II. The method of payment in acquisitions is a major signaling effect from

management. It is a sign of strength when an acquisition is paid for with

cash while stock payment reflects uncertainty regarding potential

synergies.

III. Synergy is achieved when the value of the combination of the two firms

is greater than the sum of the two stand-alone values.

A. I and II only B. I and III only C. II and III only D. I, II and III

E. None of the choice combinations given in A., B., C., and D. are correct.

Question 8

Which of the following statements is correct about raising capital?

I. A benefit of going public is having better access to capital: Public

companies typically have access to much larger amounts of capital

through the public markets.

II. Road show is a process used by underwriters for coming up with an offer

price based on customers’ expressions of interest.

III. Most IPOs experience a large initial first day return but poor long-run

performance.

IV. Seasoned equity offerings (SEO) are generally viewed as a good signal

that the firm has excess cash flow generated from its operations.

A. I and II only B. I and III only

C. I, II, and IV only D. I, III, and IV only

E. None of the choice combinations given in A., B., C., and D. are correct.

Question 9

Which of the following statements must be correct regarding case study “Victoria

Chemicals plc: the Merseyside project”?

I. Greystock is correct when including the changes in net working capital

as a result of the Merseyside project in his capital budgeting forecast.

II. It is reasonable for Greystock to include the preliminary engineering cost

in the capital budgeting for Merseyside because it was spent over the

past nine months on efficiency and design studies of the renovation of

Merseyside.

III. The proposal to include the EPC project in Merseyside is an issue with

project independence and agency problem.

A. I only B. II only

C. I and III only D. I, II, and III

E. None of the answers in A., B., C., and D. are correct.

Question 10

Which of the following statements is correct regarding case study “GE’s proposed

acquisition of Honeywell”?

I. Holding the long and short positions helps Gallinelli hedge against the

changing market conditions that may affect the acquirer’s stock price.

II. Gallinelli faces the risk of the proposed acquisition being rejected by the

European Commission.

III. Gallinelli’s key decision when the European Commission announces that

it would initiate an antitrust investigation on the proposed deal is to

determine if she should liquidate her positions on this deal.

A. I and II only B. I and III only C. II and III only D. I, II, and III

E. None of the choice combinations given in A., B., C., and D. are correct.

SECTION B: Problem Solving Questions

(50 marks – answer both Questions 11 and 12)

Instructions: You must show all your work including all intermediate steps, formulas

and calculations. Use four decimals in all calculations. If you believe there is

information necessary to solve a problem but not given in the question, you can make

what you believe to be the most reasonable assumption within the context of the

question, state clearly why you make that assumption, and then continue to answer

the question based on the assumption. However, do not make such assumptions

unless you have very carefully read through the question and assessed the

implications of the information provided.

Question 11

On January 5, 2014, Cressent Vetition Corp (ACQ) made an acquisition bid of $128

per share for all of Transamerica Exchange Inc (TAR) equity. Analysts forecast TAR’s

income statement and balance sheet information to be as follows. “Year” denotes the

fiscal year ending 31^stDecember.

(in million $) Actual Projected . Steady

Year 2013 2014 2015 2016

Sales 2500 3000 3700 4300

Costs 2000 2400 2800 3200

Depreciation 80 100 140 210

EBIT 420 500 760 890

Interests and taxes 60 70 80 90

Net income 360 430 680 800

Current assets 600 660 680 720

Net fixed assets 1400 1500 1700 1900

Total assets 2000 2160 2380 2620

Current liabilities 500 520 540 560

Long term debt 600 660 670 680

Shareholders equity 900 980 1170 1380

Total liabilities and equity 2000 2160 2380 2620

Other information for TAR as of December 5, 2013

Market Value of Debt $600 million

Current Debt Rating A^–

Common Stock Price $100 per share

Common Shares Outstanding 40 million shares

Marginal Tax Rate 40%

Analysts forecast that starting from 2016, TAR’s free cash flow will settle to a growth

rate of 3% per year indefinitely. They believe that TAR aims to keep the current debt

ratio constant in the future. The Weighted Average Cost of Capital (WACC) is the

appropriate discount rate for TAR. Analysts also believe that a beta based on analyses

of recent past returns is appropriate to access TAR’s risk level in the future. They found

from recent stock return analyses that: the variance of TAR’s returns is 0.16, the

variance of the market returns is 0.04, and the correlation coefficient between TAR’s

returns and the market returns is 0.455.

Analysts identify the following recent mergers and acquisitions that they believe to be

appropriate to value the acquisition of TAR by ACQ. Analysts conclude that they will

rely on the mean “Enterprise Value / EBITDA” to value TAR using the “valuation

multiple” method, and on the mean “Merger Premium” using the “comparable

transaction” method. Merger premium is defined as the percentage difference between

the offer price per common share outstanding and the target firm’s stock price four

weeks before the merger announcement. Analysts also include all merger synergies

in their cash flow forecast (presented in the above income statement and balance

sheet) and valuation multiples (presented below).

Effective date Acquirer Target Ent Value / Merger

EBITDA premium

Dec 14, 2013 Northern Xe Inc Solar Spring 11.35 25%

Sep 11, 2013 Bates Express Pa Intercont’l 8.56 29%

Aug 30, 2013 Carson Electron Avolent Corp 13.66 30%

May 18, 2013 Turino Elposo Barrier Excess 10.88 25%

Mar 21, 2013 Old Exploration Topa Expedition 13.15 26%

Debt Rating and Default Premium

(in basis points, 1 basis point = 0.01%)

Maturity (years)

Debt Rating 1 2 3 10

Aaa/AAA 5 10 15 30

Aa1/AA+ 10 15 20 40

Aa2/AA 15 25 30 50

Aa3/AA^–20 30 35 55

A1/A+ 30 40 45 63

A2/A 40 49 56 71

A3/A^–50 64 69 80

Baa1/BBB+ 60 75 88 101

Baa2/BBB 70 85 105 117

Baa3/BBB^–80 95 115 130

Capital Market Information:

Treasury Yield

1-year T-STRIPS Yield 2.00%

2-year T-STRIPS Yield 2.30%

3-year T-STRIPS Yield 2.75%

10-year T-STRIPS Yield 4.20%

Risk Premiums

Market – 1-year T-STRIPS 7.20%

Market – 2-year T-STRIPS 6.90%

Market – 3-year T-STRIPS 6.45%

Market – 10-year T-STRIPS 5.00%

Value TAR using 3 methods: (1) the discounted cash flow method, (2) the valuation

multiple method, and (3) the comparable transaction method. Assess whether ACQ’s

bid of $128 per share for TAR’s equity is a reasonable offer from ACQ’s perspective.

(35 marks)

Question 12

Dunkin Donuts is considering a new breakfast sandwich to add to their menu. The

project requires an initial capital investment of $110,000 per franchisee and will

generate an expected cash flow of $12,000 per year forever. Consumer acceptance,

however, is uncertain. The firm believes the product “newness” will generate the first

year’s cash flow. At the end of the first year, however the firm will have a better

understanding of consumer demand. If demand is high, the sandwich will generate

$14,500 per year. But there is a 20% chance that demand will be low, in which case

the cash flow will be $2,000 per year. At the first year, the firm could terminate the

project and sell the assets for $82,500. The discount rate is 12%. What is the NPV of

the project taking into account the option to abandon?

(15 marks)

SECTION C: Essay Question

(25 marks – answer Question 13)

Instructions: Answer the following question. Your answer should be elaborated using

examples and empirical evidence. Your answer can be in essay and/or bullet point

format where appropriate. This essay should be typed and limited to 1000 words.

Question 13

In October 2019, a leading Silicon Valley venture capitalist argued that investment

bankers often view initial public issues as a border wall under their exclusive control

but have sensed that this barrier has been breached.

Discuss the role of investment banks in a traditional Initial Public Offering (IPO) and

the associated advantages and disadvantages of using investment banks for the firm

going public. Discuss the merits and drawbacks of the alternative IPO method implied

by the leading Silicon Valley venture capitalist as a way for private firms to obtain

equity capital when going public without having to go through a traditional IPO process.

(25 marks)

END OF EXAM PAPER

SOLUTIONS

Section A

Question 1 E (I and IV only) Question 6 E (I only)

Question 2 A Question 7 C

Question 3 D Question 8 B

Question 4 D Question 9 C

Question 5 E (IV only) Question 10 D

Note: You don’t need to state which statements from I, II, III and IV are actually correct if you

choose answer E.

Section B

Question 11:

Full 5 marks will be deducted for each step that results in a wrong result regardless of the type

of mistakes made in the step. However, the wrong result from the previous step will be

assumed to be correct to be carried on to the next step. In this next step using the wrong input

from the previous step, if the equation or calculation is wrong, full 5 marks will be deducted.

No partial credits out of 5 marks are given in each step.

Calculate beta



_TXA= (0.16)^1/2= 0.4 

_M= (0.04)^1/2= 0.2 Cov(R_TXA, R_M) = 

_{TXA, M}_TXA_M= 0.455 x 0.4 x 0.2 = 0.0364

β 

Cov R R

( , )  0.0364 

CFK M

Var(R ) 0.04

0.91

(5 marks)

Calculate WACC

r_d= R_f+ default premium

= 4.2% + 0.8% = 5%

r_e= R_f+ β (R_M– R_f)

= 4.2% + 0.91 x 5% = 8.75%

 E   D 

WACC r_e r_d1 t 

   

  

D  E D  E

   

= 8.75% (4000/4600) + 5% (1 – 0.40) (600/4600)

= 8% (5 marks)

Discounted Cash Flow method

2013 2014 2015 2016 EBIT 500 760 890

– Tax (40% on EBIT) 200 304 356

+ Depreciation 100 140 210

Operating cash flow (1) 400 596 744

Ending net fixed assets 1500 1700 1900

– Beginning net fixed assets 1400 1500 1700

+ Depreciation 100 140 210

Net capital spending (2) 200 340 410

Ending NWC 140 140 160

– Beginning NWC 100 140 140

Change in NWC (3) 40 0 20

FCF = (1) – (2) – (3) (5 marks) 160 256 314

Terminal value ₂₀₁₅= FCF₂₀₁₆/(r-g) = 314 / (0.08 – 0.03) = 6280

Enterprise value = 160/1.08 + (256 + 6280)/1.08²= 5751.7147

Terminal value ₂₀₁₆= FCF₂₀₁₇/(r-g) = FCF₂₀₁₆(1+g)/(r-g)

= 314(1+0.03) / (0.08 – 0.03) = 6468.4

Enterprise value = 160/1.08 + 256 /1.08²+ (314 + 6468.4)/1.08³= 5751.7147 (5 marks)

Equity value = Enterprise value – Debt = 5751.7147 – 600 = 5151.7147

Equity value per share = 5151.7147 / 40 = 128.79 per share (5 marks)

Multiple valuation method

Mean EV/EBITDA = (11.35 + 8.56 + 13.66 + 10.88 + 13.15) / 5 = 11.52

EBITDA = 2500 – 2000 = 500 Enterprise value = 500 x 11.52 = 5760

Equity value = Enterprise value – Debt = 5760 – 600 = 5160 Equity value per share = 5160 / 40 = 129 per share (5 marks)

Comparable transaction method

Mean Premium = (25% + 29% + 30% + 25% + 26%) / 5 = 27%

Stock price (Dec 5) = 100

Equity value per share = 100 x (1+27%) = 127 per share (5 marks)

Question 12:

Draw the decision tree.

Time 0 Time 1 Time 2

14.5K forever (high case) 80%

-110K 12K

20% 2K forever (low case)

82.5K (option to abandon) (5 marks)

PV (low case cash flows) at time 1: PV_low,1= 2000 / 0.12 = 16666.6667 < 82500

(Note that this is a perpetuity)

This PV is lower than what the company would get if it chose to sell the assets and get

82500. So, Dunkin Donuts should abandon the project in year 1 in case of low

consumer demand. (5 marks)

We have an initial investment of 110000 at time 0, a cash inflow of 12000 at time 1,

80% chance getting 14500 a year from time 2 until forever and 20% chance of getting

82500 at time 1 from the abandonment value.

PV (high case cash flows) at time 1: PV_high,1= 14500 / 0.12 = 120833.33

(Note that this is a perpetuity)

Now, we have an initial investment of 110000 at time 0, a cash inflow of 12000 at

time 1, 80% chance getting 120833.33 at time 1 (which is the PV of the high case

cash flows) and 20% chance of getting 82500 at time 1 (abandonment value).

푁푃푉_{ꢀꢁꢂꢃꢀꢄ}= −110000 +

(5 marks)

12000 + 0.8 x 120833.3333 + 0.2 x 82500

1.12

= 1755.95

Section C

Question 13

When a company intends to make a public offering, the first step is to select an underwriter

Most firms usually select an investment bank to advise it and perform the underwriting

functions in connection with the issue. The selection process of the investment bank

typically depends on the general reputation and expertise, prior banking relationships

the issuer has with specific banks in the investment bank community. IPOs can be made

by one underwriter or by multiple underwriters. When there are multiple underwriters, one

investment bank is selected as the lead underwriter. The lead underwriter always appears

on the cover on the left of the cover of the tombstone, and plays a major role throughout

the transaction. The lead underwriter makes all the arrangements with the issuer,

establishes the issue schedule and has the primary responsibility of the due diligence,

pricing and distribution of the stock. Investment banks are able to leverage their expertise and

price the stock optimally to ensure that no money is left on the table and also so that investors

do not get poor returns. The lead underwriter also assembles a group of underwriters

(syndicate members) to assist in the sale of the shares to the public. The advantage of using

investment banks as underwriters is that they can leverage their relationships with their

standing brokerage firms as well as their asset management services. This can help reduce

the cost of price discovery and thus offer issuance cost savings. However, the main

disadvantage of using an investment bank as an underwriter is the cost (Forbes, 2007):

hiring an underwriter will cost about 3.5% to 7% of the offering (PWC, 2020). The underwriting

fee usually comprises of large direct cots that a company incurs as it goes through the IPO as

well as the legal accounting and tax costs.

The traditional method in which investment banks bring the firm public is “firm commitment”.

This entails the underwriter agreeing to assume all inventory risk and purchase all the

securities for an IPO to directly sale to the public. In firm commitment, the underwriter acts as

a dealer and assume responsibility for the stock and makes profit based on the spread

between the price paid to the issuer and the price received from investors when the stock is

sold. For example: Goldman Sachs and Morgan Stanley underwrote Facebook's IPO. They

made a firm commitment to sell Facebook's stock to the public. At the same time, they shorted

it and used the green-shoe option and made millions in the process.

The alternative method implied for the question is direct offering: the company lists

outstanding shares directly onto a stock exchange without underwriters, thereby forgoing the

traditional IPO roadshow and book-building process. Existing shareholders, such as

founders, employees, and early-stage investors, are free to sell their shares on the stock

exchange selected by the company (but are not obligated to do so). Notable direct listings

include Spotify (2018), Slack (2019), and Watford Re (2019).

The advantages include: (1) Market-based price discovery: In a traditional IPO, the price for a

company’s stock is determined based on demand from a small number of large institutional

investors for a limited supply of a company’s shares (often 10-20% of the entire company).

This scarcity in supply results in a stock price following an IPO that isn’t necessarily reflective

of what a purchaser of the stock would pay for the shares if more shares were available in the

open market. This explains the stock price decline that companies often experience in

advance of the lock-up expiration. In theory, a direct listing allows for true market-based

discovery since all of a company’s shares are available for sale and purchase on the first day

of trading. (2) Lower investment banking fees: Due to the more limited role that investment

banks play in a direct listing, there is no need to have a large group of banks advising on a

direct listing. This results in smaller overall fees being split amongst a smaller group of

investment banks. The fees are generally for direct listing. For example: Spotify did its direct

listing at a $29 billion market capitalization and paid $35 million in advisory fees; Snap

went public at a $24 billion market capitalization and paid $85 million in underwriting fees.

Some of the disadvantages include: (1) the board and the company are not able to set the

price for the shares or control investor allocations. The trading price of the stock following the

direct listing is completely at the mercy of the market. Moreover, companies can’t pick

and choose which investors they want to allocate the shares to. Unlike a traditional IPO, where

companies have a say in the allocation of shares, and are able to place the shares with

long-term, high-quality institutional investors, companies in a direct listing will have a

stockholder base composed of any investor that decides to buy the shares on the open market.

(2) Management has to educate investors: Because the investment bankers in a direct listing

are not involved in setting up and attending investor meetings and with no traditional roadshow

and research analyst modeling process, the company’s management team to take control of,

and run, the investor education process. Companies that do not have a management team

that is experienced with navigating the complex public offering landscape may be better

served by a traditional IPO, in which the investment bankers are able to assist with the investor

education process.

TIME VALUE OF MONEY

Problem 1

Suppose you will receive $300, 4 years from now. Your required rate of return is 8%. What would you pay for it today?

0 1 2 3 4 ~~| | | | |~~

? 300 PV = 300 / (1.08)4 = 220.51

Problem 2

You’re at year 2012. You will receive $200 in 2014 and will invest that $200 until 2019 with a required rate of return of 6%. What will you get in 2019?

12 13 14 15 16 17 18 19 ~~| | | | | | | |~~

200 ? FV = 200 x (1.06)5 = 267.65

Problem 3

You have just received notification that you have won the $1 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect at that time!), 80 years from now. What is the present value of your windfall if the appropriate discount rate is 9%?

0 1 … 79 80 ~~| | | | |~~

? $1 mil PV = 1,000,000 / (1.09)80 = 1,013.63

Problem 4

Your coin collection contains fifty 1952 silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2054, assuming they appreciate at a 4.5% annual rate?

1952 1953 … 2053 2054 ~~| | | | |~~

50 ? Math: FV = 50 x (1.045)102 = 4,454.84

Problem 5

At 9% interest, how long does it take to double your money? To quadruple it?

When $ is not given, make up one and solve the problem!

Double: 2 = 1 (1+9%)T àT = ln(2) / ln(1.09) = 8.04 or 300 = 150 (1+9%)T àT = 8.04

(results are the same as long as FV is twice as much as PV -- meaning of “double”) Quadruple: 4 = 1 (1+9%)T àT = 16.09

Problem 6

Which offer will you select if your required return is 5% annually? - Offer 1: You will receive $2,000 a year from now.

- Offer 2: You will receive $2,500 four years from now.

To be able to compare offers that involve $ at different points in time, you have to “move” $ to the same point in time and then do the comparison.

0 1 2 3 4 Offer 1 ~~| | | | |~~

2000

0 1 2 3 4 Offer 2 ~~| | | | |~~

2500 $2000 in offer 1 is at time 1 while $2500 in offer 2 is at time 4. You cannot make comparison when $$$ are at different points in time. You should pick a point in time, move all $$$ to that time and then do the comparison. Now let’s say time 1.

- Offer 1: $ at time 1 is $2000, no need to do any “moving”

- Offer 2: $ at time 4 is $2500, move it back to time 1: PV = 2500 / (1.05)3 = 2159.59 So $2500 at time 4 is equivalent to $2159.59 at time 1.

Offer 1 gives $2000 while offer 2 gives $2159.59 at time 1, so choose offer 2. You cannot just choose offer 2 because $2500 > $2000. Other ways to solve:

(1) move $2000 and $2500 back to time 0 and compare,

(2) move $2000 from time 1 to time 4 and compare it to $2500, which is already at time 4.

Problem 7

The current balance in your bank account is $10,000. How much do you have to put into your bank account now in order to have $15,000 four years from now? Suppose the bank gives you a 3% annual interest on your account.

0 1 2 3 4 ~~| | | | |~~

? 15000 To get 15,000 in four years, your account must have 13,327.31 today.

PV = 15000 / (1.03)4 = 13,327.31

You’ve already had $10,000 sitting in your account, so you need to put $3,327.31 (=13,327.31–10,000) more into your account now to have $13,327.31 today. This 13,327.31 today will grow to $15,000 in four years at 3% annual interest.

Problem 8

The balance in your bank account was $15,000 four years ago. You made a major addition of $10,000 into your account two years ago. What is the balance in your bank account today, suppose the bank has been giving you a fixed 3% annual interest on your account, and you have not made any withdrawal?

0 1 2 3 4 ~~| | | | |~~ 15000 ? ~~| | | | |~~

10000 ?

$15,000 will grow to $16,882.63 in four years: FV = 15,000 x (1.03)4 = 16,882.63 $10,000 will grow to $10,609 in two years: FV = 10,000 x (1.03)2 = 10,609 Totally you will have 16,882.63 + 10,609 = 27,491.63 at time 4.

Problem 9

At what rate of interest would you be indifferent between $7,721.73 today and $1,000 per year for the next 10 years?

0 1 2 ……. 10

1000 1000 …….. 1000 7721.73

7721.73 = 1000 x ADF(r,10) à ADF(r,10) = 7.7217 à Look up the annuity table, get r = 5% Use Excel: =rate(10,1000,-7721.73) !!! Notice the negative sign for PV 7721.73

Problem 10

New information database helps generate $65,000 annual revenue each year for the next 8 yrs. Interest rate 8.5%. What is present value of the saving?

Timeline: 0 1 2 ….. … 8

? 65K 65K 65K

PV = 65,000 / (1.085)1 + 65,000 / (1.085)2 + …….. + 65,000 / (1.085)8 = 65,000 x ADF(8.5%,8) = 65,000 x 5.6392 = 366,546.89

How to get ADF from Excel: =PV(r,T,1) (i.e. the PV of annuity of one)

Problem 11

You borrow $300,000 from the bank to finance your 2011 Silverton39 Motoryacht. The terms of this 5-year loan requires you to make quarterly payments. Assuming the APR is 8%. What is your quarterly payment? Given ADF(8%,5)=3.9927, ADF(2%,20)=16.3514, ADF(0.6667%,60)=49.3184

Compounding period is not on an annual basis (period now is in quarter) à convert to quarters: T = 5 years x 4 quarters = 20 quarters

r = 8% / 4 = 2%

0 1 2 ……. 20

300,000 ? ? ?

300,000 = C / (1.02)1 + C / (1.02)2 + …….. + C / (1.02)20 300,000 = C x ADF(2%,20)

300,000 = C x 16.3514 à C = 18,347.02

Problem 12

You bought a house for $500,000 by putting $100,000 for down payment and financing the remainder. According to the terms of this 30-year mortgage, you will have to make monthly payments of $2,554.64. What is the APR of this mortgage? Given ADF(0.55%,30)=27.5860, ADF(0.55%,360)=156.5778

0 1 2 ……. 360

2,554.64 2,554.64 2,554.64 400,000

Period: Month àT = 30 x 12 = 360

400,000 = 2,554.64 / (1+r)1 + 2,554.64 / (1+r)2 + …….. + 2,554.64 / (1+r)360 400,000 = 2,554.64 x ADF(r,360)

à ADF(r,360) = 156.5778

à r = 0.55% -- this is r per month àAPR = 0.55% x 12 = 6.6%

Problem 13

You will receive an annuity that pays $4,000 every year for 6 years. The first $4,000 in the annuity will be paid to you 4 years from today. If interest rate is 5%, what is this annuity worth today?

4K 4K 4K 4K 4K 4K ? ?

PV3 = 4000 x ADF(5%,6) = 4000 x 5.0757 = 20,302.80 -- this PV is at time 3

We need PV at time 0, so move the PV at time 3 back to time 0.

PV = 20,302.80 / (1.05)3 = 17,538.32

Problem 14

You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.45% compounded daily. Loan B offers a rate of 7.5% compounded semi-annually. Which loan will you choose?

Calculate EAR for each loan:

Loan A: ( 1 + 0.0745 / 365 )365 –1 = 7.73% Loan B: ( 1 + 0.075 / 2 )2 –1 = 7.64%

Loan B charges you less interest, so choose B.

What if these are not loans, but Certificates of deposit (CDs) that offer the same terms. Which CD will you choose?

Calculate EAR for each CD (same method as for loan): CD A: 7.73% CD B: 7.64%

CD A pays you more interest, so choose A.

Problem 15

You invest in a project that pays $4,000 in 5 years, $5,000 in 6 years and $7,000 in 7 years. If interest rate is 6%, what is the value of your investment today?

0 1 2 3 4 5 6 7 | | | | | | | |

4K 5K 7K ? ?

PV4 = 4000 / 1.06 + 5000 / 1.062 + 7000 / 1.063 = 14,100.90 -- this is at time 4 We need PV at time 0, so move the PV at time 4 back to time 0.

PV = 14,100.90 / (1.06)4 = 11,169.24

PV = 4000 / 1.065 + 5000 / 1.066 + 7000 / 1.067 = 11,169.24

Excel: =NPV(6%,0,0,0,0,4000,5000,7000)

Problem 16

You joined an investment banking firm that offers you two different arrangements. You can have $50,000 per year for the next 3 years or $25,000 per year for the next 3 years, along with a $50,000 signing bonus today. If the market interest rate is 8%, which salary would you prefer?

Offer A

0 1 2 3 ~~| | | |~~

? 50K 50K 50K

Calculator: I PV PMT N 8 50,000 3

à PV = $128,854.85 -- this PV is at time 0 Offer B

0 1 2 3 ~~| | | |~~

50 25K 25K 25K

Calculator: I PV PMT N 8 25,000 3

à PV = $64,427.42 + $50,000 = $114,427.42 -- this PV is at time 0

Choose offer A.

Problem 17

Suppose you need to save money for your future MBA. You need $25,000 each year for 2016 and 2017. Your rich uncle is willing to support your graduate dream by putting an equal amount of money to the bank every year starting today from 2010 to 2014, total of 5 payments. If you assume that interest is constant at 5%, what will your uncle have to deposit annually so that you do not have to worry about your tuition?

10 11 12 13 14 15 16 17 ~~| | | | | | | |~~

25K 25K ? ? ? ? ?

Step 1:

10 11 12 13 | | | |

ordinary annuity

14 15 16 17 | | | |

25K 25K ?

To have 2 payments of 25K in 2016 and 2017, you need $46,485.2608 at 2015. Ordinary annuity: T = 2, r = 5%, C = 25,000 à PV = 25000 x ADF(5%,2) = $46,485.2608

Step 2:

09 10 11 12 13 14 15 16 17 ~~| | | | | | | | |~~

46,485 ? ? ? ? ?

Convert to ordinary annuity by moving 46,485 from 2015 to 2009: 46,485.26 / (1.05)6 = 34,687.82

ordinary annuity Step 3:

09 10 11 12 | | | |

? ? ? 34,687.82

13 14 15 16 17 | | | | |

? ?

Having $34,687.82 in 2009 allows your uncle to make 5 payments of $8,012 every year from 2010 to 2014.

T = 5, r = 5%, PV = 34,687.82 à C = ?

34,687.82 = C x ADF(5%,5) à C = 34687.82 / 4.3295 = 8,012

Problem 18

You need a 30-year fixed-rate mortgage to buy a new home for £220,000. If the interest rate is 6.8%APR for this mortgage, construct the amortization schedule? You make monthly payments. At the end of year 5, what is the principal balance? Given ADF(6.8%,30)=12.6625, ADF(6.8%,25)=11.87, ADF(6.8%,5)=4.1222, ADF(0.5667%,360)=153.3918, ADF(0.5667%,300)=144.0773, ADF(0.5667%,60) =50.7435.

First, calculate the monthly payment (ordinary annuity):

0 1 2 …… 360 ~~| |~~

? ? …… ? 220,000

T = 30 x 12 = 360, r = 6.8% / 12 = 0.5667%, PV = 220,000 220,000 = C x ADF(0.5667%,360)à C = 1434.24

Interest portion = Balance from previous period Í interest rate per period Principal portion = Payment – Interest portion

Principal balance = Principal balance from previous period – Principal portion

Period	Payment	Interest Portion	Principal portion	Principal balance
0				220,000.00
1	1434.24	1,246.67	187.57	219,812.43
2	1434.24	1,245.60	188.63	219,623.80
… …
359	1434.24	16.12	1,418.12	1,426.15
360	1434.24	8.08	1,426.15	0.00

Remember: The principal balance at any time is the PV of the remaining payments.

The principal balance at the end of year 5:

At the end of year 5, you have 300 payments remaining (you’ve already made 60 pmts).

PV = 1434.2353 / (1.005667)1 + 1434.2353/(1.005667)2 + … + 1434.2353/(1.005667)300

PV = 1434.24 x ADF(0.5667%,300) = 206,640.70

Problem 19

You decide to purchase a 2020 Bentley Continental Flying Spur for $120,000 by putting $20,000 in down payment and financing the remainder. "Your best friend" car dealer charges you an annual percentage rate (APR) of 12%.

a) You want to pay a quarterly payment of $3000. How many years will it take to pay off the loan?

b) You want to pay off the loan in 5 years. The payments are made every quarter. How much do you need to pay each quarter to meet your debt free goal?

§ Loan amount = Purchase price – Down payment = 120000 – 20000 = 100000

§ Quarterly rate r = 12% / 4 = 3%

§ Loan amount = Payment x ADF(r,T)

100000 = 3000 x ADF(r,T)

à ADF(r,T) = 100000 / 3000

Quarterly rate r = 12% / 4 = 3% à Interest charged on initial balance = 100000 x 3% = 3000

Period Beg. Balance Payment Interest Principal Ending balance 100,000

1 100,000 3,000 3,000 0 100,000 2 100,000 3,000 3,000 0 100,000 3 100,000 3,000 3,000 0 100,000

….

When you only pay the interest portion of the loan, you will never be able to reduce the balance. As a result you will never be able to pay off the loan.

§ 5 years = 20 quarters

§ Loan amount = Payment x ADF(3%,20)

àPayment = 100000 / 14.8875 = 6721.57

Problem 20

Your tech friend told you to invest £10000 in the Nasdaq index 5 years ago on 14 Oct 2016. How much is the annual return on the index as shown in the chart? How much would you have on 8 Oct 2021?

FV = PV (1+r) t 14579.54 = 5214.16 (1+r)5

r = 22.83%

FV = PV (1+r) t

= 10000 (1+22.83%)5 = £ 27961

STOCK VALUATION

Problem 1

The next dividend payment by Top Knot, Inc. will be $2.50 per share, the dividends are anticipated to maintain a 5% growth rate forever. If the stock currently sells for $48.00, what is the required return?

0 1 2 3 …… ∞

| | 5% | 5% | 5%

2.50 2.625 2.7563 P0

True math:

48= + + +......+

2.5 2.625 2.7563 D¥ 1+r (1+r)2 (1+r)3 (1+r)¥

Important: You need D1 to D∞ to calculate P0. D1=$2.50

D2=$2.50 x 1.05 = $2.625

D3=$2.625 x 1.05= $2.7563 (or 2.625 x 1.05, Be careful about rounding)

.50

P = r -1g = r 20.05 = 48.00

2.50

r -0.05= 48.00 = 0.0521 r= 0.1021

or 10.21%

Problem 2

No More Corp. pays a constant $11 dividend on its stock. The company will maintain this dividend for the next eight years and will cease paying dividends forever. If the required return on this stock is 10 percent, what is the current share price?

0 1 2 …… 8 9 …… ∞

| | | | |

11 11 11 0

Calculate as an annuity.

PV = 11 / (1.1)1 + 11 / (1.1)2 + …….. + 11 / (1.1)8 = 11 x ADF(10%,8)

= 58.6842

Problem 3

No dividend will be paid on The Jonas’s stock over the next nine years. The company will pay a $10 per share dividend in 10 years and will increase the dividend by 6% per year thereafter. If the required return on this stock is 13%, what is the current share price?

0 1 2 …… 9 10 11 12 …… ∞

| | | | | 6% | 6% |

0 0 0 10 10.60 11.2360

True math: P9

10 11 12

(1.13)

∞

P = 10 + 10.60 + 11.236 + ......+ D∞ (1.13) (1.13) (1.13)

D10=$10

D11=$10 x 1.06 = $10.60

D12=$10 x (1.06)2 = $11.2360 (or 10.60 x 1.06)

The first “behaving” dividend is D10 because it is the first one that will grow at 6% until infinity.

- -

Step 1: Calculate the value of stock at time 9 P = rD1 g = 0.13100.06 =142.8571

Step 2: Move P9 back 9 periods to get P0 (no other dividends in between). Calculate PV

P0 = 142.8571 / 1.139 = 47.5550

Problem 4

Spears, Inc. has just paid a dividend of $7 per share and has announced that it will increase the dividend by $4 per share for each of the next four years, and then never pay another dividend. If the required return on this stock is 11%, what is the current share price?

0 1 2 3 4 5 …… ∞

| | | | | |

7+4=11 11+4=15 15+4=19 19+4=23 0

Important: You need D1 to D4 to calculate P0. So D0 is irrelevant! Just use D0 to get D1 and then please discard D0!

PV = 11 / (1.1)1 + 15 / (1.1)2 + 19 / (1.1)3 + 23 / (1.1)4 = 51.1277

Problem 5

Formula 51 Corp. just paid a dividend of $1.45 per share. The dividends are expected to grow at 30% for the next 3 years and then level off to a 7% growth rate indefinitely. If the required return on this stock is 13%, what is the price of the stock today?

0 1 2 3 4 5 …… ∞

| 30% | 30% | 30% | 7% | 7% |

1.8850 2.4505 3.1857 3.4086 3.6473

P2 True math:

P = + + + + +......+

1.8850 2.4505 3.1857 3.4086 3.6473 D¥

0 1.13 (1.13 )2 (1.13 )3 (1.13 )4 (1.13 )5 (1.13 )¥

Important again: You need D1 to D∞ to calculate P0. So D0 is irrelevant! Just use D0 to get D1 and then please discard D0!

D0=$1.45

D1=$1.45 x 1.30 = $1.8850 D2=$1.45 x 1.302 = $2.4505 D3=$1.45 x 1.303 = $3.1857 D4=$3.1857 x 1.07= $3.4086 D5=$3.4086 x 1.07= $3.6473

The first “behaving” dividend is D3 because it is the first one that will grow at 7% until infinity. g=7%, not 30% because the dividends that grow at 30% will not continue to grow at 30% in later periods.

3.1 57

Step 1: Calculate the value of stock at time 2 P = r -3g = 0.13 80.07 = 53.0950

Step 2: Calculate the present value of stock

0 1 2 3

| | | |

1.8850 2.4505

53.0950

1.13

2 2

(1.13)

D +P

à P = 1 1 + (1+r)2 = 1.8850+ 2.4505+53.0950 =1.6681+43.5003= 45.1684

Note that at time 2, you have both 2.4505 and 53.0950 (P2=53.0950 is the PV of D3, D4….,D∞)

1.33

D + P

Problem 6

Turnips and Parsley common stock sells for $39.86 a share at a market rate of return of 9.5%. The company just paid its annual dividend of $1.20. What is the rate of growth of its dividend?

0 1 2 3 …… ∞

| | | |

39.86

D (1+g)

P = r -1g = 0.095- g =39.86 0.095- g =1.2´(1+g)

39.86´(0.095- g)=1.2´(1+g) 3.7867-39.86g =1.2+1.2g 2.5867= 41.06g

g =0.063

Problem 7

The Double Dip Co. is expecting its ice cream sales to decline due to the increased interest in healthy eating. Thus, the company has announced that it will be reducing its annual dividend by 5% a year for the next two years. After that, it will maintain a constant dividend of $1 a share. Two weeks ago, the company paid a dividend of $1.40 per share. What is this stock worth if you require a 9% rate of return?

0 1 2 3 4 5 …… ∞

| | | | | |

1.33 1.2635 1 1 1

P2 D0=$1.40

D1=$1.40 x 0.95 = $1.33 D2=$1.33 x 0.95= $1.2635

Step 1:

P2 = r -3g = 0.09 = 11.1111

Step 2:

0 1 2 3 4 5 …… ∞

| | | | | |

1.33 1.2635

11.1111 à

P0 = (1D1 r) + (1+ r) 2 = 1.09

1.2635 + 11.1111

1.09 2

= 1.2202 + 10.4155 = 11.6357

P = =

Problem 8

Beaksley, Inc. is a very cyclical type of business which is reflected in its dividend policy. The firm pays a $2.00 a share dividend every other year. The last dividend was paid last week. Five years from now, the company is repurchasing all of the outstanding shares at a price of $50 a share. At an 8% rate of return, what is this stock worth today?

0 1 2 3 4 5 6 …… ∞

| | | | | | |

0 2 0 2 0 P5=50

PV = 2 / (1.08)2 + 2 / (1.08)4 + 50 / (1.08)5= 37.2139

Problem 9

The Mad Cow’s stock you are interested in paid a dividend of $1 last week. The anticipated growth rate in dividends and earnings is 20% for the next year and 10% the year after that before settling down to a constant 5% growth rate. The discount rate is 12%. Calculate the expected price of the stock.

0 1 2 3 4 …… ∞

| 20% | 10% | 5% | 5% |

1 1.2 1.32 1.386 1.4553

P1 D0=$1

D1=$1 x 1.20 = $1.20 D2=$1.20 x 1.10= $1.32 D3=$1.32 x 1.05= $1.3860 D4=$1.3860 x 1.05= $1.4553

Step 1:

1.32

P = r -2g = 0.12 - 0.05 = 18.8571

Step 2:

0 1 2 …… ∞

| | |

1 1.2

18.8571

D1 + P 1.2 + 18.8571 0 (1+ r)1 1.12 1

= 17.9082

Problem 10

Today you purchase a share of Burke Industries convertible preferred stock. The preferred stock pays an annual dividend of $4. Comparable yields are 9%. The preferred stock is convertible into Burke common stock at a conversion rate of 1 share of preferred for 3 shares of common stock. Burke’s common stock paid a dividend of $2.20 yesterday. Dividends are expected to grow at 8%. Your required rate of return is 15%.

0 1 … … 5 6 …… ∞

| | | |

2.376 3.2325 3.4911

D0=$2.2

D5=$2.2 x 1.085 = $3.2325

D1=$2.2 x 1.08 = $2.3760 D6=$2.2 x 1.086 = $3.4911

a) Calculate the current price of the preferred stock

Ppreferred

D preferred

rpreferred

= 0.09 = 44.44 -- Preferred stock problem is a “perpetuity” problem.

If comparable yield is not given, use required rate of return.

b) Calculate the current price of the common stock

2 6

P0 = r -1g = 0.15.370.08 = 33.94

c) Calculate the price of the common stock 5 years from now.

3. 1

P5 = r -6g = 0.154910.08 = 49.87

d) If you were to buy the preferred stock today and convert it to common stock in 5 years. Verify that the return on your investment over the five-year investment horizon is 33.47%

The value of the preferred stock is worth 3 x 49.87 = 149.61 at the time you convert it to common stock. One preferred stock can be traded for 3 common stocks, which means that the value of preferred stock should be 3 times as much as that of the common stock.

You invest $44.44 and get 5 payments of $4 from year 1 to year 5 and $149.61 at year 5. The rate of return over the whole investment period is the “r” you get from the following math (similar to bond valuation when you get r or YTM):

44.44

4 4 4 4 4 +149.61

= + + + +

(1+ r)1 (1+ r)2 (1+ r)3 (1+ r)4 (1+ r)5

4 4 4 4 4+149.61

= + + + +

44.44

(1.3347 )1 (1.3347 )2 (1.3347 )3 (1.3347 )4 (1.3347 )5

(verified!)

Problem 11

Peter Luger Steak House has been selling porterhouse steaks since the late 1800s. The demand for their steak has been so stable in this period that earnings have been $1,479,000 per year for the last 100 years, with no change expected in the future. The owners have been contemplating a new catering venture that would require a $750,000 investment two years from now and will start producing a 30% return from the third to the seventh year and the new venture would cease to exist after that. Note: r = 6%

a. What is the value of the firm if the new project is not undertaken?

100 years ~ perpetuity

PV = E / r = 1,479,000 / 0.06 = 24,650,000

b. What is the value of the firm if they go ahead with the new venture?

0 1 2 3 4 5 6 7

| | | | | | | |

-750K 225K 225K 225K 225K 225K

Cash inflow each year from year 3 to year 7: 30% x 750,000 = 225,000

NPV2 = -750,000 + 225,000 x ADF(6%,5) = -750,000 + 225,000 x 4.2124 = 197,790

Firm value = 24,650,000 + 197,790 / (1.06)2 = 24,826,000

176,000 known as NPVGO

c. What is Peter Lueger’s price-to-earnings ratio?

P/E = 24,826,000 / 1,479,000 = 16.8

or P/E = 1/r + 176,000 / 1,479,000 = 16.8

Note: P/E is the inverse of the cost of capital when NPVGO equals zero.

Problem 12

NCH, which markets cleaning chemicals, insecticides, and other products, paid dividends of $2 per share on earnings of $4 per share. The book value of equity per share was $40, and earnings are expected to grow 5% a year in the long term. The cost of equity is 11.675%.

a. Estimate the price/book value for NCH

The current payout ratio = 2/4 = 0.5.

Using the DDM: Value per share = 2(1.05) / (0.11675 - 0.05) = $31.76

The price/book value ratio = 31.76 / 40 = 0.79

b. The current stock price is $60 per share. What long term growth rate is implied in the firm’s current price? How much would the return on retained earnings have to be to justify the price/book value ratio at which NCH sells for currently?

The actual share price is $60. We can use this to solve for the value of g using 60 = 2 (1+g) / (0.11675 – g) à g = 8%.

If g = 8%, then we need a return on retained earnings such that 0.08 = 0.5 x return on retained earnings à return on retained earnings = 16%.

Problem 13

Time Warner is considering a sale of its publishing division. The division had earnings EBITDA of $550 million in the most recent year (depreciation was $150 million), growing at an estimated 5% a year (and assuming that depreciation grows at the same rate). ROA in the division is 15%, and the corporate tax rate is 40%. If the cost of capital for the division is 9%, estimate the following multiples:

a. Value / FCF to the firm b. Value / EBIT

c. Value / EBITDA

Expected growth rate g = 5% Return on capital ROA = 15%

g = Reinvestment rate x ROAàReinvestment rate = g / ROA = 5/15 = 33.33% EBIT = EBITDA – Depreciation = 550-150 = 400

EBIT(1-t) = (EBITDA – Depreciation) (1- tax rate) = (550-150) (1-0.4) = 240 FCFF = EBIT (1-t) (1- Reinvestment Rate) = 240 (1-0.3333) = 160

Value of firm = FCFF (1+g) / (Cost of capital –g) = 160(1.05) / (0.09-0.05) = $4,200 million

Value / FCFF = 4200/160 = 26.25 Value / EBIT = 4200/400 = 10.5 Value / EBITDA = 4200/550 = 7.64

Problem 14

National City, a bank holding company, reported earnings per share of $2.4 and paid dividends per share of $1.06. Dividends are now expected to grow at 6% a year in the long run. The cost of equity is 12.775%.

a. Estimate the P/E ratio for National City

Payout ratio = Dividends / Earnings = 1.06 / 2.40 = 44.17%

P = D1 / (r – g) = D0 (1+g) / (r – g)

P/E = ( D0 / E ) [ (1+g) / (r – g) ] = Payout ratio x [ (1+g) / (r – g) ] = (0.4417) (1.06) / (0.12775-0.06) = 6.91

b. The stock currently trades 10 times earnings. What long term growth rate is implied in the firm’s current P/E ratio?

Actual PE = (0.4417) (1+g) / (0.12775-g) = 10 àImplied Growth Rate g = 8% or

P0 = P/E x E = 10 x 2.4 = 24 = D0 (1+g) / (0.12775-g) àg = 8%

Problem 15

You are trying to estimate a price per share on an IPO of a company involved in environmental waste disposal. The company has a book value per share of $20 and earned $3.5 per share in the most recent time period. Although it does not pay dividends, the capital expenditures per share were $2.5 higher than depreciation per share in the most recent period, and the firm uses no debt financing. Analysts project that earnings for the company will grow 25% a year for the next 5 years. You have data on other companies in the environment waste disposal business. The average debt/equity ratio of these firms is 20% and tax rate is 40%.

a. Estimate the average Price/Book value ratio for these comparable firms. Would you use this average to price the IPO?

The average Price/Book Value ratio = 1.66. I wouldn’t necessarily use this ratio to price the new issue because of the heterogeneity amongst these firms. In particular, the firms have very different payout ratios, growth rates and returns on equity.

b. What subjective adjustments would you make to the Price/Book value ratio for this firm, and why?

I would expect the IPO to trade at a much higher multiple of price to book than the sector since it has a substantially higher ROE (3.50/20 = 17.5%) and growth rate (25%) than the sector.

Problem 16

The following were the P/E ratios of firms in the aerospace/defense industry with additional data on expected growth and risk.

a. Estimate the average and median P/E ratios. What, if anything, would these averages tell you?

The average P/E ratio = 13.2, while the median P/E ratio = 12.25, which is the average of the 7th ranking and 8th ranking firm’s P/E ratios. The fact that the mean and the median are relatively close to each other means that there are no great extreme values. We can, therefore, interpret either number as a measure of the market’s valuation of earnings for a typical firm in the sector.

b. Universal Machines Tools Corp (UMT) operates in the same aerospace/defense industry and has the most recent earnings of 1.2 billion USD. The firm has 200 million shares outstanding on the market. How much is UMT worth per share of equity using the mean industry P/E multiple?

Market value of equity valuation UMT / Earnings UMT = 13.2

à Market value of equity valuation UMT = 13.2 x 1.2 billion = 15.84 billion

à Per share of equity valuation UMT = 15.84 billion / 200 million shares = $79.2

c. An analyst concludes that Thiokol is undervalued because its P/E ratio is lower than the industry average. Under what conditions is this statement true? Would you agree with it in this case?

This would be true if Thiokol’s riskiness were equal or less than that of the industry, on average and its expected growth matched or beat the average for the sector. In Thiokol’s case, the low PE can be attributed to low growth.

d. Using the PEG ratio, assess whether Thiokol is undervalued. What are you assuming about the relationship between value and growth when you use PEG ratios?

Using the estimated PEG ratio, it would seem that Thiokol is overvalued, since the average PEG ratio works out to 1.5682, while Thiokol’s PEG ratio is 1.5818. Using the PEG ratio however assumes that value is proportional to growth.

e. Using a regression, control for differences across firms on risk and growth, we find that: PE = -1.55 + 34.68 (Growth) + 12.27 (Beta) (Note: the coefficient on payout is insignificant) Specify how you would use this regression to spot under- and overvalued stocks. What are the limitations of this approach?

Using this regression, the third to last column gives us the estimated P/E ratios based on the payout ratio, risk and growth of each company. The second to last column, which represents the difference between the actual P/E ratio and the estimated P/E ratio gives us an estimate of relative under- or over-valuation. Positive values imply overvaluation, while negative values imply undervaluation. In this case, the limitation of this approach is the small sample and the high error on the prediction. More generally, this approach assumes linear relationships between PE and each of the independent variables and no correlation between the independent variables.

Problem 17 – M&A valuation

On January 5, 2014, Cressent Vetition Corp (CVT) made an acquisition bid of $128 per share for all of Transamerica Exchange Inc (TXA) equity.

Analysts forecast TXA’s income statement and balance sheet information to be as follows. “Year” denotes the fiscal year ending 31st December.

(in million $) Actual Projected . Steady

Sales Costs

Depreciation EBIT

Interests and taxes

Net income

Year 2013 2014 2500 3000 2000 2400

80 100 420 500 60 70

360 430

2015 2016 3700 4300 2800 3200 140 210 760 890 80 90

680 800

Current assets Net fixed assets Total assets

Current liabilities Long term debt Shareholders equity

Total liabilities and equity

600 660 1400 1500 2000 2160

500 520 600 660 900 980

2000 2160

680 720 1700 1900 2380 2620

540 560 670 680 1170 1380

2380 2620

Other information for TXA as of December 5, 2013

Market Value of Debt $600 million

Common Stock Price Common Shares Outstanding

Marginal Tax Rate

$100 per share 40 million shares

40%

Analysts forecast that starting from 2016, TXA’s free cash flow will settle to a growth rate of 3% per year indefinitely. They believe that TXA aims to keep the current debt ratio constant in the future. TXA has maintained an insignificant amount of cash in the balance sheet (assuming cash equals zero throughout). The Weighted Average Cost of Capital (WACC) of 8% is the appropriate discount rate for TXA.

Analysts identify the following recent mergers and acquisitions that they believe to be appropriate to value the acquisition of TXA by CVT. Analysts conclude that they will rely on the mean “Enterprise Value / EBITDA” to value TXA using the “valuation multiple” method, and on the mean “Merger Premium” using the “comparable transaction” method. Merger premium is defined as the percentage difference between the offer price per common share outstanding and the target firm’s stock price four weeks before the merger announcement. Analysts also include all merger synergies in their cash flow forecast (presented in the above income statement and balance sheet) and valuation multiples (presented below).

Effective date Dec 14, 2013 Sep 11, 2013 Aug 30, 2013 May 18, 2013

Mar 21, 2013

Acquirer Northern Xe Inc Bates Express Inc Carson Electron Turino Elposo

Old Exploration

Target

Solar Spring Sys Pa Intercontinental Avolent Corp Barrier Excess

Topa Expedition

EV/EBITDA 11.35

8.56 13.66 10.88

13.15

Merger premium 25%

29% 30% 25%

26%

Question: Value TXA using 3 methods: (1) the valuation multiple method, (2) the comparable transaction method, and (3) the discounted cash flow method. Assess whether CVT’s bid of $128 per share for TXA’s equity is a reasonable offer from CVT’s perspective.

Solution

(1) Multiple valuation method

Mean EV/EBITDA = (11.35 + 8.56 + 13.66 + 10.88 + 13.15) / 5 = 11.52

EBITDA = 2500 – 2000 = 500

Enterprise value = 500 x 11.52 = 5760

Equity value = Enterprise value – Debt = 5760 – 600 = 5160

Equity value per share = 5160 / 40 = 129 per share

(2) Comparable transaction method

Mean Premium = (25% + 29% + 30% + 25% + 26%) / 5 = 27%

Stock price (Dec 5) = 100

Equity value per share = 100 x (1+27%) = 127 per share

Equity value = 127 x 40 = 5080

Enterprise value = Equity value + Debt = 5080 + 600 = 5680

(3) Discounted Cash Flow method

EBIT

– Tax (40% on EBIT) + Depreciation

Operating cash flow (1)

Ending net fixed assets

– Beginning net fixed assets + Depreciation

Net capital spending (2)

Ending NWC

– Beginning NWC Change in NWC (3)

FCF = (1) – (2) – (3) Terminal value

Enterprise value

2013 2014 500 200 100 400

1500 1400 100 200

140 100 40

160

5751.7147

2015 2016 760 890 304 356 140 210 596 744

1700 1900 1500 1700 140 210 340 410

140 160 140 140 0 20

256 314

6280

Terminal value = FCF2016/(r-g) = 314 / (0.08 – 0.03) = 6280

Enterprise value = 160/1.08 + (256 + 6280)/1.082 = 5751.7147

Equity value = Enterprise value – Debt = 5751.7147 – 600 = 5151.7147

Equity value per share = 5151.7147 / 40 = 128.79 per share

Assess the acquisition offer

CVT’s offer for total TXA’s equity = 128 x 40 = 5120

Enterprise value = 5120 + 600 = 5720

This value is within the valuation range obtained from the three methods (Discounted Cash Flow, Valuation multiple, and Comparable transaction). Therefore CVT’s offer is reasonable.

BOND VALUATION

Problem 1

Cutler Co. issued 11-years bonds a year ago at coupon rate of 7.8%. The bonds make semiannual payments. If the YTM on these bonds is 8.6%, what is the current price? ADF(8.6%,11)=6.9357, ADF(4.3%,22)=14.0455, ADF(8.6%,10)=6.5322, ADF(4.3%,20)=13.2363. Par value is $1000.

Timeline: 0 1 2 3 4 ….. … 19 20

39 39 39 39 Number of years until maturity: 11 – 1 = 10

T r PV 10 x 2=20 8.6 / 2 = 4.3% ??

39 1,039

C FV 39 1,000

PV = 39 / (1.043)1 + 39 / (1.043)2 + …….. + 39 / (1.043)19 + 1039 / (1.043)20 = 39 x ADF(4.3%,20) + 1000 / (1.043)20

= 947.05

Excel: =PV(4.3%,20,39,1000)

Problem 2

Ngata Corp issued 12-year bonds 11 years ago at a coupon rate of 9.2%, semiannual payments. Bonds currently sell for 105.05% of par ($1000), calculate YTM?

0 1 2 ~~| | |~~

46 46 + 1000 1050.5

Number of years until maturity: 12 – 11 = 1 à semiannual periods = 1 x 2 = 2 Price = 1,000 x 105.05% = 1050.5

1050.5 = 46 / (1+r)1 + 1046 / (1+r)2

1050.5 (1+r)2 = 46 (1+r) + 1046

1050.5 (1+r)2 – 46 (1+r) – 1046 = 0

(1+r)2 – 0.0438 (1+r) – 0.9957 = 0 (quadratic equation: aX2+bX+c=0)

∆ = b2 – 4ac = (–0.0438)2 – 4 x (–0.9957) = 3.9847

(1+r) = (–b+√∆)/2a = (0.0438 + 1.9962) / 2 = 1.0200 àr = 0.0200 (semiannually)

YTM = 0.02 x 2 = 0.04 or 4.00%

Excel: =RATE(2,46,-1050.5,1000)

Problem 3

Bonds on market have 15 years to maturity, an YTM of 6%, and current price is $1,136.50. The bonds make semiannual payments. What is the coupon rate of these bonds? Given ADF(6%,15)=9.7122, ADF(3%,30)=19.6004.

Timeline: 0 1 2 ….. 29 30

-1,136.5 ? ? ? 1,000+??

T r

15 x 2 = 30 6 / 2 = 3%

PV C FV -1,136.5 ? 1,000

1136.5 = C/(1.03)1 + C/(1.03)2 + .. + C/(1.03)29 + (1000+C)/(1.03)30 1136.5 = C x ADF(3%,30) + 1000 / (1.03)30

1136.5 = C x 19.6004 + 411.9868

à C = 36.9642 (semiannually) or 36.9642 x 2 = 73.9284 annually

Coupon = Coupon rate x Par àCoupon rate = Coupon / Par = 73.9284 / 1000 = 7.39%

Excel: =PMT(3%,30,-1136.5,1000)

Problem 4

Suppose your company needs to raise $20 million and you want to issue 30-year bonds for this purpose. Assume the required return on your bond issue will be 7%, and you are evaluating two issue alternatives: a 7% annual coupon bond and a zero coupon bond.

a. How many of the coupon bonds would you need to issue to raise the $20 million? Coupon bond sell at par à Price of the bond = par value = $1,000

Number of coupon bonds you need to issue = $20,000,000/$1,000= 20,000

b. How many of zero coupon bonds would you need to issue?

0 1 2 ….. … 30

? 1,000 à PV = 1000 / (1.07)30 = 131.3671

Number of zero coupon bonds you need to issue = $20,000,000/$131.37= 152,241

c. In 30 years, what will your company’s repayment be if you issue the coupon bond? Coupon bond: last coupon payment plus par value

Coupon bonds repayment = 20,000x($1,070) = $21,400,000

d. What will the repayment in c. be if you issue the zeroes?

Zero coupon bond: no coupon payment, just par Repayment = 152,242x($1,000) = $152,241,760

Problem 5

In 2009, you purchased a 10 year, 8% semiannual coupon bond with $1000 par value. The YTM on comparable 10 year securities at the time of the purchase was 6% compounded semi-annually. If you could sell it today (2010) for $1,091.50, what is the annual rate of return you earned over the 1 year investment horizon? What is the effective annual rate of return you earned over that 1 year investment horizon? Given ADF(6%,10)=7.3601, ADF(3%,20)=14.8775.

Note: Semiannual mode for the whole problem!

Step 1: Find the price that you paid for the bond in 2009

0 1 2 ………. 19 20

40 40 40 40 + 1000 ?

PV = 40 x ADF(3%,20) + 1000 / (1.03)20 = 1148.78

Step 2: Find the return over the period 2009-2010 (taking into account the coupons received during that period)

0 1

40 1148.78

40 + 1091.50

1148.78 = 40 / (1+r)1 + 1131.50 / (1+r)2

1148.78 (1+r)2 = 40 (1+r) + 1131.50

1148.78 (1+r)2 – 40 (1+r) – 1131.50 = 0

(1+r)2 – 0.0348 (1+r) – 0.9850 = 0 (quadratic equation: aX2+bX+c=0)

∆ = b2 – 4ac = (–0.0348)2 – 4 x (–0.9850) = 3.9412

(1+r) = (–b+√∆)/2a = (0.0348 + 1.9852) / 2 = 1.0100 àr = 0.0100 (semiannually)

àAnnual rate of return = 0.01 x 2 = 0.02 or 2%

Effective annual rate of return = (1+0.01)2 – 1 = 0.0201 or 2.01%

Problem 6

Two years ago, you bought a 30 year, original maturity, 9% semi-annual coupon bond at a price of $1113. You expect to sell the bond in 3 years, and project that at that time, market rates will be 2% higher than when you purchased the bond. Based on your projections, what will you sell the bond for? Given ADF(4%,60)=22.6235, ADF(4%,30)=17.2920, ADF(5%,50)=18.2559, ADF(5%,25)=14.0939.

Timeline: 0 1 2 … ….. … 59 60

45 45 45 1,045 1113

Step 1: Find YTM 2 years ago (when you bought the bond, the bond will mature in 30 years)

1113 = 45 x ADF(r,60) + 1000 / (1+r)60 1113 = 45 x 22.6235 + 1000 / 1.04 Verified from the given ADFs, r = 4%

YTM = 4% x 2 = 8%

Step 2: YTM three years from now is: 8% + 2% = 10%

(Note back to step 1: the problem says 2% higher than the rate when you bought the bond, you so need to find the rate when you bought the bond first, not the rate today or when you sell the bond. So in step 1, N=60, not 56 or 54)

Step 3: Find bond price three years from now (when you sell the bond)

One year from now, the bond will mature in 25 years.

Timeline: 0 1 2 … ….. … 49 50

45 45 45 1,045 ?

PV = 45 x ADF(5%,50) + 1000 / (1.05)50 = 908.72

Problem 7

Homer Simpson is considering buying the following three bonds (all AAA rated):

1. Springfield Nuclear Power Plant: 5-year, 7% semi-annual coupon, $1,000 par 2. Duff Beer: 5-year, 5% semi-annual coupon, $1,000 par

3. Quickie Mart: 5-year, 11% semi-annual coupon, $1,000 par

Each of these bonds has the same yield to maturity of 4.75% and Homer’s broker charges a $108.65 commission to purchase the portfolio of all three bonds at once (one each). What is the most Homer should be willing to pay for this portfolio (before commission)? What is Homer’s expected rate of return on this portfolio?

Step 1: Calculate the price of each bond

N = 10; I/Y = 2.375%; FV = 1,000; PMT = 35; PV = -$1,099.10

N = 10; I/Y = 2.375%; FV = 1,000; PMT = 25; PV = -$1,011.01

N = 10; I/Y = 2.375%; FV = 1,000; PMT = 55; PV = -$1,275.28

Step 2: Find the price of the portfolio.

Price = 1099.10+1011.01+1275.28 = $3,385.39

Step 3: Find the rate of return on the portfolio.

N = 10; PV = -(3385.39+108.65); FV = 3,000; PMT = 35+25+55; I/Y = ? = 2% x 2 = 4%

COST OF CAPITAL

Problem 1

Jake’s Sound Systems has 210,000 shares of common stock outstanding at a market price of $36 a share. Last month, Jake’s paid an annual dividend in the amount of $1.593 per share. The dividend growth rate is 4%. Jake’s also has 6,000 bonds outstanding with a face value of $1,000 per bond. The bonds carry a 7 % coupon, pay interest annually, and mature in 4.89 years. The bonds are selling at 99% of face value. The company’s tax rate is 34%. What is Jake’s weighted average cost of capital?

Debt: 6,000 ´ $1,000 ´ .99 = $5.94m Common equity: 210,000 ´ $36 = $7.56m

Total = $5.94m + $7.56m = $13.50m

Re = [($1.593 ´ 1.04) ¸ $36] + 0.04 = 0.08602

Calculate the cost of debt by solving for the YTM of the bond: Enter 4.89 ±990 70 1000

N I/Y PV PMT FV Solve for 7.250

Use Excel: =RATE(4.89,70,-990,1000) will get 7.25%

$7.56m $5.94m

( )( )

WACC= $13.50m×0.08602 + $13.50m×0.07250×(1−0.34) =

= 0.04817+0.02105= 0.06922= 6.9%

Problem 2

Phil’s Carvings, Inc. wants to have a weighted average cost of capital of 9%. The firm has an after-tax cost of debt of 5% and a cost of equity of 11%. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

Denote We and Wd as the weight of equity and debt respectively. Note: We + Wd =1

0.09 = [We ´ 0.11] + [(1 – We) ´ 0.05) 0.09 = 0.11We + 0.05 - 0.05We

0.04 = 0.06We We = 0.6667

à Wd = 1 - We = 1 – 0.6667 = 0.3333

Debt-to-equity ratio = 0.3333% ¸ 0.6667 = 0.5 or ½

Problem 3

Use the information provided to compute the weighted average cost of capital (WACC) for CFK Global. Assume that the firm’s D/E ratio remains constant and does not change from current levels. This WACC will be used for a long-term valuation analysis.

1-yr. T-STRIPS Yield 2.00% 3-yr. T-STRIPS Yield 2.75% 10-yr. T-STRIPS yield 4.20% Historical Risk Premiums:

Stocks – 1-yr T-STRIPS 6.80% Stocks – 3-yr T-STRIPS 6.05% Stocks – 10-yr T-STRIPS 4.60%

Default Premium Table:

B+ A- A

1 Year 2% 0.50% 0.20% 3 Year 3% 0.90% 0.50% 10 Year 6% 1.40% 0.95%

Common Stock Price Common Stock Dividend Common Shares Outstanding Market Value of Debt

Book Value of Equity Book Value of Debt Tax Rate

Current Debt Rating Regression outputs: Std dev of CFK returns

Std dev of market returns Covariance(CFK, Market)

$20.00 $0.50 300,000 $2,000,000 $1,200,000 $1,800,000 25%

A-

0.09 0.04 0.00224

a. What is the cost of equity for CFK?

CFK’s beta = Covariance(CFK,Market) / Variance(Market) = 0.00224 / (0.04)2 = 1.4

Use the CAPM equation: re = Rf + βCFK [E(RM) – Rf] = 4.2% + 1.40 x 4.6% = 10.64%

b. What is the cost of debt for CFK?

rd is the 10-yr yield plus default premium for the corresponding debt rating (A- with 10 year maturity).

4.2% + 1.4% = 5.6%

c. What is the WACC of CFK?

Use the WACC formula with D = $2,000,000 and E= 300,000 x 20 = $6,000,000 WACC = 10.64% x [6/(2+6)] + 5.6% x [2/(2+6)] x (1 – 25%) = 9.03%

d. What if we use an Industry Asset β of 1.2, not CFK’s β from regression output?

This approach is called “bottom up”:

(

βEquity= βUnlevered 1+ (1− t)D) = 1.2 (1+(1-25%)2/6) = 1.5

Use the CAPM equation to find cost of equity:

re = Rf + βCFK [E(RM) – Rf] = 4.2% + 1.50 x 4.6% = 11.1%

Use the WACC formula:

WACC = 11.1% x 0.75+ 5.6% x (1 – 25%) x 0.25 = 9.375%

Problem 4

Boise Cascade had debt outstanding of $1.7 billion and a market value of equity of $1.5 billion. The corporate marginal tax rate is 36%. The current beta is 0.95.

a. Estimate the unlevered beta for the company.

0.95/(1+(1-0.36)(1.7/1.5)) = 0.55

b. How much of the risk in the company can be attributed to business risk and how much to financial leverage risk?

The proportion of the risk of the firm’s equity that can be attributed to business risk is 0.55/0.95 = 58%, while the remainder is due to financial leverage risk.

Problem 5

Biogen, a biotech firm, has a beta of 1.70. It has no debt outstanding.

a. Estimate the cost of equity for Biogen if the T-bond rate is 6.4% and the market risk premium is 5.5%.

0.064 + 1.70(0.055) = 15.75%

b. What effect will an increase in T-bond rates to 7.5% have on Biogen’s cost of equity?

If long term bond rates rise to 7.5%, the market return will be: 5.5% + 6.4% = 11.9% Risk premium: 11.9% - 7.5% = 4.4%

Cost of equity: 7.5+1.7 (11.9-7.5)=14.98%

c. How much of Biogen’s risk can be attributed to business risk?

Since Biogen had no debt, all of its risk is due to business risk.

Problem 6

Novell, which had a market value of equity of $2 billion and a beta of 1.5, announced that it was acquiring WordPerfect, which had a market value of equity of $1 billion and a beta of 1.3. Neither firm had any debt in its financial structure at the time of the acquisition and the corporate tax rate is 40%.

a. Estimate the beta for Novell after the acquisition, assuming that the entire acquisition was financed with equity.

[ 2 / (1+2)] 1.5 + [ 1 / (1+2)] 1.3 = 1.43

b. Assume that Novell had to borrow the $1 billion to acquire WordPerfect. Estimate the beta after the acquisition.

1.43(1+(1-0.4)(1/2)) = 1.86

Problem 7

You are analyzing the beta for Hewlett Packard (HP) and have broken down the company into 4 broad business groups, with market values and unlevered betas for each group. HP had $1 billion in debt outstanding and this debt is allocated to the divisions in proportion to the market value of equity of the divisions. The T-bond rate is 7.5% and the market risk premium is 5.5% HP’s marginal tax rate is 36%.

Business group Market value of equity Beta Mainframes $2 billion 1.1 Personal computers $2 billion 1.5 Software $1 billion 2 Printers $3 billion 1

a. Estimate the beta for HP as a company. Is it equal to the beta estimated by regressing past returns on their stock against a market index? Why or why not?

Firm Value = Value of equity + Value of debt = $ 8 billion + $ 1 billion = $ 9 billion

We will assume that the debt is allocated to the divisions in proportion to the market value of equity of the divisions.

The unlevered for Hewlett Packard as a company can be computed as 1.10 (2.25/9) + 1.50 (2.25/9) + 2.00 (1.125/9) + 1.00 (3.375/9) = 1.275 (assuming that the betas for the divisions are unlevered betas)

Using the debt to equity ratio of 1/8, we can estimate HP’s levered beta to be 1.275 ( 1 + (1-0.36) (1/8)) = 1.377

Since the divisional structure and leverage of Hewlett Packard has probably changed over the years, the beta obtained by regressing past returns of HP against a market index will not be the same as 1.377.

b. Estimate the cost of equity for HP and for each division. Which cost of equity would you use to value the printer division?

Mainframes

Personal Groups

Software

Printers

Levered Beta = 1.1 (1+(1-0.36) (1/8)) = 1.19 Cost of equity = 0.075+1.19(0.055) = 14.03% Levered Beta = 1.5(1+(1-0.36) (1/8)) = 1.62 Cost of equity = 0.075+1.62(0.055) = 16.41% Levered Beta = 2.0(1+(1-0.36) (1/8)) = 2.16 Cost of equity = 0.075+2.16(0.055) = 19.38% Levered Beta = 1.0 (1+(1-0.36) (1/8)) = 1.08 Cost of equity = 0.075+1.08(0.055) = 13.44%

To value the printer division, we would use a cost of equity of 13.44%.

c. Assume that HP divests itself of the mainframe business for $2.25 billion and use the proceeds to buy back stock. Estimate the beta for HP after the divestiture.

We will assume that the mainframe division is sold for its estimated value of $2.25 billion. The value of the remaining divisions is now $ 6.75 billion. After the divestiture, we’d have the unlevered beta equal to:

(2.25/6.75) 1.5 + (1.125/6.75) 2.0 + (3.375/6.75) 1.0 = 1.333

If the proceeds are used to buy back stock, the market value of equity will drop to $5.75 billion. Using the information that HP had debt outstanding equal to $1.0 billion, the levered beta equals 1.333(1+(1-0.36)(1/5.75))=1.48

Problem 8

You run a regression of monthly returns of Amgen, a large biotech firm, on returns on the S&P500 index and come up with the following output.

RAmgen = 3.28% + 1.65 RS&P500 R2 = 20%

The T-bond rate is 4% and market risk premium is 5%. There are 265 million shares outstanding and the current market price is $30/share. The firm has a debt to equity ratio of 3%. The firm’s tax rate is 40%.

a. What would an investor in Amgen’s stock require as a return?

The regression beta is 1.65

The expected return over the next year = 0.04 + (1.65)(0.05) = 12.25%.

b. What proportion of this firm’s risk is diversifiable?

(1-R2) = 80% of this firm’s risk is diversifiable

c. Amgen plans to issue $2 billion in new debt and acquire a new business for that amount with the same risk level as the firm’s existing business. What will be beta be after the acquisition?

The current unlevered beta = 1.65/(1+(1-0.4)(0.03)) = 1.62.

The new leverage ratio: [2000+0.03(265)(30)]/(265)(30) = 0.2816

The new levered beta becomes 1.62(1+(1-0.4)(0.2816)) = 1.89

Problem 9

Calculate the unlevered beta for each comparable firm: Levered beta / [1+(1-t)D/E]

Company Genoxys Inc

Lovarmaceutical Inc Fanepill Corp

Udo Laboratory Inc Refillobos Corp Average

Beta (levered) 1.6 1.9 1.5 1.3 1.5

D/E ratio Tax 0.5 40% 1.0 35% 0.4 38% 0.2 40% 0.3 35%

Unlevered beta 1.2308 1.1515 1.2019 1.1607 1.2552 1.2000

Beta of RWP: Unlevered beta x [1+(1–t)D/E] = 1.2 x [1+(1–40%)(600/4000)] = 1.3080

Cost of equity: re = Rf + β (RM – Rf) = 3% + 1.3080 (7% – 3%) = 8.2320% Cost of debt: 252.5725 = 1000 / (1+YTM)40 àrd = YTM x 2 = 7%

WACC = re [E/(D+E)] + rd (1–t) [D/(D+E)]

= 8.2320% (4000/4600) + 7% (1 – 40%) (600/4600) = 7.7061%

RAISING CAPITAL TUTORIAL

Problem 1 – IPO returns and costs

Avista is about to go public by issuing 10 million shares at an offer price of €25 per share. The underwriter will charge a 7% underwriting fee. On the first day of trading Avista opens with a stock price of €28.

a) What is the initial return of the offering?

b) How much money does Avista raise?

c) What is the total cost (direct and indirect) of the offering for Avista?

Solution

a) What is the initial return of the offering?

b) How much money does Avista raise?

c) What is the total cost (direct and indirect) of the offering for Avista?

Problem 2 – Hot, normal and cold IPOs

Suppose there are three equally frequent types of IPOs: hot, normal, and cold. Hot IPOs are oversubscribed 10 to 1 (there are ten subscriptions for each offered share) and have an initial return of 60%. Normal IPOs are oversubscribed 4 to 1 and return 10% initially. Cold IPOs are not oversubscribed and decline 10% in value initially. Assume that oversubscribed issues are allocated on pro rata basis.

a) What is the average initial return in the IPO market?

b) What average return can you expect if you start investing in IPOs, and cannot distinguish between the exact types?

Solution

a) What is the average initial return in the IPO market?

b) What average return can you expect if you start investing in IPOs, and cannot distinguish between the exact types?

INVESTMENT DECISION RULES

Problem 1

Calculate the payback period for the E-print project with the following cash flows

Year	CF	Cumulative
0	-$18,000	-18,000
1	6,500	-11,500
2	7,000	-4,500
3	7,500	3,000
4	8,000

Payback period = 2 + ( 4500 / 7500 ) = 2.6 years

Problem 2

Calculate the discounted payback period for the E-print project assuming the discount rate is 14%.

Year	CF	Discounted CF	Cumulative
0	-$18,000	-$18,000.00	-$18,000.00
1	6,500	5701.75	-12,298.25
2	7,000	5386.27	-6,911.98
3	7,500	5062.29	-1849.69
4	8,000	4736.64	2886.95

Discounted payback period = 3 + ( 1849.69 / 4736.64 ) = 3.39 years

Problem 3

Required return: 18%. Calculate IRR given IRR is between 21% and 23%.

Year	Cash flow
0	-$30,000
1	13,000
2	19,000
3	12,000

“True math” (IRR equation):

0= -C0 +1C1r + (1+r)2 + (1+r)3

0 30 000

, , ,

= , + + +

13 000 19 000 12 000 1+r (1+r)2 (1+r)3

where IRR = r

Trial and error:

r = 21%, NPV = 494.7445 r = 23%, NPV = -423.6250

= 21% + [ 494.7445 / (494.7445 + 423.6250) ] (23% – 21%) = 22.08%

Excel:

A1 -30000 A2 -13000 A3 -19000 A4 -12000

A5 =IRR(A1:A4)

Notes on calculators:

TI BA II plus

CF0= –30,000→ENTER→↓ → C01= 13,000→ ENTER→↓ →F01=1→↓ → C02= 19,000→ ENTER→↓ →F02=1→↓ → C03= 12,000→ ENTER → F03=1 Calculate IRR: →IRR →CPT

Calculate NPV: →NPV →input I=18→ ENTER →↓ → CPT

TI 83

Finance menu

IRR(–30000, {13000,19000,12000}) NPV(18, –30000,{13000,19000,12000})

Problem 4

WorldTravelers Inc considers investing in a far-east expedition project. The project costs $110,000 upfront and expects to generate nine annual cash inflows of $24,000 each year.

0 1 2 8 9 | | | … … | |

-110,000 24,000 24,000 24,000 24,000

a. Calculate NPV at 8% required return

1 2

C C

3 9

C C

NPV = -C0 +1+ r + (1+ r)2 + (1+ r)3 +...(1+ r)9

2 3 9

(1+8 ) (1+8 ) (1+8 )

1+8

-110,000 + 24,000 + 24,000 + 24,000 +... 24,000 = 39,925.31

b. Calculate NPV at 20% required return

NPV= -13.256.80

c. At what discount rate would you be indifferent between accepting and rejecting the project?

This question asks for IRR. Use trial and error or any other methods to get 16.15%.

Problem 5

Matt is analyzing two mutually exclusive projects of similar size and has prepared the following data. Both projects have 5 year lives.

Net present value Payback period

Average accounting return Required return

Required AAR

Project A $17,090 2.56 years 9.3% 8.3% 9.0%

Project B $14,693 2.51 years 9.6% 8.0% 9.0%

Matt has been asked for his best recommendation given this information. What should be his recommendation?

His recommendation should be to accept project A and reject project B based on their net present values.

Problem 6

Kalissa Productions can purchase a new surveillance truck for the hit TV series “Exposed.” The truck’s price is $3,600. The truck has a two-year life, will produce a cash flow of $600 in the first year and $4,200 in the second year. The interest rate (discount rate) is 15%.

0 1 2

-3600 600 4200

a. Calculate the project's payback assuming steady cash flows.

Cumulative cash flows after the first year: -3600 + 600 = -3000 Cumulative cash flows after the second year: -3000 + 4200 = 1200 Project pays back between the first and second year.

Payback = 1 + 3000 / 4200 = 1.7143

b. Calculate the project’s profitability index

PI = PVCFs / Initial investment = ( 600 / 1.15 + 4200 / 1.152 ) / 3600 = 1.0271

c. Calculate the project's NPV.

NPV = -3600 + 600 / 1.15 + 4200 / 1.152 = 97.54

d. Calculate the project's IRR. Hint: It’s between 16% and 17%.

Trial and error:

r = 16%, NPV = 38.5256 r = 17%, NPV = -19.0226

= 16% + [ 38.5256 / (38.5256 + 19.0226) ] (17% – 16%) = 16.67%

Problem 7

You are considering two mutually exclusive projects with the following cash flows. Will your choice between the two projects differ if the required rate of return is 8% rather than 11%? If so, what should you do?

Year Project A 0 -$240,000 1 $ 0 2 $ 0 3 $325,000

Project B -$198,000

$110,800 $ 82,500 $ 45,000

Yes. Select A at 8% and B at 11%.

At 8%: NPVA=17995.48 NPVB=11045.50

At 11%: NPVA=-2362.80 NPVB= 1682.28

Problem 8

You would like to invest in the following project.

Year Cash Flow 0 -$55,000 1 $30,000 2 $37,000

Victoria, your boss, insists that only projects that can return at least $1.10 in today’s dollars for every $1 invested can be accepted. She also insists on applying a 10% discount rate to all cash flows. Based on these criteria, should you accept the project?

PI = ( 30000 / 1.1 + 37000 / 1.12 ) / 55000 = 1.05

Reject the project because the PI is 1.05. The minimum Victoria requires is 1.10.

Problem 9

The Ziggy Trim and Cut Company can purchase equipment on sale for $4,300. The asset has a three-year life, will produce a cash flow of $1,200 in the first and second year, and $3,000 in the third year. The interest rate is 12%. Calculate the project's Discounted Payback and Profitability Index assuming end of year cash flows. Should the project be taken? If the Average Accounting Return was positive, how would this affect your decision?

Time 0 – Cash flows = $-4,300, Present Value of Cash flows = $-4,300

Time 1 and 2 – Cash flows = $1,200 each period, Present Value of Cash flows = $2,028.06 for both periods, Sum of Present Value of Cash flows = $-2,271.94 at the end of time 2

Time 3 – Cash flows = $3,000, Present Value of Cash flows = $2,135.34, Sum of Present Value of Cash flows = $-136.60

Discounted Payback cannot be calculated as NPV < 0; NPV = $-136.60

PI = ∑CF /Initial Investment = $4,163.40/$4,300 = 0.968 = 0.97

Both measures indicate rejection. A positive accounting rate of return should not change the decision. DPP and PI indicate that the cost of capital is not being covered.

Problem 10

You are analyzing the following two mutually exclusive projects and have developed the following information. What is the incremental IRR? Hint: It’s between 17% and 18%.

Year Project A Cash Flow 0 -$84,500

1 $29,000 2 $40,000 3 $27,000

Project B Cash Flow -$76,900

$25,000 $35,000 $26,000

Difference -$7,600

$4,000 $5,000 $1,000

Use trial and error:

r = 17%, NPV = 95.7417 r = 18%, NPV = -10.6165

= 17% + [ 95.7417 / (95.7417 + 10.6165) ] (18% – 17%) = 16.67%

IRR = 17.9%

Problem 11

IBM is considering 2 alternative production methods for a new hand-held computer. Costs (in million $) and lives associated with the equipment necessary for each method are:

Year Method 1 Cost Method 2 Cost 0 900 800

1 20 80 2 20 80 3 20 80

4 80 .

The relevant opportunity cost of capital is 10%.

a) What method should IBM choose if they do not replace the equipment when it wears out. NPVM1 = –900 – 20 / 1.1 – 20 /1.12 – 20/1.13

= –900 – 20 ADF(10%,3) = –900 – 20 x 2.4869 = –949.74 NPVM2 = –800 – 80 / 1.1 – 80 /1.12 – 80/1.13 – 80/1.14

= –800 – 80 ADF(10%,4) = –800 – 80 x 3.1699 = –1053.59 Use method 1 (lower NPV of costs)

b) What method should IBM choose if they replace the equipment when it wears out? We need to find the equivalent annual cost (EAC) for each method.

Method 1: Find the payment of a 3 year annuity: NPVM1 = EACM1 x ADF(10%,3) à EACM1 = NPVM1 / ADF(10%,3) = -949.74 / 2.4869 = -381.90

Method 2: Find the payment of a 4 year annuity: NPVM2 = EACM2 x ADF(10%,4) à EACM2 = NPVM2 / ADF(10%,4) = -1053.59 / 3.1699 = -332.38

IBM should choose method 2 (lower equivalent annual cost)

c) What method should IBM choose if matching cycle criteria is used to evaluate the 2 methods?

Matching cycle for projects with 3 and 4 years of life should be 12 years.

0 1 2 3 4 5 6 7 8 9 10 11 12 | | | | | | | | | | | | |

M1 -900 -20

M2 -800 -80

-20 -20

-900 -20 -20

-80 -80 -80

-800 -80

-900 -20 -20

-80 -80

-20 -20

-900 -20 -20 -20

-800 -80 -80 -80 -80 -80

NPVM1 = – 949.74 – 949.74 / 1.13 – 949.74 / 1.16 – 949.74 / 1.19 = -2602.18 NPVM2 = –1053.59 –1053.59 / 1.14 –1053.59 / 1.18 = -2264.71

IBM should choose method 2 (lower cost)

CAPITAL BUDGETING

Problem 1

You are an analyst for a sporting goods corporation that is considering a new project that will take advantage of excess capacity in an existing plant. The plant has a capacity to produce 50,000 tennis racquets, but only 25,000 are being produced currently, although sales of the rackets are increasing 10% a year. You want to use some of the remaining capacity to manufacture 20,000 squash rackets each year for the next 10 years (which will use up 40% of the total capacity), and this market is assumed to be stable (no growth). An average tennis racquet sells for $100 and cost $40 to make. Assume that the production of tennis racquets will be cut back when you run out of capacity. The corporate tax is 40% and the discount rate is 10%. Is there an opportunity cost involved? If so, how much is it?

Year Potential sales 1 27,500 2 30,250 3 33,275 4 36,603 5 40,263 6 44,289 7 48,718 8 50,000 9 50,000 10 50,000

Lost sales 0

250 3,275 6,603 10,263 14,289 18,718 20,000 20,000 20,000

Lost profits 0

9,000 117,900 237,690 369,459 514,405 673,845 720,000 720,000 720,000

PV lost profits 0

7,438 88,580 162,345 229,405 290,368 345,789 335,885 305,350 277,591

Opportunity cost = $2,042,753

This is based on the assumption that the production of tennis racquets will be cut back when you run out of capacity and that you lose $36 per racquet not sold (100 – 40 x 0.4)

Problem 2

Tropicana hires you to value orange groves that produce 1.6 billion oranges per year. Oranges currently sell for $0.10 per 100. Assuming no unexpected hard freezes occur, this level of production can be sustained with normal maintenance. Variable costs are $1.2 million per year. Fixed costs are negligible. The nominal discount rate is 18%, and the inflation rate is 10%.

a. Assuming that orange prices and the variable costs change with inflation, what is the value of the groves? (ignore taxes and depreciation)

Unit price = 0.1 / 100 = 0.001

Revenues from sales = 1.6 billion oranges x $0.001 each = $1.6 million Expenses = $1.2 million

Operating cash flow = 1.6 – 1.2 = $0.4 million per year (ignore depreciation & taxes)

Could we treat the $0.4 million as perpetuity and divide it by 0.18 to get NPV? No. The $0.4 million is in current dollar and does not reflect future inflation. The 18% discount rate is a nominal discount rate.

So we cannot divide a real cash flow by a nominal discount rate.

Find real discount rate using the Fisher equation: (1+18%) / (1+10%) – 1 = 7.2727% PVperpetuity = $0.4 million / 0.072727 = $5.5 million

Or you can use the dividend discount model (nominal cash flows are real cash flows growing at 10% until forever) to discount the cash flows.

D1 = 0.4 million x (1+10%) = 0.44 million

P0 = D1 / (r – g) = $0.44 million / (0.18 – 0.10) = $5.5 million

b. Suppose prices increase at the inflation rate, but costs increase at half the inflation rate. What is the value of the orange groves?

If costs increase by only 5% per year, then in real terms, the costs are decreasing (because inflation is 10%).

Using nominal cash flows:

Next year’s revenues = $1.6 million x (1+10%) = $1.76 million NPV of future revenues = $1.76 million / (0.18 – 0.10) = $22 million

Next year’s costs = $1.2 million x (1+5%) = $1.26 million

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