Business 35801

Corporation Finance for Executives

Professor Amit Seru

Sample Midterm

Instructions: You have 1 hour and 40 minutes to complete this exam. The total possible score you can
achieve is 125. Make sure to read the questions carefully and budget your time. Do not turn this page until
instructed.

1. True/False- Short Explanation Questions (25 points)

Indicate whether the statements below are true or false. If the answer is true, explain why
it is true. If the answer is false, explain why it is false. Feel free to give examples or
counter examples. Although there may be a variety of reasons answers are true or false, I
am looking specifically for reasons discussed in the lectures, readings, and cases of this
course.

(a) Two firms have the exact same cash flows from the project on the asset side and those
cash flows have identical covariance with the market. These firms have the same
NPV (5 points)

True: Discount rate of such firms r_A will be the same since they have same
covariance with the market. Since cash flows are the same, value will be the same.

(b) Does Not Exist Corp (DNEC) is a firm with operating assets. As DNEC’s leverage
increases, the empirical data show that both its required return on equity (rE) and
required return on debt (rD) increase. Therefore, as leverage increases, DNEC’s value
decreases (5 points)

False. Discount rate r_A is independent of the leverage of the firm. Thus value of the
firm should not change with leverage.
(c) Under CAPM, the higher the volatility of stock returns the higher the expected returns
demanded by investors (5 points)

False. CAPM tells us that only the risk that is correlated with the systematic risk is
priced by investors. Thus, if a given stock has high volatility but only small
systematic risk (think California REIT in the Beta Management case), its expected
returns will be lower.

(d) You are trying to estimate cost of capital for a project taken by Firm X. There are no
taxes. Based on business risk of Firm X's project you identify three comparables --
Firm a, Firm b and Firm c. The data tells you that the equity beta βE_a = 0.90, βE_b =
1.00 and βE_c = 1.10 and the market value of Debt/(Debt+Equity) ratio of the three
firms are 25%, 35% and 50% for firms a, b and c respectively. If the βD_a = βD_b
=βD_c=0, the asset beta for Firm X's project is 1.00. (10 points).

False. The asset beta for Firm A is 0.90*(1-25%)+0 = 0.675. Similarly the asset beta
for Firm B is 0.65 and Firm C is 0.55. The asset beta for Firm X should be picked to
be average across comparables (to reduce idiosyncratic noise in the estimates --
based on law of large numbers). Doing so gives Asset beta for Firm X's project =
0.625
2. Diving right into Free Cash Flows (25 points)
You are given the information below from the projected balance sheet and income
statement of the Last Gasp Scuba Diving School. The firm’s cost of capital (rA) is 10%,
and the corporate tax rate is 40%.

a.) Find the firm’s expected free cash flows for 2006-2010, excluding any terminal value.
Assume that current assets and current liabilities had the same values in 2005 as they do
in the 2006 projections. Assume no new capital expenditures. Space is provided in the
table for your calculations and answers. (15 points).
b.) Suppose that the firm’s free cash flows are constant from 2010 to eternity. Calculate
the discounted value of the firm’s cash flows from 2011 to eternity as of the end of the
year 2010. (10 points)

The question tells us that this will be a constant perpetuity. Thus terminal value
standing in 2010 for cashflows that will be constant at 204 (cashflows in 2010)
forever will be:

204
𝑃𝑉!"#" =   = $2040
0.1
3.) Can you dance like CAPM? (25 points)

Your uncle, Ryan-with-a-Secret, who produces the show “Dancing with the Stars” has
asked you for some financial advice. His retirement savings are currently invested as
follows: $30,000 in the risk-free asset and $70,000 in GM stock. He wants to know if this
is a sensible portfolio. You decide to analyze it based on the CAPM model.

You look in a Beta Book and find that GM stock has a Beta 1.20 and the R2 of the
regression is 0.30.

a.) If rf is 7% and the expected excess return on the market (rm – rf) is 8%, what is the
expected return on his portfolio? (7 points)

The beta of the portfolio is:

30,000 70,000
𝛽= ∗0+ ∗ 1.2 = 0.84
100,000 100,000

Therefore the expected return on the portfolio is E[rp] = 7% + 0.84 * 8% = 13.72%.

b.) Suggest a different portfolio for your uncle that has the same expected return as the
old portfolio but is efficient (i.e., has the smallest variance possible for that level of
expected return). (10 points)

Efficient, or optimal, portfolios are combinations of the market portfolio and the
risk free asset. A portfolio with the same expected return as the portfolio in part (a)
must have a beta of 0.84.

We can construct this by investing xf = 16% in Treasury bills and xM = 84% in the
market, since the beta of an efficient portfolio, which we will denote βep here, is βep
= xf *0 +xM*1 = xM.
c.) If the market return has a standard deviation of 22%, compute the variance and
standard deviation of his current portfolio (using information provided by the R2
value) and compare it to the variance and standard deviation of the portfolio you are
suggesting in part (b). (8 points)

Let “ep” denote the efficient portfolio and “p” denote the current portfolio. Then:

𝝈ep = 𝟏 − xf ∗ 𝝈𝑴 = 𝟎. 𝟖𝟒 ∗ 𝟎. 𝟐𝟐 = 𝟎. 𝟏𝟖𝟒𝟖

The standard deviation of the current portfolio return is

𝝈p = 𝟎. 𝟕 ∗ 𝝈𝑮𝑴

To determine this, we need to find σGM. Since the R2 of the regression of GM's
return on the market return is 0.3, we know that:

!
𝛽!" 𝝈𝟐𝑴  
  = 𝟎. 𝟑
𝝈𝟐𝑮𝑴

𝟏.𝟐𝟐 𝟎.𝟐𝟐𝟐 𝟏.𝟐∗𝟎.𝟐𝟐

so that 𝝈𝟐𝑮𝑴
= 𝟎. 𝟑 and thus 𝝈𝑮𝑴 = 𝟎.𝟑
= 0.482

As a result, 𝝈p = 𝟎. 𝟕 ∗ 𝟎. 𝟒𝟖𝟐 = 𝟎. 𝟑𝟑𝟕𝟒.

The efficient portfolio has a standard deviation of 0.1848 and Ryan's current
portfolio has a standard deviation of 0.3374. However both portfolios have the same
expected return!
4. Mining to Extract Betas (25 points)
Gold et al, a mining conglomerate, is considering an $100 million investment in a
newcopper mine that will create cash flows of $100 million in year 1 and grow at 10%
until the end of time. The main competitor of Gold et al is Silver. Both of these
companies mine a similarly broad range of minerals, including copper and gold.
In determining the relevant discount rate at which to discount the cash flows for the new
copper factory, Gold has researched several other corporations, including the Mine-it-all
(a company mining both copper and gold) and the Copper Corp., which mines only
copper. The CEO of Gold et al compiled the following historical information:

Firm Debt Values Equity Values Betas

Book Market Book Market Equity Debt
Gold et al 300 325 400 470 1.0 0
Silver 80 100 125 150 1.5 0
Mine-it-all 70 50 50 100 2.5 0
Copper Corp 20 25 50 75 2.0 0

Assume all debt betas are zero, that the risk-free rate is 5%, and the market risk premium
is 10%.

a. What is the proper comparable company for valuing the new copper mine? Why are
others that you rejected not good comparables? (5 points)

Copper Corp is the only comparable since it is the only firm that mines only copper.
Gold et al., Silver and Mine-it-all are not good comparables since they have “several
other” lines of business besides copper.
b. Compute 𝛽!  for the comparable company in part a by unlevering the equity beta and
debt beta. (10 points)

Since we have only one comparable firm, step 3 needs to be applied only to this firm.
Using market values of D and E gives us:

𝐸 𝐸 7.5
𝛽! = 𝛽! + 𝛽! = 2. = 1.5
𝐸+𝐷 𝐸+𝐷 100

c. Calculate the proper discount rate for valuing the copper mine project and NPV of the
investment (10 points)

Applying CAPM

𝑟! = 𝑟! + 𝛽! 𝑟! − 𝑟! = 5% + 1.5 10% = 20%

To calculate NPV note that FCF at t=0 is -100M and FCF from t=1 are a growing
perpetuity starting with FCF at t=1 of 100M and “g” of 10%. Using the discount
rate computed above and growing perpetuity formula:
𝟏𝟎𝟎
𝑵𝑷𝑽 = −𝟏𝟎𝟎𝑴 + 𝟐𝟎%!𝟏𝟎% = 𝟗𝟎𝟎𝑴
5. A Problem of Acquisition (25 points)
In 1989, General Motors (GM) was evaluating the acquisition of Hughes Aircraft
Corporation. Recognizing that the appropriate WACC for discounting the projected cash
flows for Hughes was different from General Motors' WACC, GM assumed that Hughes
was of approximately the same risk as Lockheed or Northrop which had low-risk defense
contracts and products that were similar to those of Hughes. Specifically, assume:

Firm βE D/E
GM 1.20 0.40
Lockheed 0.90 0.90
Northrop 0.85 0.70

• GM's target D/E after acquisition of Hughes is 1

• Hughes’s expected after-tax real asset cash flow next year = $300 million each
year in perpetuity
• Corporate tax rate = 34%
• rm = 11.7% and rf = 4%
• Debt is riskless, so that the appropriate rD = rf, and βD = 0.

a.) Analyze the Hughes acquisition (which never took place) by first computing the betas
of the comparison firms, Lockheed and Northrop, as if they were all equity financed (i.e.
by unlevering the betas). (5 points).

Answer:
𝐸 𝐷
𝛽! = 𝛽! + 𝛽
𝐸+𝐷 𝐸+𝐷 !

Since the appropriate discount rate for the debt is the riskless rate, all debt betas are zero (
!
β D = 0 ). This implies that 𝛽! = !!! 𝛽! , from which we get
1
𝛽! = 𝛽
1 + 𝐷/𝐸 !

Therefore:
1
𝛽!!"#$!!!" = 0.9 = 0.474
1 + 0.9
1
𝛽!!"#$!!"# = 0.85 = 0.5
1 + 0.7
b.) Compute βA the beta of the operating assets of the Hughes acquisition by taking the
average of the betas of the operating assets of Lockheed and Northrop. (5 points).

0.474 + 0.5
𝛽! = = 0.487
2

c.) Compute the βE for the Hughes acquisition at the target debt level. (5 points).

Answer: Relever using the following formula:

𝐸 𝐷
𝛽! = 𝛽! + 𝛽
𝐸+𝐷 𝐸+𝐷 !
Since the appropriate discount rate for the debt is the riskless rate, all debt betas are zero (
E
β D = 0 ). This implies that β A = β E from which we get
E+D
1 1
𝛽! = 𝛽! = 𝛽
1 + 𝐷/𝐸 1+1 !

𝛽! = 2𝛽! = 2 ∗ 0.487 = 0.974

d.) Compute the value of Hughes using the most appropriate method. (5 points).

Answer: First, note that it is appropriate to use WACC because GM has a target D/E
ratio for the combined firm after the acquisition. To compute WACC, we need all the
inputs to the formula:
E D
WACC = rE + (1 − τ C )rD .
E+D E+D

Since D/E =1, for every $1 of equity there is $1 of debt in the capital structure of the
firm, so D/(D+E) = E/(D+E) = 0.5.

The required return on equity at GM's target capital structure after the acquisition is:
 rE = 4%+0.974(11.7% - 4%) = 11.5%

Using the assumption that all debt is riskless, rD = rf = 4%.

We therefore have:

WACC =.5(11.5%)+.5(1-.34)(4%) = 7.07%.

PV = $300M / 0.0707 = $4.24 billion.

e.) Now suppose that GM decides it does not have a target D/E ratio for the combined
firm after the acquisition. Instead, GM plans to use $3 billion of fixed perpetual debt as
external financing for the acquisition. What method is now most appropriate for valuing
Hughes? What is the value of Hughes using this method? (5 points).

Answer: With fixed perpetual debt, the APV method is most appropriate. First, compute
the value of the operating assets of the Hughes acquisition. Next, compute the present
value of the tax shield. Finally, add the two numbers.

To compute the value of Hughes if all-equity financed, we must first compute the
market’s expected return for the unlevered Hughes assets using the asset beta and the
security market line formula:
𝑟! = 4% + 0.487 11.7% − 4% = 7.75%

The value of Hughes if all-equity financed is, therefore,

300𝑀
𝑉! = = $3.871  𝑏𝑖𝑙𝑙𝑖𝑜𝑛
0.0775

To this, we must add the value of the tax shields. Fixed perpetual debt of $3 billion
generates a tax shield with a present value of tcD = (0.34*$3000M)=$1,020M.

The total value of the firm is therefore $3,871M+1,020M= $4,891M.