This preview shows page 1. Sign up to view the full content.
Unformatted text preview: UNIVERSITY OF SOUTHERN CALIFORNIA
Marshall School of Business
INTERNATIONAL FINANCIAL MANAGEMENT
FBE 436
Aris Protopapadakis
ANSWERS TO PROBLEM SET # 3: Problem #3.1:
Below is the relevant cash flow report for a project. If the corporate tax rate is 34%, the
Debt/Equity ratio is 1.00, the Cost of Debt is 11.0% and the unlevered Cost of Equity is 22.0%
for this project, what is the Net Present Value? What is the current beta of the firm’s equity,
assuming that Rf is 6.0%, and the market risk premium, ERPm, is 8.0%. Year 1 Free Cash Flow 2 3 2,772.00 Interest Tax Shield 3,102.00 3,036.00 340.00 400.00 410.00 Answer: Below are the discounted cash flows:
PV of the Cash Flows
Year 1 Free Cash Flow 2 3 2,272.13 Interest Tax Shield 2,084.12 306.31 324.65 1,671.95
299.79 Total Present Value: $6,958.94
Free Cash Flow is discounted at 22% CoE(u) and the interest tax shields are discounted at
11% CoD.
We can infer the current equity beta by first calculating the levered CoE, CoE(L), and then
reversing the CAPM equation. Reverse the CoE(u) equation to get: CoE (L ) = CoE (u ) + [CoE (u ) − CoD ](1 − τ c ) D
.
E FBE 436
Answers to Problem Set #3 This gives CoE(L) = 29.26% From the CAPM we have 29.26% = 6% + β(L)8%, which gives,
β(L) = 2.9075. Problem #3.2a:
Given the information below, what is the Cost of Equity that should be applied to the free cash
flows?
CoE(levered) CoD(levered) Debt/Equity 28.00% 10.00% 1.25 Corporate
Tax Rate
34.0% Risk Free
Rate
4.50% Market Risk
Premium
6.00% The CoE(u) is the applicable discount rate. Use the formula to get: 19.86% Problem #3.2b:
Ralphson is an allequity firm, and has a Japanese subsidiary. Given the information below,
what is the Cost of Equity that should be applied to the Yen free cash flows of its subsidiary?
The betas are refer to the firm betas
Beta World Beta Japan 0.45 1.20 E(RP) –World
In ¥
6.0% E(RP) –Japan
In ¥
5.0% RF In ¥
1.05% The data are available to evaluate the CoE using the IAPM. Since this is an allequity firm, the
resulting CoE is CoE(u).
CoE = 1.05% + 0.45x6.0% + 1.20x5.0% = 9.75% 2 FBE 436
Answers to Problem Set #3 Problem #3.3:
The following cash flows are expected from the UK subsidiary, Beckham Ltd. The UK
corporate tax rate is 45%. For year 3 and thereafter, quantity sold is expected to grow at 2.5%,
prices at 4%, and CoGS at 6.6%. Capital Expenditures and Net Working Capital also grow at
6.6%. Furthermore, Rf = 7.0%, CoD = 11%, E(RPM) = 6.0%, the firm’s beta = 1.8, and the
debttoequity ratio is 1.4. What is the value of BJC Ltd. in £s?
Year: 1
3,000
£150
£105 2
3,200
£ 165
£ 115 £ 10,000 £ 10,660 Interest
Taxable Income
After Tax Income £ 27,500 £ 27,500 Year:
Capital Expenditures
Changes in NWC 1
£25,000.00
£2,000.00 2
£26,650.00
£2,132.00 Quantity Sold
Price
Unit Costs
Sales
Cost of Goods Sold
Depreciation
EBIT Expand the table above to three years in order to compute the terminal values. Use the growth
rates given above to compute the year3 cash flows. Year: 1
3,000
£150.00
£105.00
£450,000.00
£315,000.00
£ 10,000.00
£135,000.00 2
3,200
£ 165.00
£ 115.00
£528,000.00
£368,000.00
£ 10,660.00
£160,000.00 3
3,280
£171.60
£119.60
£562,848.00
£392,288.00
£11,363.56
£170,560.00 Interest
Taxable Income
After Tax Income £27,500.00
£97,500.00
£53,625.00 £27,500.00
£121,840.00
£67,012.00 £27,500.00
£131,696.44
£72,433.04 Year:
Capital Expenditures
Changes in NWC 1
£25,000.00
£2,000.00 2
£26,650.00
£2,132.00 3
£28,408.90
£2,272.71 Quantity Sold
Price
Unit Costs
Sales
Cost of Goods Sold
Depreciation
EBITDA 3 FBE 436
Answers to Problem Set #3 From the levered beta and the CAPM we have CoE(L) = 17.80%. From this, CoE(u) = 14.84%.
FCF has to be discounted at 14.84% and the interest tax shield has to be discounted at 11%
Use FCF’s definition including cap expenditures and changes in NWC to get the table below. Year: 3 £64,015.00 £68,239.99 £12,375.00 Terminal Value for
TFCF
Terminal Value for
Tax Shields
(discounted at
CoE(u))
Present Value of
FCF
Present Value of
Tax Shields 2 £51,750.00 TFCFs to be
discounted at CoE(u)
Interest tax shields 1 £12,375.00 £12,375.00 £827,973.56 £83,379.33
£48,537.98 +
£627,792.94
£10,043.83 +
£63,220.56 £45,061.99
£11,148.65 (1) Compute the projected Year3 cash flows; they are entered under Year 3.
CashFlow_Y3 = CashFlow_Y2 *(1+g)
(2) Compute the perpetuity value of these cash flows. These use the perpetuity with growth
formula, and they are the terminal values for the respective cash flows. The perpetuity
CashFlow _ Y 3
formula gives the Terminal Values for Year 2.
CoE (u ) − 0.066
(3) Present Value all the cash flows according to the year
Alternatively, the Year 0 present values for the perpetuities can be calculated directly from
2 ⎞
CashFlow _ Y 3 ⎛
1
*⎜
⎜ 1 + CoE (u ) ⎟ .
⎟
CoE (u ) − 0.066 ⎝
⎠
Total Value = £749,595.31. The value of the project without the terminal value = £114,792.44. 4 FBE 436
Answers to Problem Set #3 Problem #3.4:
Consider the FCFs and tax shields (in ¥1,000). Use the market information given below. What
is the $value of these cash flows (translating to $s before valuing)?
Cash Flows in 1,000 Yen
1
2
¥ 1,400,000
¥ 1,400,000
¥ 50,000
¥ 62,000 Year
FCF
Int Tax Shields FX Forecasts:
125.00
118.00 ¥/$ 3
¥ 1,750,000
¥ 65,000 115.00 US Market Data:
D/E Ratio
Corp Tax Rate
Risk_Free
E(RPM)
CoD
Beta 1.20
46%
2.20%
5.50%
7.20%
2.30 The implied CoE(L) and CoE(u) for the US market are, respectively, 14.85% and 11.84% Year
FCF
Int Tax Shields Cash Flows in $
1
2
$11,200,000
$11,864,407
$400,000
$525,424 3
$15,217,391
$565,217 Discount by the appropriate discount factors to get: $31,665,673.
Year
PV(FCF)
PV(Int Tx Shield) 1
$10,014,128
$373,134 2
$9,484,976
$457,215 3
$10,877,411
$458,808 PY(Total) $10,387,262 $9,942,191 $11,336,219 5 FBE 436
Answers to Problem Set #3 Problem #3.5:
Consider the FCFs and tax shields (in ¥1,000). Use the market information given below. What
is the PV of these cash flows in ¥? What is the translated value in $s.?
Cash Flows in 1,000 Yen
1
2
¥ 1,400,000
¥ 1,400,000
¥ 50,000
¥ 62,000 Year
CFC
Int Tax Shields 3
¥ 1,750,000
¥ 65,000 Japanese Market Data:
D/E Ratio
Corp Tax Rate
Risk_Free
E(RPM)
FX Rate
CoD
Beta 1.20
46%
0.50%
5.41%
125 ¥/$
5.42%
2.30 The implied CoE(L) and CoE(u) for the Japanese market are, respectively, 12.94% and 9.98%
Discount by the appropriate discount factors to get: ¥ 3,904,521, which translates into
$31,236,172. Year
PV(CFC)
PV(Int Tx Shield)
PY(Total) Cash Flows in 1,000 Yen
1
2
¥ 1,272,940
¥ 1,157,412
¥ 47,431
¥ 55,792
¥ 1,320,371 6 ¥ 1,213,204 3
¥ 1,315,461
¥ 55,486
¥ 1,370,947 FBE 436
Answers to Problem Set #3 Problem #3.6:
Arena Enterprises is considering a Greenfield investment in an unnamed emerging market in the
same line of business. The operation will supply local markets. The UScalculated beta for
Arena’s business is 2.80. Below are some data for the US and the Erehwon (an emerging
market) index returns. What would be a reasonable estimate for the beta of this new direct
foreign investment, from the point of view of US investors?
Would your answer be affected if the investment were a manufacturing facility built to supply
the US market exclusively?
US Market Returns
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15 Erewhon Market Returns 0.05404
0.04397
0.21570
0.39305
0.19710
0.12424
0.33244
0.13923
0.10223
0.02427
0.05886
0.24168
0.03351
0.35500
0.42762 0.48405
0.48861
0.58540
0.10285
0.53323
0.61405
0.22483
0.77756
0.11051
0.15833
0.11867
0.15495
0.18853
0.16877
0.47577 The question suggests that there aren’t enough quality data to estimate the beta directly. Apply
Std (Foreign )
the beta equation, β Foreign = Corr (Foreign, US )
, to get the beta of the Erewhon
Std (US )
market. The correlation between the US and Erewhon returns is 0.1356. Std(US) = 0.2342 and
Std(For) = 0.3867. Then the country beta = 0.1356*0.3867/0.2342 = 0.224.
Apply the equation, bProject,Local = bProject,US xbForeign Country , to get a reasonable estimate of
the project beta: 0.224*2.8 = 0.627.
Var (FCountry )
Var (U .S .)
If the operation was to supply the US market only, then it is hard to see why the beta would be
anything other than 2.80! Presumably the FX risk can be hedged, and the operation would not be
subject to most of the local market conditions and shocks (except for the cost of labor). β FCountry = Corr (FCountry ,U .S .) 7 FBE 436
Answers to Problem Set #3 Problem #3.7:
Below are available market data on bond yields and inflation forecasts for 5 years. You are
asked to provide marketbased FX rate forecasts suitable for translating future cash flows into $s,
to be used for valuation purposes. Assume that you are at the end of year 0.
Current spot rate is 7.80 SK/$.
1
7.9466 Government Debt Yields
(SK by maturity year)
Expected $ Inflation:
Expected SK Inflation: 3
n.a. 4
n.a. 5
n.a. 1.90% Forward (SK/$)
Treasury Bond Yields
($ by maturity year) 2
n.a.
3.50% 4.20% 4.80% 5.00% 3.75% 5.10% 5.65% n.a. n.a. 2.10%
3.00% 2.50%
4.00% 3.00%
4.25% 3.30%
4.00% 3.20%
3.75% Best Available Forecast:
Forecast Spot Rate (SK/$)
Use 7.9466
Forward
Rate 8.0430 8.1302 8.1853 8.2289 UIRP UIRP PPP PPP 8.1356 8.1789 ALL PPP Forecast:
Forecast Spot Rate (SK/$) 7.8688 7.9839 8.0808 For the UIRP forecast, the correct approach is to forecast each FX value using the spot rate and
the interest rates of the appropriate maturity (interest rates are cumulative, and not just for that
year). So, for the 2year forecast you square the (1+i) terms, for the 3year forecast you cube,
etc. The PPP forecasts should be done dynamically, because the inflation rates are given for
each year, and are not cumulative. Problem #3.8:
There aren’t sufficient data in Baht to value Baht cash flows. Accordingly, the US parent,
Harkes Inc., plans to translate US CoC’s and apply those to the Baht cash flows.
The following data are relevant. The “betas” refer to the business risk of the project to be
valued.
Beta World E(RP) –World Rf 1.25 7.30% 1.40% 8 TBond 1 Yr
2.50% Gov Sec 1 Yr
(Baht)
12.45% FBE 436
Answers to Problem Set #3 Harkes’ current cost of debt is estimated at 5.65%
What are the appropriate Baht CoE (u) and CoD (L) that Harkes Inc. should use? The problem implies that Harkes will compute CoE (u) and CoD (L) from US data and convert
1 + GovSec
= 1.0971.
that to Baht. The IRP “factor” is:
1 + TBond $ CoE(u) = 0.0140 + 1.25*0.073 = 10.53%, and $ CoD(L) is given as 5.65%.
Apply the IRP correction to get:
Baht CoE(u) = (1+0.1052)*1.0971 – 1 = 0.2125 21.25% Baht CoD(L) = (1+0.0565)*1.0971 – 1 = 0.1591 15.91% We have not discussed international taxation issues and you are not responsible for any of that
material. However, you might want to try to work out this small taxation problem. Problem #3.9:
The foreign and domestic corporate tax rates are shown below “Withholding Taxes” are taxes
paid on dividends or interest remitted, over and above income taxes. What taxes does the
corporate entity pay, if dividends are remitted immediately? Dividends equal earnings in this
case. Assume that a tax treaty exists in this case. A tax treaty allows taxes paid abroad to be
fully deductible from taxes paid in the US.
Taxable Income = $200,000 (translated to $s). Tax Rates
U.S.
Foreign
Withholding 34%
28%
5% The subsidiary pays 200,000*0.28 = $56,000 in foreign taxes.
Earnings are 200,000 – 56,000 = $144,000, which are remitted as dividends immediately.
It also pays $7,200 for remitting the earnings (144,000*0.05).
From the US point of view, taxes payable are $68,000 (200,000*0.34). So, the parent has to pay
an additional $4,800 to the IRS. 9 FBE 436
Answers to Problem Set #3 Problem #3.10:
Consider the valuation of a startup, Robinho Enterprises, without an established track record of
positive cash flows and profits. Its current revenue is $2.45/share. In its IPO prospectus, the
investment bank proposes a share price of $16.50, for 10,000,000 shares. (Hint: Use the Perkins
approach; details in Tom.com) (1)
(2)
(3)
(4) What average growth rate does Robinho’s stock price need to achieve in order to make
this a good investment?
What should the price of Robinho’s share have to be in 5 years?
What revenues must Robinho generate in 5 years’ time?
What is the implied CAGR? The Perkins data suggests that the average return should be 15%  25%.
(1)
The price per share would have to be between $33 and $50.
(2)
Just compute 16.50(1.15)^5 = 33 or 16.50(1.25)^5 = 50.
(3) Between $5.53 and $50.35 per share. The smallest number uses the lower price ($33), a
P/E of 40, and a profit margin of 15%, while the largest number uses the higher price
($50), a P/E of 20, and a profit margin of 5%.
Earn = 33/40 = $ 0.83, and Rev = 0.83/0.15 = $5.53, and Earn = 50/20 = $ 2.52, and Rev =
2.52/0.05 = $50.35.
(4) The implied CAGR is 17.7% for the lower revenue and 83.1% for the higher revenue. 10 FBE 436
Answers to Problem Set #3 Problem #3.11:
Crouch Inc. is contemplating a foreign acquisition; it’s debt is currently rated AAA. The
Finance VP assigned the task of valuing the foreign company to a team of young experts, and
they produced an apparently very thorough estimate of the PV of the company cash flows. Their estimate is $140 Million. The VP noticed however, that 70% of the value of the company
came from the “Terminal Value”. Here is what she found, upon closer examination.
Market Data:
3 Month TBill
5.25%
L.T. Foreign 10.00% 3Year TNote 6.60%
Like Risk U.S.
Market Beta 1
1.60 20Year TBond
7.20% 8.60% 3Month
Foreign
8.40% Foreign
Inflation
4.00% 3Month
Foreign
7.50% AAA Yield U.S Inflation 2.50% Calculated or Assumed Values:
Rf 7.20%
1 Exp U.S. Mkt
Premium
6.50% CoD(L) CoE(u) 8.60% 17.6% Approximate
S.T. Growth
17.0% L. T. Growth 10.50% The business beta of the “likerisk” firms was calculated from quarterly data. How good do you think the team’s analysis was? What would you change? There are several difficulties with the team’s analysis.
They take the riskfree rate to be 7.20% (the 20year bond rate). This is clearly inconsistent with
the time interval over which the beta is estimated. Using the more nearly correct rate of 5.25%
(3month rate) reduces the CoE(u) by 1.95%. The 3month rate seems reasonable, because a
2.5% inflation implies a real rate of 2.75%, if anything a little higher than average.
Their long term growth assumption seems incredibly generous and almost surely a bad
assumption. The 10.5% L.T. rate that applies to the terminal value implies a real growth rate of
6.5% forever, assuming no predicted rise in inflation. We don’t know for sure about the
inflation rate, because as in most developing countries, there are no wellorganized longterm
debt markets. But if there is substantial worry about inflation, the valuation ought to be done in
real currency, using real CoEs.
Problem #3.12: 11 FBE 436
Answers to Problem Set #3 Given the following information on a simple nooptions bond, what would be its market value
per $?
Calculated or Assumed Values:
Coupon
6.00% Maturity
22 Coupon Frequency
Every 6 months Current Yield
8.40% The market price of a $1 bond is given by the specialized form of the PV equation.
⎡
⎤
⎥
1
1
Coupon ⎢
+
.
P=
⎢1 −
Mat * Freq ⎥
Mat * Freq
Yield ⎢ ⎛ Yield
⎞
⎞
⎥ ⎛1 + Yield
1+
Freq ⎟
Freq ⎟
⎢⎜
⎥⎜
⎠
⎠
⎣⎝
⎦⎝
Apply the formula to get: $0.7610. 12 ...
View
Full
Document
This note was uploaded on 01/16/2010 for the course FBE 436 at USC.
 '09
 PROTOPAPADAKIS

Click to edit the document details