Download UNIT 7 SEM PROBLEMS

UNIT 7 SEM PROBLEMS
What impacts the cost of
capital?
RISKINESS
OF
EARNING
S
FINANCIAL
SOUNDNESS
OF THE FIRM
THE DEBT TO
EQUITY MIX
OF THE FIRM
INTEREST RATE
LEVELS IN THE
US/GLOBAL
MARKETPLACE
Cost of equity capital-CAPM
•
1.
•
Various approaches for computing the cost of
equity capital
CAPM model
Re = Rrf + ß (Rrm - Rrf)
Where:
Re
= Cost of equity
Rrf
= Risk-free rate
Rm = Equity market required return (expected
return on the market portfolio)
ß
= beta
Cost of equity capital-CAPM
• Example:
• Let us calculate the cost of equity
capital for a company whose Risk-free
rate =10%, equity market required
return =18% with a beta of 0.5.
•
Re
= 0.10 + 0.5(0.18 - 0.10)
= 0.14 or 14%.
Cost of equity capital
Bond Yield Plus Risk Premium Approach
• In this approach, a judgmental risk premium
to the observed yield on the long-term bonds
of the firm is added to get the cost of equity.
Cost of equity = Yield on long-term
bonds + Risk Premium.
•
Given, the yield on debt is 10% and the risk
premium as 5%, calculate the cost of equity.
•
Cost of equity = 0.10 + 0.05 = 0.15 or 15%.
Cost of equity capital Bond Yield
Plus Risk Premium Approach
• Challenge to this approach is the
determination of the risk premium.
There is no objective way to determine
it and hence many financial analysts
look at the operating and financial risks
of the business and arrive at a
subjectively determined risk premium
that ranges between 2 percent and 6
percent.
Dividend Growth Model
Approach -DCF
• The price of an equity stock depends
ultimately on the dividends expected
from it. It can be represented as follows
and solving for r, we get
Simplifying this equation, we get:
Dividend Growth Model
Approach
• A company has issued 5000 equity shares of $100
each. Its current market price is $95 and the current
dividend is $4.5 per share. The dividends are
expected to grow at the rate of 6%. Compute the cost
of equity capital.
Here, D1 = $4.5 + growth rate 6% = $4.77 per share
P0 = $95
Ke = $4.77 + 6% = 0.11 or 11%
$95
Hurdle rates:
• Hurdle rates are the required rate of return
used in capital budgeting. Simply put,
hurdle rates are based on the firm’s
WACC
• Large companies, with divisions that have
different levels of risk, may choose to have
divisional hurdle rates.
WEIGHTED AVERAGE COST OF CAPITAL
(WACC)
Cost of Capital
• WACC = wd (cost of debt) + ws (cost of
stock/RE) + wp (cost of pf. stock)
THE FIRM’S
CAPITAL
STRUCTURE IS
THE MIX OF
DEBT AND
EQUITY USED
TO FINANCE
THE BUSINESS.
wd
ws
wp
Think of the firm’s capital structure as a
pie, that you can slice into different
shaped pieces. The firm strives to pick the
weights of debt and equity (i.e. slice the
pie) to minimize the cost of capital.
The firm’s WACC is the cost of Capital for the firm’s mixture of
debt and stock in their capital structure.
PROBLEM #1
• 1. Acme Company, and you were provided with the
following data
• with the following data:
• Target capital structure:
• 40% debt,
• 10% preferred, and
• 50% common equity.
• The after-tax cost of debt is 5.00%, the cost of
preferred is 8%
• the cost of retained earnings is 10%. The firm will
not be issuing any new stock. What is the firm’s
WACC?
PROBLEM #1
• WACC= .4(.05)+ .10(.08)+.5(.10)=.078
PROBLEM #2
BEST CO sold a $1,000 par value bond
that now has 10 years to maturity
• and an 8.00% annual coupon that is
paid SEMI- ANNUALLY. The bond
currently sells for $700 and the
company’s tax rate is 40%.
• What is the component cost of debt for
use in the WACC calculation?
PROBLEM #2
•
•
•
•
•
•
•
•
•
•
Step 1- Find the rate
Nper=10X2=20 periods
Pmt=$80 divided by 2=$40 per period
PV= current price negative $700
FV=1000
Type =0
You will get the rate per period= .0678
Multiply with 2 to get annual rate= .1356 or 13.56%
Step 2 –Calculate cost of debt
Rd= .1356(1-.4 tax rate )= 8.4%after tax cost of debt.
PROBLEM #3
•
Tapley Inc. recently hired you as a consultant to estimate the
company’s WACC. You have obtained the following information.
•
(1) Tapley's bonds mature in 25 years, have a 7.5% annual coupon, a
par value of $1,000 and a market price of $936.49.
(2) The company’s tax rate is 40%.
•
•
•
•
•
•
(3) The risk-free rate is 6.0%, the market risk premium is 5.0
and the stock’s beta is 1.5.
(4) The target capital structure consists of 30% debt and 70% equity.
Tapley uses the CAPM to estimate the cost of equity, and it does not
expect to have to issue any new common stock
• What is its WACC?
PROBLEM #3- interest rate on debt
•
•
•
•
•
•
•
Step 1- Find the rate
Nper=25 periods
Pmt=$75 per period
PV= current price negative $936.49
FV=1000
Type =0
You will get the rate per period= .081
PROBLEM #3
• Step 2 –Calculate cost of debt
• Rd= .081(1-.4 tax rate )= 4.86%after tax cost
of debt.
• Next- Cost of Capital calculation
• CAPM= Risk free rate+ Beta times ( risk
premium)
•
=6%+ 1.5 times( 5% risk premium)
•
= 6%+7.5%
•
=13.5%
PROBLEM #3
• Last step WACC Calculation
• WACC= % of debt times Cost of Debt +
% of Stock times Cost of stock
•
=30% ( 4.86%after tax cost of
debt) +70% equity times(13.5%)
PROBLEM #4
• You were hired as a consultant to Locke Company,
and you were provided with the following data
• Target capital structure:
• 40% debt,
• 10% preferred
• 50% common equity.
• The interest rate on new debt is 8%
• yield on the preferred is 5%
• the cost of retained earnings is 6%,
• The tax rate is 50%
• The firm will not be issuing any new stock.
• What is the firm’s WACC?.
PROBLEM #4
Cost of debt after tax= . 08 (1-.5 tax rate )
or.04
• WACC Calculation=.04 (40% debt or.40 )
+ .05 times (10% preferred or .10 ) + .06
times (50% common equity or .5)
• =.016+.005+.03
• WACC=.051
PROBLEM #5 quiz
• To help finance a major expansion, Dimkoff
Development Company sold a bond several years
ago that now has 20 years to maturity. This bond
has a 7% annual coupon, paid quarterly, and it now
sells at a price of $1,103.58.
• The bond cannot be called and has a par value of
$1,000.
•
• If Dimkoff’s tax rate is 40%, what component cost of
debt should be used in the WACC calculation?
PROBLEM #5
•
•
•
•
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•
•
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Step 1- Find the rate
Nper=20 periods times 4=80
Pmt=$70 per period divide by 4= $17.50
PV= current price negative $1103.58
FV=1000
Type =0
You will get the rate per period as = 1.52 %
Multiply with 4 to get annual rate=1.52% times 4
=6.1%
• Cost of debt after tax= Annual rate(1-tax Rate)
•
.061%(1-.40)=.0366
PROBLEM #6
• 6. A company’s perpetual preferred
stock currently trades at $50 per share
and pays a $4.50 annual dividend per
share.
• If the company were to sell a new
preferred issue, it would incur a
flotation cost of 10%. What would the
cost of that capital be?
PROBLEM #6
• Step 1- Find the net price of stock after
floatation cost
•
$50( 1-.10 or 90% of $50) = $45
•
Dividend paid is $4.50
• Cost of that capital = D1 divided by
price of stock after floatation Cost
•
=$4.50/45= 10%
PROBLEM #7
• Assume that you are a consultant to
Acme Inc. and you have been provided
with the following data
• D1 = $1.00;
• P0 = $25.00;
• g = 6% (constant).
• What is the cost of equity from retained
earnings based on the DCF
PROBLEM #7
• We know Po= D1
•
r-g
•
$25 = 1.00
•
r- 6%
• Cross multiply to get $25(r-6%) = 1.00
• Divide both sides by $25 to get (r-6%) = 1.00
•
$25
•
(r-6%)= .04
•
Add 6% to both sides to solve
•
R= 10%
PROBLEM #8
• 8. Heinz Inc. hired you as a consultant to
help them estimate their cost of capital. You
have been provided with the following data:
• rRF = 4.0%;
• MRP = 6.0%;
• b = 1.2
• Based on the CAPM approach, what is the
cost of equity from retained earnings?
PROBLEM #8
• CAPM= Risk free rate+ Beta times ( risk
premium)
•
= 4%+ 1.2(6%)
•
=4%+7.2%
•
=11.2%
Payback
• Example
•
Examine the three
projects and note the
mistake we would
make if we insisted on
only taking projects
with a payback period
of 2 years or less.
C3
Payback
Project
C0
C1
C2
A
- 2000
500
500
B
- 2000
500
1800
0
2
- 58
C
- 2000 1800
500
0
2
 50
Period
5000
3
NPV@ 10%
 2,624