# Fin331 Ch10 Spring 2010 Lecture Notes 100429 1

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```					Chapter10. The Cost of Capital (Funding, Financing)

* Basic Definitions
- Marginal cost of raising extra one \$! (the minimum rate of return (e.g., 8.6%) on the last one
\$ to generate from the project to satisfy every investor (creditors, equity investors (=shareholders),
preferred stock investors, etc, since they would not invest if the firm fails to provide what they are
seeking at minimum)
- Here, we try to determine the cost of capital. A low cost of funding is good!

* The cash flows an investor faces and the cash flows from a firm’s (an issuer’s) perspective are a
kind of mirror image; -Po followed by C1, C2, C3, - - - versus PoN followed by -C1, -C2, -C3, - - -.
The cash flow at 0 may be different due to PoN = Po – FC, FC=Flotation Cost. Note that
investors determine the projected ROI (return on investment) for various security investment
from the security projected cash flows: YTM (or YTC depending on whether it is likely to be
called for a callable bond), Projected Total Return on Stock (                          Projected
Total Return on Preferred Stock ( ).

* Where are the money from (how to finance/fund)?
- Look at the Right Hand Side of the B/S
- Here, we are mainly focusing on the long-term financing (forget about current liabilities)
- Different funding sources:
Equity: Internal (using R/Es) & External (issuing new common stock shares)
Debt: Bonds (and long-term loans. We mainly talk about bonds in this class. Why?)
Preferred Stock
 Capital structure,
 What is optimal capital structure? e.g., 40%, 50%, 10%. This is a Fin439 topic, Here,
the capital structure is given in terms of % numbers or \$ amounts (=> we need to
get % structure)

* To raise capital, what do you need to do?
- Need to offer each group of investors (E, D, P), what they seek! => How can you find out what
they are asking for? 1) a survey?, 2) each group’s required rate of return from Chapters 7, 8, and 9.
- Take into consideration extra costs & benefits (flotation costs, tax benefits, etc)
- E.g., Try to raise \$10m for a new project, Given the capital structure above, and the cost of
Equity (10%), Debt (7%), Pref Stock (8%) => WA(M)CC = .4*10% + .5*7% + .1*8% = 8.3%

Real Life Example using Apples:
US: VA (5¢) with a limited qty of 30 apples, unlimited quantity of WA (6¢)
Chile: (4¢) with a 40% quota (=> wus, wch ?)
Note: For US apples, always buy VA apples whenever possible! Why?
How many from US (6)? how many from C (4)? How many from VA(6)?
Total Cost = 46¢ = 6*5¢ + 4*4¢
Average Cost = 4.6¢ = TC/total#
Marginal Cost when you buy the 11th = TC11 – TC10 = 50.6 – 46 = 4.6¢ or
= wus*MCus + wch*MCch = .6*5¢ + .4*4¢ = 4.6¢ (60% of the one last apple from
the US, actually from VA, 40% from Chile)
Note: AC = MC
2) When do I need to switch from VA to WA?
When the total # of apples from the US becomes 30, or the TOTAL # of apples becomes
X, where (.6)X = 30 => Backfigure X=?
3) At 250 apples
Where are the apples from? Since 250*0.6 = 150 US applies and 100 from Chile.
Among the US apples, 30 from VA (buy out all the VA apples), 120 WA
TC = 1270¢ or \$12.70 = 30*5¢ + 120*6¢ + 100*4¢
AC = 5.08¢ = ?
MC = TC251 – TC250 or
= .6*6¢ + .4*4¢ =5.2¢ (from 250 to 251 apples, US applies are only from WA)
4) WA(M)CC schedule by looking at MCs,
In terms of US apples, the MC increases when we buy out all VA applies as we have to
start buying more expensive WA apples. The break point is at 30 US apples.
In terms of TOTAL # of apples. The break point is at 50 total number of applies.

=> Now, in terms of Equity (Internal and External) and Debt?
* Cost of Debt (bonds)
- Reviewing: Cash flow stream from an investor’s perspective
{- Po, C, C, C, - - - , C, C+F}, n periods
=> YTM (return (yield) on the bond)
Ex1: Po and FV=\$1,000, coupon rate=8.75%, annual, 30 year bond? YTM=8.75%
=> Ex2: Po = \$1,025, FV=1,000, coupon rate=8%, semi-annual, 20 years?
(-1025 PV, 40 PMT, 1000 FV, 40 N, CPT i/Y=YTM=3.88%*2=7.76%)
- How about the cash flow stream from issuer (firm)’s perspective?
- Cash inflows and outflows are switched
- Instead of Po, (Po – FC)=PoN will be used, where FC=flotation cost
=> {PoN , -C, -C, -C, - - - , -C, -C-FV}
Aside) For the flotation costs and the interest (coupon) payments, the issuer can
enjoy TAX benefits. How much? (C+F/n)*t, where t is the tax rate - - -
=> HERE, compute YTM before tax, kb from the cash flows { }(Using a financial
calculator, PoN PV, -C PMT, -F FV, n (number of periods) N, CPT i/Y). Then compute
ka = kb *(1-t) to determine the after-tax cost of debt.
=> Ex2 above: FC is a 4% of Po, PoN =1025*(1-0.04)=\$984, so {984, -40, - - , -40-1000}
(kb = 8.16%, and ka = 5.30% based on t=35%

Aside) The cost of funding increases with a FC (compare 7.76% vs. 8.16%). A simple example
is Co=100, C1 =-100 (=> cost of funding?) vs Co=95, C1 =-100 (=> ?)

* Cost of Equity (=cost of common stock)
=How much the firm has to deliver to shareholders to make them happy (delivering what they
are asking for, required rate of return). The flotation cost can be considered, if exists.
- Internal Equity Financing using retained earnings. No floatation costs.
There are two approaches, one is using the DCF (discount cash flow) = DDM (discount
dividend model), the other one is CAPM
DCF(=DDM): In this case, ki = kre =
Ex1: Po = \$23.06, D1 = \$1.25, g=8.3%, ki = 13.7%
CAPM: Ex2: Risk free rate is 5.6%, Expect Market Return (r m)=10.6%, Beta=1.48
 ki = 5.6% + (10.6% - 5.6%)*1.48 = 5.6% + 5%*1.48 = 13%
(note that the market risk premium = rm – rf = 5% )
- External Equity Financing by issuing new common equity shares (basically, we use DCF
approach. However, we need to use PoN because of the FC), ke = D1/PoN + g
Ex3: The same as Ex1 except the FC is 10% of the share price. PoN = 23.06*(1-0.1)=\$20.75
ke = 1.25/20.75 + 0.083 = 14.3%
* Cost of Preferred Stock
kp = Dp /PoN
Ex: Dp = \$10, Po = \$100 with the FC is 2.5% of the pref stock price. kp = 10/97.5 = 10.3%

Note: unlike debt (bond) financing, no tax benefits for equity and preferred stock financing for
dividend payments and flotation costs.

* The Financing (Capital, Funding) Structure before the Break Point and after
- What causes the break point? Using more expensive External Equity Financing when you
switch from Internal Equity Financing (using retained earnings) to External Equity Financing
- Where is the Break Point? In terms of Equity Financing Amount? When you use up all
retained earnings.
- Where is the Break Point in terms of total new financing amount? Try to find out the total
new financing amount based on the capital structure. For example, if you finance 35% of the
capital from equity and the size of retained earnings is \$7 million, then the total new financing
would be \$7m/0.35=\$20m. You can confirm that 35% of \$20m is indeed \$7m. In general, the
breakpoint in terms of total new capital = Addition to retained earnings for the year/Equity
fraction p.320.

* Calculating the Overall Cost of Capital (WA(M)CC)
- Prior to the Break Point = wdka + wski + wpkp Note ka = kb*(1-T). wd, ws, and wp are
fractions of funding from debt, stock equity, and preferred stock.
Ex1: wd=45%, ws= 53%, and wp = 2% with ka = 5.3%, ki = 13.7%, and kp = 10.3%
WACC = 0.45*5.3% + 0.53*13.7% + 0.02*10.3% = 9.85%
- After the Break Point = wdka + wske + wpkp Note that ki = cost of internal equity financing
(or cost of retained earnings) is replaced by ke = cost of external equity financing
WACC = 0.45*5.3% + 0.53*14.3% + 0.02*10.3% = 10.17%

- Cost of Capital Schedule: You can plot WACC against the total new capital amount. WACC
prior to the breakpoint would be flat at 9.85%, then WACC jumps to a new higher level at
10.17%

- Which projects to accept? Investment Opportunity Schedule: If the projected return of a
project is higher than WACC, you want to take the project. If not, you don’t want to take the
project.

Aplia #6-2: If the market is in equilibrium, the cost of equity=projected return on stock. Note that
= projected dividend yield + projected capital gains yield. Also note that the projected capital
gains yield=the projected dividend growth rate (g).

Note that the Growth rate = ROE*(1-dividend payout ratio) p.281. Comments: there is a trade-off
between current dividends and future dividends as the firm pays out more now, they have a
smaller addition to retained earnings and you expect a slower future growth of business, resulting
in less future dividends. Many of fast growing (IT) companies pay little or no dividends as they
want to plow back their earnings into their business for them to grow faster.

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