Cost of Capital

1.         The Beta for Dollar tree stores is 0.45 and for Family Dollar store it is 0.04. Yahoo finance was used to determine these values. The values were current as of March 10, 2009 and can be found under Key Statistics of individual stock profile.
DLTR Beta = 0.45 (Ref 1.1)
FDO Beta = 0.04 (Ref 1.2)

2.         The YTM of Treasury Bills can be calculated by the following formula.

Yield %=(Face Value – Purchase Price)  x (             360_______)    x 100%
                        Face Value                             Days till maturity
Using values from www.treasurydirect.gov, a 52 Week Treasury Bill purchased on 03/12/2009 and a maturity date of 03/11/2010 the value is
=0.00707778 x 1x 1 = 0.007= 0.70% (Ref 2.1)
For 30 Yr Bond with Issuance at 2-17-2009 and maturity at 2-15-2039 the YTM is 3.540%. (Ref 2.2)

3.         For T-Bill, Adding 7 % will make it 7.70%
For Bonds, Adding 7 % will make it 10.540%
Risk Premium = 7 %

4.         Shareholder required rate of return = risk free rate + beta (market risk premium)
FOR DOLLAR TREE STORES
Using Bonds = 3.540% + 0.45(7%) = > 3.540% + 3.15% => 6.690 %
Using T-Bill = 0.70% + 0.45(7%) => 0.70%+ 3.15% => 3.85 %
FOR FAMILY DOLLAR STORES
Using Bonds = 3.540% + 0.04(7%) = > 3.540% + 0.28 % => 3.82 %
Using T-Bill = 0.70% + 0.04(7%) => 0.70 % + 0.28 % => 0.98 %

5.         Cost of Equity for DLTR = Risk Free Rate + (Beta*Equity Risk Premium)
= 3.540% + (0.45×7%) = 6.69%
Cost of Equity for FDO = Market Risk Premium x Equity Beta + Risk free Interest Rate
= 3.540% + (0.04×7%) = 3.82%
Note: The value of equity risk premium is derived from question 3 whereas the Daily Treasury Yield from Historical Interest Rates Statistics (Ref 5).
As expected the cost of equity for Dollar Tree stores is higher due to the inherent risk in the historical volatility of the stock which is less than the average S&P 500. Average S&P 500 would have a market premium of 7% which is slightly greater than the cost of equity for DLTR (6.69%).

6.         Cost of Equity for Target = Market Risk Premium x Equity Beta + Risk free Interest Rate
= 3.540% + (1.04×7%) = 10.82 %
Cost of Equity for Wal-Mart = Market Risk Premium x Equity Beta + Risk free Interest Rate
= 3.540% + (0.26×7%) = 5.36 %
Note: Beta values are calculated from Yahoo Finance
7.         The cost of equity for Wal-Mart and Target when compared with the chosen stores (DLTR and FDO) provides evidence that Beta is, in most cases, has very strong relationship with cost of equity.

8.         We can also calculate the cost of equity by using the dividend growth model. It is the sum of historical dividend yield and the expected growth in dividends. In contrast APT involves calculating several distinct risk factors and the sensitivity is calculated by respective beta coefficient. The calculation is complex and consists of risk free premium, microeconomic factors, risk free rates, type of asset and its relationship to other factors etc.

References

(1.1) http://finance.yahoo.com/q/ks?s=DLTR
(1.2) http://finance.yahoo.com/q/ks?s=FDO
(2.1) http://www.treasurydirect.gov/RI/OFBills
(2.2) http://www.savingsbonds.gov/RI/OFNtebnd
(5) http://www.ustreas.gov/offices/domestic-finance/debt-management/interest-rate/yield.shtml