Question

No excel or financial calculator, please.

13. Cloned Cow Dairy Farms (CC) is a private company that operates a group of dairy farms in Wisconsin where the state motto is "Come Smell Our Dairy Air". Four years ago, CC raised funds through a bond offering with a term to maturity of five years. The bonds, which mature in one year, have a face value of $1000, a current price of $1038.32 and a coupon rate of 11.11% paid annually. CC is taxed at a rate of 40%.

a. Calculate the cost of debt for the company. (Hint: it is either 7%, 8%, or 9%)

b. A comparable company, Dolly Sheep is trading on the stock market. Dolly’s shares are highly correlated with the market – the coefficient of correlation between Dolly and the market is 0.7. If the standard deviation of Dolly Sheep is 12% and that of the market is 16%, compute Dolly’s beta. Dolly is taxed at the same rate as CC.

c. If the expected return on the market is 14% and the risk-free rate is 6%, compute the cost of equity capital for Dolly Sheep.

d. If CC has a 20% debt-to-value ratio, what is the overall cost of capital for CC?

Answers:

7%, 0.525, 10.2%, 9.00%

Answer 1

(a) Cost of debt

Total Payments received after 1 year      

Coupon Payment                                             111.11

Principal Payment                                           1000

Total Payments received after 1 year       1111.11

Current Price                                                      1038.32

1038.32 = 1111.11/(1+i)

1+i = 1111.11/1038.32 = 1.07

i = 1.07 - 1 = 0.07 = 7%

(b)         

standard Deviation of Dolly sheep (Sds)                                 12%

Standard Deviation of Market (SDm)                                       16%

correlation (Rsm)                                                                             0.7

Beta of Dolly sheep (SDs/ SDm*Rsm)                                      0.525

( c)         

Expected Return (Rm)                                                    14%

Risk free rate (Rf)                                                             6%

Cost of Equity Capital (Rf+ Beta ( Rm-Rf))              10.20%

(d)
Debt to value Ratio	20%
Debt weight	20%
Equity Weight	80%
Debt Cost	7%
Equity Cost	10.20%
Overall Cost of Capital (20%*7%*40%)+(80%*10.2%)	9.00%

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