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Answer.. 2.4 Problem IV

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Answer.

(a) The general formula for a portfolio of two securities is

Vα r (α ra + (1 − α ) rb) = α 2σ 2a+ (1 − α )2σ 2b + 2α (1 − α ) ρ abσ aσ b.

If α = 0. 5 and securityα is a treasury bill, σ a = 0 and ρ ab = 0.

If security b is stock P then σ b = 0. 14.

We conclude

Vα r (α ra + (1 − α ) rb) = (0. 5)2 (0. 14)2 and the standard deviation is

σ = =0, 07 or 7%

 

(b) If α = 0. 5, securityα is stock Q, and security b is stock R then σ a = 0. 28, σ b = 0. 26.

1. If Q and R have perfect positive correlation then ρ ab = 1 then

Var (α ra + (1 − α ) rb) = (0. 5)2 (0. 28)2 + (0. 5)2 (0. 26)2 + 2 (0. 5)2* 1 * 0. 28 * 0. 26 = 0. 0729 and the standard deviation is

σ = √ 0. 0729 = 0. 279or 27%

2. If Q and R have perfect negative correlation then ρ ab = -1 then

Vаr(1/2 ra + 1/2 rb) ¶ = (0. 5)2 (0. 28)2 + (0. 5)2 (0. 26)2 − 2 (0. 5)2* 1 * 0. 28 * 0. 26 = 0. 0001 and the standard deviation is σ = √ 0. 0001 = 0. 01 or 1%

3.  If Q and R have zero correlation then ρ ab = 0 then

V ar(1/2 ra + 1/2 rb) ¶ = (0. 5)2 (0. 28)2 + (0. 5)2 (0. 26)2 = 0. 0365 and the standard deviation is σ = √ 0. 0365 = 0. 19105 or 19, 1%

(c).

(d). No, because risk is measured by beta not by standard deviation. Beta measures non-diversifiable risk whilst standard deviation measures total risk. Investors are only compensated with a risk premium for holding non-diversifiable risk

 

2. 4 Problem IV

The task.

The information for Golden Fleece Financial is given in table 3.

Table 3 – The information for Golden Fleece Financial

Long-term debt outstanding $300, 000
Current yield to maturity (rdebt) 8%
Number of shares of common stock 10, 000
Price per share $50
Book value per share $25
Expected rate of return on stock (requity) 15%

 

Calculate Golden Fleece’s company cost of capital. Ignoretaxes.

 

Answer:

The total market value of outstanding debt is $300, 000. The cost of debt capitalis 8 percent.

For the common stock, the outstanding market value is: $50× 10, 000 = $500, 000.

The cost of equity capital is 15 percent.

Lorelei’s weighted-average cost of capital is:

rassets=( (300000/(300000+500000)*0, 08))+((500000/(300000+500000)*0, 15))

rassets= 0. 124 = 12. 4%

 

 


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