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V125BC [204]
2 years ago
14

The Xu Corporation uses a periodic inventory system. The company has a beginning inventory of 2,150 units at $24 each on January

1. Xu purchases 2,400 units at $23 each in February and 1,150 units at $25 each in March. There were no additional purchases or sales during the remainder of the year. Xu sells 1,100 units during the quarter. If Xu uses the weighted average method, what is its cost of goods sold for the quarter
Business
1 answer:
jekas [21]2 years ago
7 0

Answer:

$26,159

Explanation:

Cost of goods available for sale = (2,150 units * $24) + (2,400 units * $23) + (1,150 units * $25)

Cost of goods available for sale = $51,600 + $55,200 + $28,750

Cost of goods available for sale = $135,550

Number of units available for sale = 2,150 units + 2,400 units + 1,150 units

Number of units available for sale = 5,700 units

Weighted average cost per unit = Cost of units available for sale / Number of units available for sale

Weighted average cost per unit = $135,550 / 5,700

Weighted average cost per unit = $23.7807

<em>Xu sells 1,100 units during the quarter.</em>

Cost of goods sold = 1,100 units * $23.7807 per unit

Cost of goods sold = $26,159

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<em>Solution</em>

Given that:

Now,

The Jensen’s alpha of a Portfolio is computed by applying  the formula  below:

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The Risk free rate of return = 3. 1%

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1. Portfolio Return

2. Portfolio Beta

3.Market Rate of Return

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The formula for calculation of Portfolio Return is  given as:

E(RP) = ( RA * WA )+ ( RB * WB )

Where

E(RP) = Portfolio Return

RA = Average Return of Portfolio A ; WA = Weight of Investment in Portfolio A

RB = Average Return of Portfolio B ;  WB = Weight of Investment in Portfolio B

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= ( 18.9 % * 0.45 ) + ( 13.2 % * 0.55 )

= 8.5050 % + 7.2600 % = 15.7650 %

(B). Calculation of Portfolio Beta:

Now,

The formula for calculating the Portfolio Beta is

ΒP = [ ( WA * βA ) + ( WB * βB ) ]

Where,

βP = Portfolio Beta

WA = Weight of Investment in Portfolio A = 45 % = 0.45 ; βA = Beta of Portfolio A = 1.92

WB = Weight of Investment in Portfolio B = 55 % = 0.55 ; βB = Beta of Portfolio B = 1.27

By Applying the above vales in the formula we have

= ( 0.45 * 1.92 )   + ( 0.55 * 1.27 )

= 0.8640 + 0.6985

= 1.5625

(C). Calculation of Market rate of return :

Now,

The Market Risk Premium = Market rate of return - Risk free rate

From the Information given in the Question we have

The Market Risk Premium = 6.8 %

Risk free rate = 3. 1 %

Market rate of return = To find

Then

By applying the above information in the Market Risk Premium formula we have

6.8 % = Market rate of Return - 3.1 %

Thus Market rate of return = 6.8 % + 3.1 % = 9.9 %

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From the following  information, we gave

Risk free rate of return = 3.1% ; Portfolio Return = 15.7650 %

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Now

Applying the above values in the Jensen’s Alpha formula we have

The Jensen's alpha = Portfolio Return − [Risk Free Rate of Return + ( Portfolio Beta * (Market Rate of Return − Risk Free Rate of Return )) ]

= 15.7650 % - [ 3.1 % + ( 1.5625 * ( 9.9 % - 3.1 % ) ) ]

= 15.7650 % - [ 3.1 % + ( 1.5625 * 6.8 % ) ]                  

= 15.7650 % - [ 3.1 % + 10.6250 % ]

= 15.7650 % - 13.7250 %

= 2.0400 %

= 2.04 % ( when rounded off to two decimal places )

Therefore, the Jensen's alpha of a portfolio comprised of 45 percent portfolio A and 55 percent of portfolio B = 2.04 %

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