fina 385 theory of finance i tutorials capm

FINA 385 Theory of Finance I Tutorials

Capital Asset Pricing Model

Copyright © 2011. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form without prior consent of Gradesavers Tutoring Inc. Tutorial notes prepared by Rohit Soni.

Le Cartier 1115 Sherbrooke, Suite 2B, Montreal QC, H3A CAPITAL ASSET PRICING MODEL

The capital asset pricing model (CAPM) is used to obtain the expected return on risky assets using the notion of diversification.

ASSUMPTIONS

1. The market is perfectly competitive

a. All investors behave has price takers

b. There exists many investors who each have a small endowment relative to the total endowment of all investors

2. All investors have a single Period Investment Horizon

3. Only considers investments that are traded financial assets (no private firms or human capital etc.) and that investors can borrow and lend at a fixed risk free rate of interest

4. No Taxes and Transactions Costs

5. All investors are rational and mean variance optimizers (all use Markowitz Portfolio selection model)

6. All investors have a homogenous expectations, which implies that they use the same inputs for the model and therefore they all obtain the same efficient frontier

www.gradesavers.net [email protected] 514.849.2586

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Le Cartier 1115 Sherbrooke, Suite 2B, Montreal QC, H3A EQUILIBRIUM CONDITIONS

1. All investors hold the same portfolio of risky assets – market portfolio

Since the capital asset pricing model (CAPM) is used to obtain the expected return on risky assets using the same set of securities, for the same time horizon who are all mean variance optimizers, they must all find the same optimal risky portfolio; the market portfolio (M).

Investors will differ only in the fraction (weight) of their complete portfolio that they have invested in the market portfolio (M) and the risk free asset.

2. The market portfolio contains all securities and the proportion of each security is the proportion of its market value relative to the market value of all securities

If the weight of a given stock in one investors optimal risky portfolio is say 5%, then when we sum the investments of all investors and obtain the market portfolio the weight for the given stock will remain 5%.

In other words an individual investors optimal portfolio is just a fraction of the market portfolio

3. Risk premium on the market depends on the average risk aversion of all investors.


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Le Cartier 1115 Sherbrooke, Suite 2B, Montreal QC, H3A

QUESTION 1

Gradesavers Tutoring Inc. manufactures wood-free pencils, which are used at their tutoring center. The production of the pencils evolves two distinct processes: moulding and packaging. The moulding department forms the compost raw material into a pencil mould. The packaging department finishes and packages the compost mould so that the packaged pencils can be transferred to finished goods inventory for sale to distributors. The following data was extracted for the month ended March 31st, 2008 pertaining to the two processes:

Moulding (in millions)

Packaging (in millions)

Work In Process - March 1, 2007 (units) 11 ???

Units Started Into Production 29 ???

Units Transferred Out 30 60

Work In Process - March 31, 2007 (units) ??? 20


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In the moulding department, materials are added at the beginning of the process, and conversion costs are incurred uniformly. In the packaging department, materials are added at

the end of the process, and direct labour at the 50% percent point. Manufacturing overhead costs are incurred uniformly.

The ending work in process in the moulding department was 60% complete. The beginning work in process had a cost of $150,000 for materials, $50,000 of transferred in costs and $200,000 of conversion costs. During the month of March, the moulding department incurred $650,000 of material costs, $150,000 of transferred in costs and $700,000 of conversion costs.

In the packaging department the beginning work in process was 60% complete and the ending work in process was 40% complete. The beginning work in process had $250,000 of transferred in costs, $400,000 of labour costs and $900,000 of conversion costs. During the month of March, the packaging department incurred $1,240,000 of prime costs, $540,000 of conversion costs, and $300,000 of factory support costs.


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Required

1. Calculate the cost of the units transferred out from the moulding department into the packaging department for the month of March. Assume that the moulding department uses the weighted average method of process costing.

2. Calculate the cost of units transferred to finished goods from the packaging department for the month of March. Assume that the packaging department uses the FIFO method of process costing.

3. Calculate the cost of the ending work in process inventory in the packaging department. Assume that the packaging department uses the FIFO method of process costing.


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QUESTION 2

Gradesavers manufactures two types of ergonomic study chairs. The items, classified as either the deluxe or executive are manufactured on a common assembly line. Although different direct materials are used, and the machine is re-tooled for each product, the direct labourers are the same for each product line. The plant-wide rate for allocating manufacturing overhead to its products is no longer acceptable. The production manager has heard about activity-based costing and has assembled some information for use in changing the cost system to a cost driver concept.

With the help of the accounting department, the manager has been able to establish the following relationships between production costs and some of the indirect manufacturing activities for August along with the production data for the two product lines:

Activity Cost DriverEstimated

MOHPractical Usage

of DriverExecutive

ChairsDeluxe Chairs

Receiving Kilograms 85,000 85,000 2,000 1,300

MachiningMachine

hours15,000 1000 205 300

Assembly Units began 1,500,000 937,500 1,000 1,300


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Inspection

Number tested

400,000 200,000 100 1,200

Direct costs: Executive Deluxe

Labour per unit $12.00 $10.00

Materials per unit $5.20 $2.00

Required:

1. Determine the total production cost of each of the two product lines for August and the cost per unit assuming all units were completed.

2. Assume that the firm were to use a single plant wide rate based on machine hours, calculate the revised unit cost of manufacturing each of the two types of chairs.

Calculate the new product costs that would be assigned to each type of chair.

3. Determine which of the overhead activities are value added activities.

4. Which method of allocating manufacturing overhead; ABC or the traditional approach is superior and why


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QUESTION 3

Gradesavers Tutoring manufactures a single product. The following information has been extracted from the firm’s records:

March – Low June - High

Units Produced 6000 9000

Cost of Goods Manufactured $168,000 $257,000

Work-in-Process: Beginning $9,000 $32,000

Work-in-Process: Ending $15,000 $21,000

Direct Material Cost per Unit $6 $6

Direct Labour Cost per Unit $10 $10

Manufacturing Overhead Cost

? ?


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Le Cartier 1115 Sherbrooke, Suite 2B, Montreal QC, H3A Required

1. For both of the above months determine the amount of manufacturing overhead costs added to production. The company had no over or under applied MOH in either month.

2. Determine the cost formula for manufacturing overhead. Express the variable portion of the formula in a variable rate per unit produced.

3. If 7000 units are produced during a month, what would be the cost of goods manufactured? Assume that there is no beginning or ending inventories.

4. If 17,000 units were produced during a month, what would be the cost of goods manufactured? Assume that there is no beginning or ending inventories.


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QUESTION 4

On September 30, 2008, there was a theft that took place at Gradesavers Tutoring Inc. warehouse. The entire work-in-process inventory of ergonomic study chairs that are manufactured by Gradesavers Tutoring Inc. was stolen, along with most of the firm’s accounting records. For some reason, the robber did not touch any of the firm’s material and finished goods inventories.

Gradesavers Tutoring Inc. uses a normal job order costing system. Selected information for the period ending August 31, 2008 and September 30, 2008 are shown below:

August 31, 2008

September 30, 2008

Stores (Including both direct and indirect materials) $79,000 $53,000

Work-In-Process Inventory $59,000 ?

Finished Goods Inventory $30,000 $63,300


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Cost of Goods Sold (year to date) $576,000 $656,000

Accounts Payable (relates to materials purchases only)

$18,000 $53,000

Manufacturing Overhead Incurred (year to date) $129,000 $163,000

Manufacturing Overhead Applied $128,700 ?

Cash Payments to Suppliers $40,000

Payroll Including ($15,000 indirect) $83,500

Indirect Materials Used $5000

Over-Applied manufacturing overhead for September only.

$1,800

Required

Calculate the normal cost of the work-process inventory that was lost as a result of the robbery. Show all calculations to support your answer.


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QUESTION 5

Gradesavers Tutoring Inc. manufactures a product that undergoes two different manufacturing processes; process X and process Y. All material costs are incurred at the beginning of the process. On September 1, 2008, the following inventory balances were obtained:

X Y

Raw Materials $5000

Work in Process 0 $3,945

Finished Goods - $7,500

The beginning inventory of work in process for department Y was made up of 500 units, 40% complete as to conversion costs. During the month of September, 9000 units were started into production in department X, and the department transferred 8,200 units to department Y at a cost of $54,940. Department Y transferred 8,600 units to finished goods. The work in process inventory at the end of the month in department Y was 50% complete as to conversion costs.


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In addition the following transactions occurred during the month of September:

Purchased $25,000 of raw materials on account

Issued raw materials for production: $16,800 for process X and $6,150 for process Y

Incurred factory labour costs of $18,770

Used direct labour of $12,230 for process X and $6,400 for packaging

Incurred $41,300 of manufacturing overhead on account

Applied manufacturing overhead at the rate of $35 per machine hour. Machine hours were 900 for process X and 300 for process Y.

Required

Answer the following questions for process Y assuming that the department uses the FIFO method for process costing:

1. How many physical units are in process on September 30, 2008?

2. What is the unit transfer in cost for the month of September?

3. What is the unit material cost for the month of September?

4. What is the unit conversion cost for the month of September?

5. What is the average cost per unit for the units started in August and completed in September?

6. What is the total cost of units started and finished in September?

7. What is the cost of the September 30, 2008 inventory?


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QUESTION 4

Given for GS firm (in millions of dollars)

Beginning and ending inventories 0

Sales . . . . . . . . . . . . . . . . . . $390

Direct materials used . . . . . . . . . . 80

Direct labour cost . . . . . . . . . . . . 180

Factory overhead . . . . . . . . . . . . ?

Period Expenses . . . ?

Gross profit . . . . . . . . . . . . . . 70

Net income (no income taxes) . . . . . . 22

Required:

Compute the following amounts of:

1. Cost of goods sold

2. Total factory overhead cost


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Le Cartier 1115 Sherbrooke, Suite 2B, Montreal QC, H3A 3. Selling and administrative expenses

4. Total product costs

5. Total period costs

6. Prime cost

7. Conversion cost

8. Cost of goods manufactured


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fina 385 theory of finance i tutorials capm

Documents

ergonomic study chairs

allocating manufacturing overhead

manufacturing overhead

net ro gradesavers

risky assets

ending inventories

finished goods

material costs