Linden Company manufactures and sells a single product. Cost data for the product follow: Variable costs per unit: Direct materials $6 Direct labor 12 Variable factory overhead 4 Variable selling and administrative 3 Total variable costs per unit $25 Fixed costs per month: Fixed manufacturing overhead $ 240,000 Fixed selling and administrative 180,000 Total fixed cost per month $ 420,000 The product sells for $40 per unit. Production and sales data for May and June, the first two months of operations, are as follows: Units Produced Units Sold May 30,000 26,000 June 30,000 34,000 Income statements prepared by the accounting department, using absorption costing, are presented below: May June Sales $ 1,040,000 $ 1,360,000 Cost of goods sold 780,000 1,020,000 Gross margin 260,000 340,000 Selling and administrative expenses 258,000 282,000 Net operating income $ 2,000 $ 58,000 Required: 1. Determine the unit product cost under absorption costing and variable costing. Unit Product Cost Absorption costing Variable costing 2. Prepare contribution format variable costing income statements for May and June. (Input all amounts as positive values except losses which should be indicated by a minus sign. Omit the "$" sign in your response.) Variable Costing Income Statement May June Sales $ $ Variable expenses: Variable cost of goods sold Variable selling and administrative expenses Total variable expenses Contribution margin Fixed expenses: Fixed manufacturing overhead Fixed selling and administrative expenses Total fixed expenses Net operating income (loss) $ $ 3. Reconcile the variable costing and absorption costing net operating incomes. (Loss amounts and amounts to be deducted should be indicated with a minus sign. Omit the "$" sign in your response.) Reconciliation of Variable Costing and Absorption Costing Net Operating Incomes May June Variable costing net operating income (loss) $ $ Add (deduct) fixed manufacturing overhead deferred in (released from) inventory under absorption costing Absorption costing net operating income (loss) $ $ Explanation: 1. Absorption Costing Variable Costing Direct materials $ 6 $ 6 Direct labor 12 12 Variable manufacturing overhead 4 4 Fixed manufacturing overhead ($240,000 ÷ 30,000 units) 8 - Unit product cost $ 30 $ 22 2. May June Variable cost of goods sold @ $22 per unit $ 572,000 $ 748,000 Variable selling and administrative expenses @ $3 per unit $ 78,000 $ 102,000 3. Fixed manufacturing overhead cost deferred in inventory under absorption costing (4,000 units × $8 per unit) = $32,000 Fixed manufacturing overhead cost released from inventory under absorption costing (4,000 units × $8 per unit) = $(32,000)

Linden Company manufactures and sells a single product. Cost data for the product follow:

Variable costs per unit:
Direct materials		$6
Direct labor		12
Variable factory overhead		4
Variable selling and administrative		3
Total variable costs per unit		$25
Fixed costs per month:
Fixed manufacturing overhead	$	240,000
Fixed selling and administrative		180,000
Total fixed cost per month	$	420,000

The product sells for $40 per unit. Production and sales data for May and June, the first two months of operations, are as follows:

	Units Produced	Units Sold
May	30,000	26,000
June	30,000	34,000

Income statements prepared by the accounting department, using absorption costing, are presented below:

	May		June
Sales	$	1,040,000	$	1,360,000
Cost of goods sold		780,000		1,020,000
Gross margin		260,000		340,000
Selling and administrative expenses		258,000		282,000
Net operating income	$	2,000	$	58,000

Required:

1.	Determine the unit product cost under absorption costing and variable costing.

		Unit Product Cost
Absorption costing
Variable costing

2.	Prepare contribution format variable costing income statements for May and June. (Input all amounts as positive values except losses which should be indicated by a minus sign. Omit the "$" sign in your response.)

Variable Costing Income Statement
	May	June
Sales	$	$
Variable expenses:
Variable cost of goods sold
Variable selling and administrative expenses
Total variable expenses
Contribution margin
Fixed expenses:
Fixed manufacturing overhead
Fixed selling and administrative expenses
Total fixed expenses
Net operating income (loss)	$	$

3.	Reconcile the variable costing and absorption costing net operating incomes. (Loss amounts and amounts to be deducted should be indicated with a minus sign. Omit the "$" sign in your response.)

Reconciliation of Variable Costing and Absorption Costing Net Operating Incomes
	May	June
Variable costing net operating income (loss)	$	$
Add (deduct) fixed manufacturing overhead deferred in   (released from) inventory under absorption costing
Absorption costing net operating income (loss)	$	$

Explanation: 1.

	Absorption Costing		Variable Costing
Direct materials	$	6	$	6
Direct labor		12		12
Variable manufacturing overhead		4		4
Fixed manufacturing overhead   ($240,000 ÷ 30,000 units)		8		-
Unit product cost	$	30	$	22

2.

	May		June
Variable cost of goods sold @ $22 per unit	$	572,000	$	748,000
Variable selling and administrative expenses @ $3 per unit	$	78,000	$	102,000

3.

Fixed manufacturing overhead cost deferred in inventory under absorption costing (4,000 units × $8 per unit) = $32,000

Fixed manufacturing overhead cost released from inventory under absorption costing (4,000 units × $8 per unit) = $(32,000)

During Denton Company’s first two years of operations, the company reported absorption costing net operating income as follows:

During Denton Company’s first two years of operations, the company reported absorption costing net operating income as follows:

	Year 1		Year 2
Sales (@ $50 per unit)	$	1,000,000	$	1,500,000
Cost of goods sold (@ $34 per unit)		680,000		1,020,000
Gross margin		320,000		480,000
Selling and administrative expenses*		310,000		340,000
Net operating income	$	10,000	$	140,000

* $3 per unit variable; $250,000 fixed each year.

The company’s $34 unit product cost is computed as follows:

Direct materials	$	8
Direct labor		10
Variable manufacturing overhead		2
Fixed manufacturing overhead ($350,000 ÷ 25,000 units)		14
Absorption costing unit product cost	$	34

   

Production and cost data for the two years are given below:

	Year 1	Year 2
Units produced	25,000	25,000
Units sold	20,000	30,000

Required:

1.	Prepare a variable costing contribution format income statement for each year. (Input all amounts as positive values except losses which should be indicated by a minus sign. Omit the "$" sign in your response.)

Variable Costing Income Statement
	Year 1	Year 2
Sales	$	$
Variable expenses:
Variable cost of goods sold
Variable selling and administrative expenses
Total variable expenses
Contribution margin
Fixed expenses:
Fixed manufacturing overhead
Fixed selling and administrative expenses
Total fixed expenses
Net operating income (loss)	$	$

2.	Reconcile the absorption costing and variable costing net operating income figures for each year. (Loss amounts and amounts to be deducted should be indicated with a minus sign. Omit the "$" sign in your response.)

Reconciliation of Variable Costing and Absorption Costing Net Operating Incomes
	Year 1	Year 2
Variable costing net operating income (loss)	$	$
Add (deduct) fixed manufacturing overhead   deferred in (released from) inventory under   absorption costing
Absorption costing net operating income (loss)	$	$

Explanation:

1. 

The unit product cost under the variable costing is computed as follows:

Direct materials	$	8
Direct labor		10
Variable manufacturing overhead		2
Variable costing unit product cost	$	20

 

	Year 1		Year 2
Variable cost of goods sold @ $20 per unit	$	400,000	$	600,000
Variable selling and administrative expenses @ $3 per unit	$	60,000	$	90,000

2.

Add (deduct) fixed manufacturing overhead deferred in (released from) inventory under absorption costing (5,000 units × $14 per unit in Year 1; 5,000 units × $14 per unit in Year 2) = $70,000

Wiengot Antennas, Inc., produces and sells a unique type of TV antenna. The company has just opened a new plant to manufacture the antenna, and the following cost and revenue data have been provided for the first month of the plant’s operation.

Wiengot Antennas, Inc., produces and sells a unique type of TV antenna. The company has just opened a new plant to manufacture the antenna, and the following cost and revenue data have been provided for the first month of the plant’s operation.

Beginning inventory		0
Units produced		40,000
Units sold		35,000
Selling price per unit		$60
Selling and administrative expenses:
Variable per unit		$2
Fixed (total)	$	560,000
Manufacturing costs
Direct materials cost per unit		$15
Direct labor cost per unit		$7
Variable manufacturing overhead cost per unit		$2
Fixed manufacturing overhead cost (total)	$	640,000

Because the new antenna is unique in design, management is anxious to see how profitable it will be and has asked that an income statement be prepared for the month.

   

Required:

1.	Assume that the company uses absorption costing.

  

a.	Determine the unit product cost. (Omit the "$" sign in your response.)

Unit product cost

$

b.	Prepare an income statement for the month. (Input all amounts as positive values except losses which should be indicated by a minus sign. Omit the "$" sign in your response.)

Absorption Costing Income Statement
Sales	$
Cost of goods sold
Gross margin
Selling and administrative expenses
Net operating income (loss)	$

    

2.	Assume that the company uses variable costing.

   

a.	Determine the unit product cost. (Omit the "$" sign in your response.)

Unit product cost

$

b.	Prepare a contribution format income statement for the month. (Input all amounts as positive values except losses which should be indicated by a minus sign. Omit the "$" sign in your response.)

    

Variable Costing Income Statement
Sales		$
Variable expenses:
Variable cost of goods sold	$
Variable selling and administrative expenses
Contribution margin
Fixed expenses:
Fixed manufacturing overhead
Fixed selling and administrative expenses
Net operating income (loss)		$

Explanation: 1.
a.
The unit product cost under absorption costing is:
 

Direct materials	$	15
Direct labor		7
Variable manufacturing overhead		2
Fixed manufacturing overhead (640,000 ÷ 40,000 units)		16
Absorption costing unit product cost	$	40

b.

Sales (35,000 units × $60 per unit) = $2,100,000

Cost of goods sold (35,000 units × $40 per unit) = $1,400,000

Selling and administrative expenses (35,000 units × $2 per unit) + $560,000 = $630,000

2.
a.
The unit product cost under variable costing is:
 

Direct materials	$	15
Direct labor		7
Variable manufacturing overhead		2
Variable costing unit product cost	$	24

b.

Sales (35,000 units × $60 per unit) = $2,100,000

Variable cost of goods sold (35,000 units × $24 per unit) = $840,000

Variable selling and administrative expense (35,000 units × $2 per unit) = $70,000

Suppose your company needs to raise $36.2 million and you want to issue 22-year bonds for this purpose. Assume the required return on your bond issue will be 8.7 percent, and you’re evaluating two issue alternatives: a 8.7 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent. Requirement 1: (a) How many of the coupon bonds would you need to issue to raise the $36.2 million? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567).) Number of coupon bonds (b) How many of the zeroes would you need to issue? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).) Number of zero coupon bonds Requirement 2: (a) In 22 years, what will your company’s repayment be if you issue the coupon bonds? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).) Coupon bonds repayment $ (b) What if you issue the zeroes? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to the nearest whole dollar amount (e.g., 32).) Zero coupon bonds repayment $ Requirement 3: Assume that the IRS amortization rules apply for the zero coupon bonds. Calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. (Do not round intermediate calculations. Input a cash outflow as a negative value and a cash inflow as a positive value. Enter your answers in dollars, not millions of dollars (e.g., 1,234,567). Round your answers to 2 decimal places (e.g., 32.16).) Coupon bond cash flow $ Zero coupon bond cash flow $ Explanation: 1: (a) The coupon bonds have a 8.7 percent coupon which matches the 8.7 percent required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price, so: Number of coupon bonds to sell = $36,200,000 / $1,000 = 36,200 (b) The number of zero coupon bonds to sell would be: Price of zero coupon bonds = $1,000/1.043544 = $153.58 Number of zero coupon bonds to sell = $36,200,000 / $153.58 = 235,709.19 2: (a) The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So: Coupon bonds repayment = 36,200($1,000) + 36,200($1,000)(.087/2) = $37,774,700 (b) The repayment of the zero coupon bond will be the par value times the number of bonds issued, so: Zeroes repayment = 235,709.19($1,000) = $235,709,193 3: The total coupon payment for the coupon bonds will be the number bonds times the coupon payment. For the cash flow of the coupon bonds, we need to account for the tax deductibility of the interest payments. To do this, we will multiply the total coupon payment times one minus the tax rate. So: Coupon bonds: (36,200)($87)(1 – .35) = $2,047,110 cash outflow Note that this is cash outflow since the company is making the interest payment. For the zero coupon bonds, the first year interest payment is the difference in the price of the zero at the end of the year and the beginning of the year. The price of the zeroes in one year will be: P1 = $1,000/1.043542 = $167.23 The Year 1 interest deduction per bond will be this price minus the price at the beginning of the year, which we found in part b, so: Year 1 interest deduction per bond = $167.23 – 153.58 = $13.65 The total cash flow for the zeroes will be the interest deduction for the year times the number of zeroes sold, times the tax rate. The cash flow for the zeroes in year 1 will be: Cash flows for zeroes in Year 1 = (235,709.19)($13.65)(.35) = $1,126,264.81 Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow. During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes. Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. (a) The coupon bonds have a 8.7% coupon which matches the 8.7% required return, so they will sell at par. For the zeroes, the price is: Enter 22 × 2 8.7% / 2 ±$1,000 N I/Y PV PMT FV Solve for $153.58 (c) The price of the zeroes in one year will be: Enter 21 × 2 8.7% / 2 ±$1,000 N I/Y PV PMT FV Solve for $167.23

Suppose your company needs to raise $36.2 million and you want to issue 22-year bonds for this purpose. Assume the required return on your bond issue will be 8.7 percent, and you’re evaluating two issue alternatives: a 8.7 percent semiannual coupon bond and a zero coupon bond. Your company’s tax rate is 35 percent.

 

Requirement 1:

(a)	How many of the coupon bonds would you need to issue to raise the $36.2 million? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567).)

 

Number of coupon bonds

 

(b)	How many of the zeroes would you need to issue? (Do not round intermediate calculations. Enter the whole number for your answer, not millions (e.g., 1,234,567). Round your answer to 2 decimal places (e.g., 32.16).)

 

Number of zero coupon bonds

 

Requirement 2:

(a)	In 22 years, what will your company’s repayment be if you issue the coupon bonds? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567).)

 

Coupon bonds repayment

$

 

(b)	What if you issue the zeroes? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars (e.g., 1,234,567). Round your answer to the nearest whole dollar amount (e.g., 32).)

 

Zero coupon bonds repayment

$

 

Requirement 3:

Assume that the IRS amortization rules apply for the zero coupon bonds.

Calculate the firm’s aftertax cash outflows for the first year under the two different scenarios. (Do not round intermediate calculations. Input a cash outflow as a negative value and a cash inflow as a positive value. Enter your answers in dollars, not millions of dollars (e.g., 1,234,567). Round your answers to 2 decimal places (e.g., 32.16).)

 

Coupon bond cash flow	$
Zero coupon bond cash flow	$

Explanation:

1:

(a)

The coupon bonds have a 8.7 percent coupon which matches the 8.7 percent required return, so they will sell at par. The number of bonds that must be sold is the amount needed divided by the bond price, so:

Number of coupon bonds to sell = $36,200,000 / $1,000 = 36,200

(b)

The number of zero coupon bonds to sell would be:

Price of zero coupon bonds = $1,000/1.043544 = $153.58

Number of zero coupon bonds to sell = $36,200,000 / $153.58 = 235,709.19

2:

(a)

The repayment of the coupon bond will be the par value plus the last coupon payment times the number of bonds issued. So:

Coupon bonds repayment = 36,200($1,000) + 36,200($1,000)(.087/2) = $37,774,700

(b)

The repayment of the zero coupon bond will be the par value times the number of bonds issued, so:

Zeroes repayment = 235,709.19($1,000) = $235,709,193

3:

The total coupon payment for the coupon bonds will be the number bonds times the coupon payment. For the cash flow of the coupon bonds, we need to account for the tax deductibility of the interest payments. To do this, we will multiply the total coupon payment times one minus the tax rate. So:

Coupon bonds: (36,200)($87)(1 – .35) = $2,047,110 cash outflow

Note that this is cash outflow since the company is making the interest payment.

For the zero coupon bonds, the first year interest payment is the difference in the price of the zero at the end of the year and the beginning of the year. The price of the zeroes in one year will be:

P1 = $1,000/1.043542 = $167.23

The Year 1 interest deduction per bond will be this price minus the price at the beginning of the year, which we found in part b, so:

Year 1 interest deduction per bond = $167.23 – 153.58 = $13.65

The total cash flow for the zeroes will be the interest deduction for the year times the number of zeroes sold, times the tax rate. The cash flow for the zeroes in year 1 will be:

Cash flows for zeroes in Year 1 = (235,709.19)($13.65)(.35) = $1,126,264.81

Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the imputed interest expense. That is, the company gets to write off the interest expense for the year, even though the company did not have a cash flow for the interest expense. This reduces the company’s tax liability, which is a cash inflow.

During the life of the bond, the zero generates cash inflows to the firm in the form of the interest tax shield of debt. We should note an important point here: If you find the PV of the cash flows from the coupon bond and the zero coupon bond, they will be the same. This is because of the much larger repayment amount for the zeroes.

 

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

 

(a)	The coupon bonds have a 8.7% coupon which matches the 8.7% required return, so they will sell at par. For the zeroes, the price is:

 

Enter

22 × 2

8.7% / 2

±$1,000

N

I/Y

PV

PMT

FV

Solve for

$153.58

 

(c)	The price of the zeroes in one year will be:

 

Enter

21 × 2

8.7% / 2

±$1,000

N

I/Y

PV

PMT

FV

Solve for

$167.23

Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 3.9 percent. Required: What was your real return? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Real return % Explanation: The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is: (1 + R) = (1 + r)(1 + h) r = [(1 + .15) / (1 + .039)] – 1 r = .1068, or 10.68%

Say you own an asset that had a total return last year of 15 percent. Assume the inflation rate last year was 3.9 percent.

Required:

What was your real return? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Real return

%

Explanation:

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is:

(1 + R) = (1 + r)(1 + h)

r = [(1 + .15) / (1 + .039)] – 1

r = .1068, or 10.68%

Volbeat Corporation has bonds on the market with 12.5 years to maturity, a YTM of 9.8 percent, and a current price of $949. The bonds make semiannual payments.

Volbeat Corporation has bonds on the market with 12.5 years to maturity, a YTM of 9.8 percent, and a current price of $949. The bonds make semiannual payments.

Required:

What must the coupon rate be on the bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Coupon rate

%

Explanation:

Here, we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:

P = $949 = C(PVIFA4.90%,25) + $1,000(PVIF4.90%,25)

Solving for the coupon payment, we get:

C = $45.42

Since this is the semiannual payment, the annual coupon payment is:

2 × $45.42 = $90.84

And the coupon rate is the coupon rate divided by par value, so:

Coupon rate = $90.84 / $1,000

Coupon rate = .0908, or 9.08%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

12.5 × 2

9.8% / 2

±$949

$1,000

N

I/Y

PV

PMT

FV

Solve for

$45.42

Annual coupon = $45.42 × 2

Annual coupon = $90.84

Coupon rate = $90.84 / $1,000

Coupon rate = 9.08%

 

App Store Co. issued 17-year bonds one year ago at a coupon rate of 6.8 percent. The bonds make semiannual payments.

App Store Co. issued 17-year bonds one year ago at a coupon rate of 6.8 percent. The bonds make semiannual payments.

Required:

If the YTM on these bonds is 5.4 percent, what is the current bond price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current bond price

$

Explanation:

To find the price of this bond, we need to realize that the maturity of the bond is 16 years. The bond was issued one year ago, with 17 years to maturity, so there are 16 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is:

P = $34.00(PVIFA2.70%,32) + $1,000(PVIF2.70%,32)

P = $1,148.73

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

16 × 2

5.4% / 2

±$68 / 2

±$1,000

N

I/Y

PV

PMT

FV

Solve for

$1,148.73