Your job pays you only once a year for all the work you did over the previous 12 months. Today,

Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $67,000 and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 10 percent of your annual salary in an account that will earn 10.7 percent per year. Your salary will increase at 4 percent per year throughout your career.

 

How much money will you have on the date of your retirement 45 years from today? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Future value

$

Explanation:

Since your salary grows at 4 percent per year, your salary next year will be:

 

Next year’s salary = $67,000 (1 + 0.040)

Next year’s salary = $69,680

This means your deposit next year will be:

Next year’s deposit = $69,680(0.10)

Next year’s deposit = $6,968

Since your salary grows at 4 percent, your deposit will also grow at 4 percent. We can use the present value of a growing perpetuity equation to find the value of your deposits today. Doing so, we find:

PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}

PV = $6,968{[1/(0.107 – 0.040)] – [1/(0.107 – 0.040)] × [(1 + 0.040)/(1 + 0.107)]45}

PV = $97,735.44

Now, we can find the future value of this lump sum in 45 years. We find:

FV = PV(1 + r)t

FV = $97,735.44(1 + 0.11)45

FV = $9,477,526.47

This is the value of your savings in 45 years.

You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years and the payments will increase 3.9 percent per year.

You have just won the lottery and will receive $1,000,000 in one year. You will receive payments for 30 years and the payments will increase 3.9 percent per year.

 

If the appropriate discount rate is 7.9 percent, what is the present value of your winnings? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Present value

$

Explanation:

We can use the present value of a growing annuity equation to find the value of your deposits today. Doing so, we find:

PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g) / (1 + r)]t}

PV = $1,000,000{[1/(0.079 – 0.039)] – [1/(0.079 – 0.039)] × [(1 + 0.039) / (1 + 0.079)]30}

PV = $16,950,607.68

You are planning to save for retirement over the next 30 years. To do this, you will invest $890 a month in a stock account and $490 a month in a bond account. The return of the stock account is expected to be 10.9 percent, and the bond account will pay 6.9 percent. When you retire, you will combine your money into an account with a 7.9 percent return.

You are planning to save for retirement over the next 30 years. To do this, you will invest $890 a month in a stock account and $490 a month in a bond account. The return of the stock account is expected to be 10.9 percent, and the bond account will pay 6.9 percent. When you retire, you will combine your money into an account with a 7.9 percent return.

How much can you withdraw each month from your account assuming a 25-year withdrawal period? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Withdrawal

$ per month

Explanation:

We need to find the annuity payment in retirement. Our retirement savings ends and the retirement withdrawals begin, so the PV of the retirement withdrawals will be the FV of the retirement savings. So, we find the FV of the stock account and the FV of the bond account and add the two FVs.

Stock account: FVA = $890[{[1 + (0.109/12)]360 − 1} / (0.109/12)] = $2,442,269.68

Bond account: FVA = $490[{[1 + (0.069/12)]360 − 1} / (0.069/12)] = $586,123.47

So, the total amount saved at retirement is:

$2,442,269.68 + 586,123.47 = $3,028,393.15

Solving for the withdrawal amount in retirement using the PVA equation gives us:

PVA = $3,028,393.15 = $C[1 – {1 / [1 + (0.079/12)]300} / (0.079/12)]

C = $3,028,393.15 / 130.68420 = $23,173.37 withdrawal per month

   

Calculator Solution:

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

Stock account:

 

Enter

360

10.9% / 12

$890

N

I/Y

PV

PMT

FV

Solve for

$2,442,269.68

 

Bond account:

 

Enter

360

6.9% / 12

$490

N

I/Y

PV

PMT

FV

Solve for

$586,123.47

Beginning three months from now, you want to be able to withdraw $2,700 each quarter from your bank account to cover college expenses over the next three years. If the account pays 0.49 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next three years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

PVA

$

rev: 11_14_2012

Explanation:

The cash flows are simply an annuity with four payments per year for three years, or 12 payments. We can use the PVA equation:

PVA = C({1 − [1/(1 + r)t]} / r)

PVA = $2,700{[1 − (1/1.0049)12] / 0.0049}

PVA = $31,391.23

 

Calculator Solution:

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

   

Enter

3 × 4

0.49%

$2,700

N

I/Y

PV

PMT

FV

Solve for

$31,391.23

 

At 6.10 percent interest, how long does it take to double your money? (Round your answer to 2 decimal places. (e.g., 32.16)) Length of time years At 6.10 percent interest, how long does it take to quadruple it? (Round your answer to 2 decimal places. (e.g., 32.16)) Length of time years Explanation: To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is: FV = PV(1 + r)t Solving for t, we get: t = ln(FV / PV) / ln(1 + r) The length of time to double your money is: FV = $2 = $1(1.061)t t = ln(2) / ln(1.061) = 11.71 years The length of time to quadruple your money is: FV = $4 = $1(1.061)t t = ln(4) / ln(1.061) = 23.41 years Notice that the length of time to quadruple your money is twice as long as the time needed to double your money (the difference in these answers is due to rounding). This is an important concept of time value of money. Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 6.10% $1 ±$2 N I/Y PV PMT FV Solve for 11.71 Enter 6.10% $1 ±$4 N I/Y PV PMT FV Solve for 23.41

At 6.10 percent interest, how long does it take to double your money? (Round your answer to 2 decimal places. (e.g., 32.16))

 

Length of time

years

At 6.10 percent interest, how long does it take to quadruple it? (Round your answer to 2 decimal places. (e.g., 32.16))

Length of time

years

Explanation:

To find the length of time for money to double, triple, etc., the present value and future value are irrelevant as long as the future value is twice the present value for doubling, three times as large for tripling, etc. We can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:

FV = PV(1 + r)t

Solving for t, we get:

t = ln(FV / PV) / ln(1 + r)

The length of time to double your money is:

FV = $2 = $1(1.061)t

t = ln(2) / ln(1.061) = 11.71 years

The length of time to quadruple your money is:

FV = $4 = $1(1.061)t

t = ln(4) / ln(1.061) = 23.41 years

  

Notice that the length of time to quadruple your money is twice as long as the time needed to double your money (the difference in these answers is due to rounding). This is an important concept of time value of money.

Calculator Solution:

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

Enter

6.10%

$1

±$2

N

I/Y

PV

PMT

FV

Solve for

11.71

Enter

6.10%

$1

±$4

N

I/Y

PV

PMT

FV

Solve for

23.41

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Whitman Corporation, a merchandising company, reported sales of 12,100 units for May at a selling

Whitman Corporation, a merchandising company, reported sales of 12,100 units for May at a selling price of $714 per unit. The cost of goods sold (all variable) was $448 per unit and the variable selling expense was $63 per unit. The total fixed selling expense was $163,800. The variable administrative expense was $28 per unit and the total fixed administrative expense was $376,100.

Required:
a.	Prepare a contribution format income statement for May. (Input all amounts as positive values. Omit the "$" sign in your response.)

Whitman Corporation Income Statement
Sales		$
Variable expenses:
Cost of goods sold	$
Variable selling expense
Variable administrative expense
Contribution margin
Fixed expenses:
Fixed selling expense
Fixed administrative expense
Net operating income (loss)		$

b.	Prepare a traditional format income statement for May. (Input all amounts as positive values. Omit the "$" sign in your response.)

                                        

Whitman Corporation Income Statement
Sales		$
Cost of goods sold
Gross margin
Operating expenses:
Selling expense	$
Administrative expense
Net operating income (loss)		$

Explanation: a.

Sales (12,100 units × $714 per unit) = $8,639,400

Cost of goods sold (12,100 units × $448 per unit) = $5,420,800

Variable selling expense (12,100 units × $63 per unit) = $762,300

Variable administrative expense (12,100 units × $28 per unit) = $338,800

b.

Sales (12,100 units × $714 per unit) = $8,639,400

Cost of goods sold (12,100 units × $448 per unit) = $5,420,800

Selling expense ((12,100 units × $63 per unit) + $163,800) = $926,100

Administrative expense ((12,100 units × $28 per unit) + $376,100) = $714,900