For each of the following, compute the future value (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

For each of the following, compute the future value (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):

 

Present Value				Years		Interest Rate			Future Value
	$	2,050		12		12	%		$
		8,352		6		10
		72,355		13		11
		179,796		7		7

Explanation:

To find the FV of a lump sum, we use:

  

FV = PV(1 + r)t

 

FV = $2,050(1.12)12	=	$	7,986.75
FV = $8,352(1.10)6	=	$	14,796.08
FV = $72,355(1.11)13	=	$	280,974.74
FV = $179,796(1.07)7	=	$	288,713.09

Calculator Solution:

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

Enter

12

12%

±$2,050

N

I/Y

PV

PMT

FV

Solve for

$7,986.75

Enter

6

10%

±$8,352

N

I/Y

PV

PMT

FV

Solve for

$14,796.08

Enter

13

11%

±$72,355

N

I/Y

PV

PMT

FV

Solve for

$280,974.74

Enter

7

7%

±$179,796

N

I/Y

PV

PMT

FV

Solve for

$288,713.09

Y3K, Inc., has sales of $4,500, total assets of $2,820, and a debt−equity ratio of 1.40. If its return on equity is 20 percent, what its net income?

Y3K, Inc., has sales of $4,500, total assets of $2,820, and a debt−equity ratio of 1.40. If its return on equity is 20 percent, what its net income?

rev: 09_17_2012

	$564.00
	$147.27
	$235.00
	$900.00
	$87.73

This is a multi-step problem involving several ratios. The ratios given are all part of the DuPont Identity. The only DuPont Identity ratio not given is the profit margin. If we know the profit margin, we can find the net income since sales are given. So, we begin with the DuPont Identity:

ROE = 0.20 = (PM)(TAT)(EM) = (PM)(S / TA)(1 + D/E)

Solving the DuPont Identity for profit margin, we get:

PM = [(ROE)(TA)] / [(1 + D/E)(S)]

PM = [(0.20)($2,820)] / [(1 + 1.40)($4,500)] = 0.0522

Now that we have the profit margin, we can use this number and the given sales figure to solve for net income:

PM = 0.0522 = NI / S

NI = 0.0522($4,500) = $235.00

You want to buy a new sports coupe for $73,500, and the finance office at the dealership has quoted you a 5.5 percent APR loan for 72 months to buy the car.

You want to buy a new sports coupe for $73,500, and the finance office at the dealership has quoted you a 5.5 percent APR loan for 72 months to buy the car.

What will your monthly payments be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Monthly payment

$

What is the effective annual rate on this loan? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Effective annual rate

%

Explanation:

We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation:

PVA = C({1 − [1 / (1 + r)t]} / r)

$73,500 = $C[1 − {1 / [1 + (0.055/12)]72} / (0.055/12)]

Solving for the payment, we get:

C = $73,500 / 61.20742 = $1,200.83

To find the EAR, we use the EAR equation:

EAR = [1 + (APR / m)]m − 1

EAR = [1 + (0.055 / 12)]12 − 1 = 0.0564, or 5.64%

 

Calculator Solution:

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

 

Enter

72

5.50% / 12

$73,500

N

I/Y

PV

PMT

FV

Solve for

$1,200.83

  

Enter	5.5%						12
		NOM			EFF			C/Y
Solve for				5.64%

If you put up $47,000 today in exchange for a 6.75 percent, 14-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

If you put up $47,000 today in exchange for a 6.75 percent, 14-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Annual cash flow

$

Explanation:

Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation:

PVA = C({1 − [1/(1 + r)t]} / r)

PVA = $47,000 = $C{[1 − (1/1.067514)] / 0.0675}

We can now solve this equation for the annuity payment. Doing so, we get:

C = $47,000 / 8.878105 = $5,293.92

   

Calculator Solution:

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

   

Enter

14

6.75%

$47,000

N

I/Y

PV

PMT

FV

Solve for

$5,293.92

An investment offers $6,700 per year for 15 years, with the first payment occurring one year from now. If the required return is 6 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Present value $ What would the value be if the payments occurred for 40 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Present value $ What would the value be if the payments occurred for 75 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Present value $ What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Present value $ Explanation: To find the PVA, we use the equation: PVA = C({1 − [1/(1 + r)t]} / r) PVA@15 yrs: PVA = $6,700{[1 − (1/1.0615)] / 0.06} = $65,072.07 PVA@40 yrs: PVA = $6,700{[1 − (1/1.0640)] / 0.06} = $100,810.19 PVA@75 yrs: PVA = $6,700{[1 − (1/1.0675)] / 0.06} = $110,254.18 To find the PV of a perpetuity, we use the equation: PV = C / r PV = $6,700 / 0.06 = $111,666.67 Notice that as the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. The present value of the 75-year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only $1,412.48. Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter 15 6% $6,700 N I/Y PV PMT FV Solve for $65,072.07 Enter 40 6% $6,700 N I/Y PV PMT FV Solve for $100,810.19 Enter 75 6% $6,700 N I/Y PV PMT FV Solve for $110,254.18

An investment offers $6,700 per year for 15 years, with the first payment occurring one year from now.

If the required return is 6 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

$

What would the value be if the payments occurred for 40 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Present value

$

What would the value be if the payments occurred for 75 years? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

Present value

$

 

What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  

Present value

$

Explanation:

To find the PVA, we use the equation:

PVA = C({1 − [1/(1 + r)t]} / r)

PVA@15 yrs: PVA = $6,700{[1 − (1/1.0615)] / 0.06} = $65,072.07

PVA@40 yrs: PVA = $6,700{[1 − (1/1.0640)] / 0.06} = $100,810.19

PVA@75 yrs: PVA = $6,700{[1 − (1/1.0675)] / 0.06} = $110,254.18

To find the PV of a perpetuity, we use the equation:

PV = C / r

PV = $6,700 / 0.06 = $111,666.67

Notice that as the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. The present value of the 75-year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only $1,412.48.

   

Calculator Solution:

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

   

Enter

15

6%

$6,700

N

I/Y

PV

PMT

FV

Solve for

$65,072.07

   

Enter

40

6%

$6,700

N

I/Y

PV

PMT

FV

Solve for

$100,810.19

   

Enter

75

6%

$6,700

N

I/Y

PV

PMT

FV

Solve for

$110,254.18

You have just received notification that you have won the $3 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 63 years from now.

You have just received notification that you have won the $3 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday (assuming you’re around to collect), 63 years from now.

 

What is the present value of your windfall if the appropriate discount rate is 10 percent? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

 

Present value

$

Explanation:

To find the PV of a lump sum, we use:

PV = FV / (1 + r)t

PV = $3,000,000 / (1.10)63 = $7,402.56

Calculator Solution:

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

Enter

63

10%

$3,000,000

N

I/Y

PV

PMT

FV

Solve for

$7,402.56

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