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