Chapter 6, Problem 6.16E

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  $Presentvalue=Futurevalue/\left(1+rate\right)n$

Where n denotes the number of periods

Also, present value can be computed from the following formula:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

Requirement a:

To calculate:

Present value if interest is compounded semi- annually

Answer to Problem 6.16E

Present value of $1, 00,000 when interest is compounded semi- annually= $46,320

Explanation of Solution

To calculate the present value of $1, 00,000 when interest is compounded semi- annually, we will be using the table indicating present value factors.

In the given problem, following information is given:

Future value to be received= $1, 00,000

Rate of interest= 16%

Time period= 5 years

Since the time period is semi- annually, the rate of interest of 16% would be halved (16/2) i.e. 8% and the time period of 5 years would be doubled (5 years*2) i.e. 10 years. By taking value from the present value table for 8% in 10^th period row, the factor value is coming out to be 0.463193. Now, the following formula would be used:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

  $Therefore,Presentvalue=\$1,00,000*0.4632=\$46,320$

Thus, present value of $1, 00,000 when interest is compounded semi- annually is $46,320.

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  $Presentvalue=Futurevalue/\left(1+rate\right)n$

Where n denotes the number of periods

Also, present value can be computed from the following formula:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

Requirement b:

To calculate:

Present value if interest is compounded quarterly

Answer to Problem 6.16E

Present value of $1, 00,000 when interest is compounded quarterly= $45,640

Explanation of Solution

To calculate the present value of $1, 00,000 when interest is compounded quarterly, we will be using the table indicating present value factors.

In the given problem, following information is given:

Future value to be received= $1, 00,000

Rate of interest= 16%

Time period= 5 years

Since the time period is semi- annually, the rate of interest of 16% would be 1/4^th(16/4) i.e. 4% and the time period of 5 years would be four times (5 years*4) i.e. 20 years. By taking value from the present value table for 4% in 20^th period row, the factor value is coming out to be 0.4564. Now, the following formula would be used:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

  $\begin{array}{l} \hfill \\ Therefore,Presentvalue=\$1,00,000*0.4564=\$45,640\hfill \end{array}$

Thus, present value of $1, 00,000 when interest is compounded semi- annually is $45,640.

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  $Presentvalue=Futurevalue/\left(1+rate\right)n$

Where n denotes the number of periods

Also, present value can be computed from the following formula:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

Requirement c:

To calculate:

Present value if discount rate of 12% is used

Answer to Problem 6.16E

Present value of $1, 00,000 when discount rate of 12%= $56,740

Explanation of Solution

For calculating the present value of $1, 00,000 when discount rate is 12%, we will be using the table indicating present value factors.

In the given problem, following information is given:

Future value to be received= $1, 00,000

Rate of interest= 12%

Time period= 5 years

Since the discount rate is 12% and time period of 5 years is given. By taking value from the present value table for 12% in 5^th period row, the factor value is coming out to be 0.5674. Now, the following formula would be used:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

  $Therefore,Presentvalue=\$1,00,000*0.5674=\$56,740$

Thus, present value of $1, 00,000 when discount rate of 12% is $56,740.

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  $Presentvalue=Futurevalue/\left(1+rate\right)n$

Where n denotes the number of periods

Also, present value can be computed from the following formula:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

Requirement d:

To calculate:

Present value if discount rate of 20% is used

Answer to Problem 6.16E

Present value of $1, 00,000 when discount rate of 20%= $40,190

Explanation of Solution

For calculating the present value of $1, 00,000 when discount rate is 20%, we will be using the table indicating present value factors.

In the given problem, following information is given:

Future value to be received= $1, 00,000

Rate of interest= 20%

Time period= 5 years

Since the discount rate is 20% and time period of 5 years is given. By taking value from the present value table for 20% in 5^th period row, the factor value is coming out to be 0.4019. Now, the following formula would be used:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

  $Therefore,Presentvalue=\$1,00,000*0.4019=\$40,190$

Thus, present value of $1, 00,000 when discount rate of 20% is $40,190.

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  $Presentvalue=Futurevalue/\left(1+rate\right)n$

Where n denotes the number of periods

Also, present value can be computed from the following formula:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

Requirement e:

To calculate:

Present value if cash is received in 3 years

Answer to Problem 6.16E

Present value of $1, 00,000 when cash is received in 3 years= $64,070

Explanation of Solution

For calculating the present value of $1, 00,000 when cash is received in 3 years, we will be using the table indicating present value factors.

In the given problem, following information is given:

Future value to be received= $1, 00,000

Rate of interest= 16%

Time period= 3 years

Since the discount rate is 16% and time period of 3 years is taken. By taking value from the present value table for 20% in 3^rd period row, the factor value is coming out to be 0.6407. Now, the following formula would be used:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

  $Therefore,Presentvalue=\$1,00,000*0.6407=\$64,070$

Thus, present value of $1, 00,000 when time period is 3 years is $64,070.

To determine

Concept Introduction:

Present value Present value, also known as discounted value is the current value for a future sum of money with a denied rate of return. The present value is computed by using discount rates on the given rate of return. It indicates whether the money received by an investor today would earn a return in the future. It helps to decide whether a particular stock is worth investing in today.

The expected cash flows are discounted at a discount rate which is actually the expected return. Further, the discount rate is inversely proportional to the future cash flows. It can be calculated using the below- mentioned formula:

  $Presentvalue=Futurevalue/\left(1+rate\right)n$

Where n denotes the number of periods

Also, present value can be computed from the following formula:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

Requirement f:

To calculate:

Present value if cash is received in 7 years

Answer to Problem 6.16E

Present value of $1, 00,000 when cash is received in 7 years= $35,380

Explanation of Solution

For calculating the present value of $1, 00,000 when cash is received in 7 years, we will be using the table indicating present value factors.

In the given problem, following information is given:

Future value to be received= $1, 00,000

Rate of interest= 16%

Time period= 7 years

Since the discount rate is 16% and time period of 7 years is taken. By taking value from the present value table for 20% in 7^th period row, the factor value is coming out to be 0.3538. Now, the following formula would be used:

  $Presentvalue=Futurevaluetobereceived*Presentvalueof\$1$

  $Therefore,Presentvalue=\$1,00,000*0.3538=\$35,380$

Thus, present value of $1, 00,000 when time period is 7 years is $35,380.