Question

You are valuing an investment that will pay you $23,000 per year for the first 8 years, $27,000 per year for the next 12 years, and $53,000 per year the following 12 years (all payments are at the end of each year). If the appropriate annual discount rate is 10.00%, what is the value of the investment to you today?

Answer 1

As per discounted cash flows, value of investment today is present value of cash flows in future.

Step-1:Calculation of present value of cash flow of first 8 years

Present value

=

Annual Cash flows * Present value of annuity of 1

=

$     23,000.00

*

5.334926

=

$ 1,22,703.30

Working:

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.10)^-8)/0.10

i

10.00%

=

5.334926198

n

8

Step-2:Calculation of present value of cash flows of next 12 years

Present Value

=

(Annual cash flows * Present value of annuity of 1 for 12 years)*Present value of 1 to be recived in 8 years

=

(

27000

*

6.81369182

)

*

0.466507

=

$     85,823.21

Working:

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.10)^-12)/0.10

i

10.00%

=

6.813691823

n

12

Present value of 1 to be received in 8 years

=

(1+i)^-n

Where,

=

(1+0.10)^-8

i

10.00%

=

0.466507

n

8

Step-3:Calculation of present value of cash flows of next 12 years

Present Value

=

(Annual cash flows * Present value of annuity of 1 for 12 years)*Present value of 1 to be recived in 20 years

=

(

53000

*

6.81369182

)

*

0.148644

=

$     53,679.03

Working:

Present value of annuity of 1

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.10)^-12)/0.10

i

10.00%

=

6.813691823

n

12

Present value of 1 to be received in 8 years

=

(1+i)^-n

Where,

=

(1+0.10)^-20

i

10.00%

=

0.148644

n

20

Step-4:Calculation of present value of total cash flows

Present value of all cash flows

=

$ 1,22,703.30

+

$ 85,823.21

+

$ 53,679.03

=

$ 2,62,205.54

Thus,

Value of investment today is

$ 2,62,205.54