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?

a. $203,969.69
b. $262,205.54
c. $1,144,000.00
d. $762,183.00
e. $1,273,500.80

Answer 1

Total PV= $262,205.54

Step-by-step explanation:

Giving the following information:

Discount rate= 10%

We need to calculate the present value of each cash flow, and then the total present value. We will start from the lasts payments to the firsts.

To calculate the present value, first, we need to determine the value at the moment of each change in cash flow:

PV= A*{(1/i) - 1/[i*(1 + i)^n]}

A= annual cash flow

53,000 for 12 years:

PV= 53,000*{(1/0.1) - 1/[0.1*(1.1^12)]}

PV= $361,125.67

27,000 for 12 years:

PV= 27,000*{(1/0.1) - 1/[0.1*(1.1^12)]}

PV= $183,969.68

23,000 for 8 years:

PV= 23,000*{(1/0.1) - 1/[0.1*(1.1^8)]}

PV= $122,703.30

Now, the value today of each part:

PV= FV / (1 + i)^n

PV1= 361,125.67 / (1.1^20)= $53,679.03

PV2= 183,969.68 / (1.1^8)= $85,823.21

PV3= 122,703.3

Total PV= $262,205.54