You have an investment with 10 semi-annual cash flows of $1000. The first payment is 6 months from today. If the EAR is 11% what is the present value of this investment?
Don't know what EAR is, but I will assume your rate is 11% per annum compounded semi-annually
i = .11/2 = .055
PV = 1000(1 - 1.055^-10)/.055
= 7537.63
To calculate the present value of an investment with multiple cash flows, we need to discount each cash flow back to its present value using the effective annual interest rate (EAR).
First, let's determine the discount rate for each cash flow. Since the EAR is given as 11%, we need to convert it to the semi-annual interest rate. The formula to calculate the semi-annual interest rate is:
Semi-annual interest rate = (1 + EAR)^(1/n) - 1
In this case, n represents the number of periods per year, which is 2 since there are semi-annual cash flows. Let's calculate the semi-annual interest rate:
Semi-annual interest rate = (1 + 0.11)^(1/2) - 1
= (1.11)^(1/2) - 1
≈ 0.0524
The semi-annual interest rate is approximately 0.0524 (or 5.24%).
Next, we can use the formula for present value of an annuity to calculate the present value of the investment with 10 semi-annual cash flows of $1000:
Present Value = (Cash Flow / Discount Rate) * [1 - (1 / (1 + Discount Rate)^n)]
Cash Flow = $1000
Discount Rate = 0.0524 (semi-annual interest rate)
n = 10 (number of semi-annual periods)
Present Value = ($1000 / 0.0524) * [1 - (1 / (1 + 0.0524)^10)]
To calculate this equation, we substitute the values and perform the calculations:
Present Value = ($1000 / 0.0524) * [1 - (1 / (1.0524)^10)]
≈ $11,355.06
Therefore, the present value of this investment is approximately $11,355.06.