The monthly income from a piece of commercial property is $1,200. Annual expenses are $3,000 for upkeep of the property and $1,000 for property taxes. The property is surrounded by a security fence that cost $4,000 to install four years ago. Required:
a. If i 8.6% per year (the MARR) is an acceptable interest rate, how much could you afford to pay now for this property if it is estimated to have a resale value of $150,000 9 years from now?
b. Let's assume that the interest rate is 5%. If the 5% interest had been a nominal interest rate, what would the corresponding effective annual interest rate have been with bi-weekly (every two weeks) compounding?

a. The amount you could afford to pay now for this property is $134,765.04.

b. Effective annual rate (EAR) = 5.12%

Explanation:

a. If i 8.6% per year (the MARR) is an acceptable interest rate, how much could you afford to pay now for this property if it is estimated to have a resale value of $150,000 9 years from now?

Step 1: Calculation of the present value of the annual net cash inflow

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PVAC = AC * ((1 - (1 / (1 + i))^n) / i) …………………………………. (1)

Where;

PVAC = Present value of the annual cash inflow = ?

AC = Annual net cash inflow = (Annual rent * Number of months in a year) – Annual property upkeep expense – Annual property tax = ($1,200 * 12) - $3,000 - $1,000 = $10,400

i = annual interest rate = 8.6%, or 0.086

n = number of years = 9

Substitute the values into equation (1), we have:

PVAC = $10,400 * ((1 - (1 / (1 + 0.086))^9) / 0.086) = $63,377.43

Step 2: Calculation of the present value of the resale value

This can be calculated using the formula for calculating the present value as follows:

PVRV = RV / (1 + i)^n (2)

Where;

PVRV = present value of the resale value = ?

RV = resale value = $150,000

i = annual interest rate = 8.6%, or 0.086

n = number of years = 9

Substitute the values into equation (2), we have:

PVRV = $150,000 / (1 + 0.086)^9 = $71,387.61

Step 2: Calculation of the amount you could afford to pay now for this property

PVAC = Present value of the annual cash inflow = $63,377.43

PVRV = present value of the resale value = $71,387.61

Amount you could afford to pay now = PVAC + PVRV = $63,377.43 + $71,387.61 = $134,765.04

b. Let's assume that the interest rate is 5%. If the 5% interest had been a nominal interest rate, what would the corresponding effective annual interest rate have been with bi-weekly (every two weeks) compounding?

The effective annual rate (EAR) can be calculated using the following formula:

EAR = ((1 + (i / n))^n) - 1 (3)

Where;

i = Annual nominal interest rate = 5%, or 0.05

n = Number of compounding periods in a year = Number of bi-week in a year = Number of weeks in a year / 2 = 52 / 2 = 26

Substitute the values into equation (3), we have:

EAR = ((1 + (0.05 / 26))^26) - 1 = 0.0512206204121786, or 5.12206204121786%

Rounding to 2 decimal places, we have:

EAR = 5.12%

answer; at prices that violate government price regulations;