(1) Assume, you will receive rent payments over a time period of 44 years. For the first 22 years, you will receive a rent of $222 at the beginning of each year. For the next 22 years thereafter, you will receive $222 at the end of each year. (a) Employing the equation for identical payments over a limited time period, show how you would alter this equation applied to this problem. (b) Assuming a discount rate of 2% calculate the net present value of this income stream

Ans: $6,534

Explanation:

The given payment cash flows are described as follows:

1st payment in the year 0 = $222

Uniform annual payments of $222 are received at the end of years 1(is the same as the start of year 2) though 21

Uniform annual payments of $222 are received at the end of years 23 through 44.

The only missing payment in the uniform annual series is at the end of year 22.

a) PW of the given cash flow = $222 + $222(P/A, 2%, 44) - $222(P/F, 2%, 22)

b) (P/A, 2%, 44) = [(1+0.02)^44 - 1]/[0.02*(0.02+1)^44] = 29.080

(P/F, 2%, 22) = 1/(1+0.02)^22 = 1/1.02^22 = 0.6468

PW = $222 + $222*29.080 - $222*0.6468 = $6,534

Ans: $6,534

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