Cameron is going to receive an annuity for 44 years of $31,596, and Kennedy is going to receive a perpetuity of that same amount. If the appropriate discount rate is 8%, how much more are Kennedy's cash flows worth today than Cameron's cash flows? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e. g., 32.16).)

Cameron:

Annual Payment = $31,596

Time Period = 44 years

Discount Rate = 8%

Present Worth = $31,596*(1-(1/1.08)^44)/0.08

Present Worth = $381,587.22

Kennedy:

Annual Payment = $31,596

Discount Rate = 8%

Present Worth = $31,596/0.08

Present Worth = $394,950.00

So, Present Worth of Kennedy is $13,362.78 more than that of Cameron.

Explanation:

$13,362.78

Explanation:

The worth of their cash flows today is known as the present value (PV). The calculations are done as follows:

1. For Cameron

Here, we are assuming Cameron's annuity is an ordinary annuity under which Cameron or any other investor receives payments at the end of each  time period over a period of time. The PV of an ordinary annuity formula is as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r]   (1)

Where

PVo = Present value of the ordinary annuity = ?

P = Periodic payment  = $31,596

r = interest rate  = 8% = 0.08

n = number of years = 44

The values above are substituted into equation (1) as follows:

PVo = $31,596 × [{1 - [1 ÷ (1 + 0.08)]^44} ÷ 0.08]

       = $31,596 × [{1 - [1 ÷ (1.08)]^44} ÷ 0.08]

       = $31,596 × [{1 - [0.925925925925926]^44} ÷ 0.08]

       = $31,596 × [{1 - 0.0338341101277985} ÷ 0.08]

       = $31,596 × [0.966165889872202 ÷ 0.08]

       = $31,596 ×  12.0770736234025  

       = $ 381,587.218205026  

Therefore, the today's worth of Cameron's cash flows is $ 381,587.218205026.

2. For Kennedy

The perpetuity means Kennedy's cash will flow periodically indefinitely. The formula for the PV of a perpetuity is as follows:

PVp = P ÷ r (2)

Where,

PVp = Present value of a perpetuity = ?

P = Periodic payment  = $31,596

r = interest rate  = 8% = 0.08

The values above are substituted into equation (1) as follows:

PVp = $31,596 ÷ 0.08

       = $394,950.00

Therefore, the today's worth of Kennedy's cash flows is $394,950.00.

3. How much more are Kennedy's cash flows worth today than Cameron's cash flows?

This is calculated as follows:

Difference = PVp of Kennedy - PVo of Cameron

Difference = $394,950.00 - $381,587.218205026

                 = $13,362.78  

Therefore, Kennedy's cash flows worth today is $13,362.78 more than Cameron's cash flows worth today.

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