Question

QUESTION 15 Cameron is going to receive an annuity for 30 years of $33.951, and Kennedy is going to receive a perpetuity of that same amount. If the appropriate discount rate is 6%, how much more are Kennedy's cash flows worth today than Cameron's cash flows? (Do not include the dollar sign ($). 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).)

Answer 1

The formula to calculate present value of an annuity is given below:

$Present\, value=Cash\, flow\times \left ( \frac{1-\left ( 1+i \right )^{-n}}{i} \right )$

$Present\, value=33,951\times \left ( \frac{1-\left ( 1+0.06 \right )^{-30}}{0.06} \right )$

$Present\, value=33,951\times \left ( \frac{0.82588986}{0.06} \right )$

Present value = 33,951 x 13.76483115

Present value = 467,329.78

The formula to calculate present value of perpetuity is given below:

$Present\, value=\frac{Cash\, flow}{Interest\, rate}$

$Present\, value=\frac{33,951}{0.06}$

The additional present amount of perpetuity is ($565,850 - $467,329.78) = 98,520.22.