Which of the following expressions represents the present value of a continuous revenue stream for n years at a constant rate of $S per year if the discount rate is r%?
A) $\frac { r } { 100 S } \left[ e ^ { \frac { - m } { 100 } } + 1 \right]$

B) $\frac { r S e ^ { \frac { - m } { 100 } } } { 100 }$

C) $\frac { \boldsymbol { r } } { 100 S } \left[ e ^ { \frac { - \boldsymbol { m } } { 100 } } - 1 \right]$

D) $\frac { 100 S e ^ { \frac { - m } { 100 } } } { r }$

E) $\frac { 100 S } { r } \left[ 1 - e ^ { \frac { - m } { 100 } } \right]$

Question

Which of the following expressions represents the present value of a continuous revenue stream for n years at a constant rate of $S per year if the discount rate is r%?
A) $\frac { r } { 100 S } \left[ e ^ { \frac { - m } { 100 } } + 1 \right]$

B) $\frac { r S e ^ { \frac { - m } { 100 } } } { 100 }$

C) $\frac { \boldsymbol { r } } { 100 S } \left[ e ^ { \frac { - \boldsymbol { m } } { 100 } } - 1 \right]$

D) $\frac { 100 S e ^ { \frac { - m } { 100 } } } { r }$

E) $\frac { 100 S } { r } \left[ 1 - e ^ { \frac { - m } { 100 } } \right]$

Quizplus · Accepted Answer

The present value of a continuous revenue stream is given by the formula PV = (C/r)(1-e^(-rt)), where C is the constant revenue stream, r is the discount rate and t is time. In this case, since the revenue stream is for n years, time will be n. Therefore, the expression that represents the present value is PV = (S/r)(1-e^(-rn)). Simplifying this expression, we get PV = (100S/r)(1-e^(-(r/100)n)). This expression matches option E, which is the correct answer.

Which of the Following Expressions Represents the Present Value of a Continuous