Question

Andrea earns a profit of $Y starting in the next period and $Z in every period after that, for an infinite number of periods. She has a discount rate δ. What is the present discounted value of this stream of payoffs?

Note: In the options below, δ^2 = δ x δ.

Group of answer choices

Z+(Y δ)/(1- δ)

Y δ +(Z δ^2)/(1- δ)

Y+Z/(1- δ)

Y+(Z δ)(1- δ)

None of the other options

Answer 1

Answer is option 4)

Y+(Z δ)(1- δ)

Present discount value of payoff =

= Y + Zδ + Zδ​​​​​2 + Zδ​​​​​3 + Zδ​​​​​4 + ...

= Y + Zδ/(1-δ)