Question

  What is the present value of a perpetual stream of cash flows that pays ​$2, 000 at the end of year one and the annual cash flows grow at a rate of 2​% per year​ indefinitely, if the appropriate discount rate is 8​%? What if the appropriate discount rate is 6​%? a. If the appropriate discount rate is 8​%, the present value of the growing perpetuity is​ $ nothing. ​ (Round to the nearest​ cent.)

Answer 1

PV of Perpetual growing annuity Next year's cash flow / (Discount rate a) Perpetual Growth rate) - Next year's cash flow $2,000 Perpetual Growth Rate 2% 8% Discount Rate $33,333.33 [$2,000 (8% - 2%) = $2,000 / 6% = $2,000/ 0.06 $33,333.33] Present value of given growing annuity PV of Perpetual growing annuity Next year's cash flow / (Discount rate - Perpetual Growth rate) b) Next year's cash flow $2,000 2% Perpetual Growth Rate 6% Discount Rate $50,000.00 [$2,000 / (6% - 2%) $2,000/4% = $2,000 / 0.04 $50,000o.00] Present value of given growing annuity