Question

1. A perpetuity of $1500 quarterly payments begins six years from now. The required return is 10%, compounded quarterly.
   1. What is the value of the perpetuity today?
   2. What is the value of the perpetuity in 4 years?
   3. What is the value of the perpetuity in 6 years?
   4. What is the value of the perpetuity in 20 years?

Answer 1

Answer Given data: -> Quaterly payments = $1,500 → Required return - 104 x 3/12 - 2.5% perquarter tirst quarterly payment is starts 6 years from today that means • 24 quarters. * Value o perpe tuity = perpetual RR * value of perpetuity on 6 years = Quarterly payment / RR = $1.500 2.54 = $60,000 * Value of perpetuily as on today = value o perpetuity on 6 years * PVIF CRR, n] >$60,000 W PVDF[25;24] - $60,000 x 0.552875 = $33,172. 52 * Value of perpetuity in A years = = value of perpetuity in Gyears x PvIF (2.5%, 18) = $60,000 * 0.820147 Discounted for years - 8 periods] = $49,244.79

→ Value & perpetuity in 6 years - $ 60,000 -> value o perpetuity in 20 years - z value of perpetuity In 6 years * FVIF (2.50), 56] for the years - 56 Q periods] Future value $ 60,000 * 3.985902 $ a39, 159.5 $ 239, 159.5 Note that: - → FVDF [1,1] - [i+1]" → PVIP [IN] = 1/(1+1)"