Perpetuity (Capitalized Cost) Occasionally, donors sponsor perpetual awards or programs by a lump sum of money earning interest.Occasionally, donors sponsor perpetual awards or programs by a lump sum of money earning interest. The interest earned each period (A) equals the funds necessary to pay for the ongoing award or program.The interest earned each period (A) equals the funds necessary to pay for the ongoing award or program. The relationship is A = P( i ) This concept is also called capitalized cost (where CC = P).This concept is also called capitalized cost (where CC = P).

Perpetuity Example A donor has decided to establish a $10,000 per year scholarship. The first scholarship will be paid 5 years from today and will continue at the same time every year forever. The fund for the scholarship will be established in 8 equal payments every 6 months starting 6 months from now. Determine the amount of each of the equal initiating payments, if funds can earn interest at the rate of 6% per year with semi- annual compounding.

Perpetuity Problem Given: A = per year, every year after Year 5 n = 8 6 mo. intervals, 6 mo. i = 6%, cpd semi-annually Find Amount of Initiating payments (A i ):

Perpetuity Problem Given: A = per year, every year after Year 5 n = 8 6 mo. intervals, 6 mo. i = 6%, cpd semi-annually Find Amount of Initiating payments (A i ):

Complex Flows and Perpetuity In some circumstances, there is a mix of recurring and non-recurring or one-time cash flows that must be capitalized for perpetuity. These mixed flows may be accounted for by: 1.) finding the NPW of all the one-time and non-recurring cash flows (= CC Part 1 ) 2.) finding the Annual Equivalent of one cycle of all the recurring cash flows, and then computing P (= CC Part 2 ) from the perpetuity relationship A = P(i) 3.) summing (1.) and (2.) to find the total capitalized cost: CC Total = CC Part 1 + CC Part 2

Capitalized Cost Example The SD School of Minds wants to build a soccer stadium. It will cost $ to construct, and $ each year to clean. In 20 years, the contractor will return to tighten all the bolts on the stadium structure, and they will charge $ (one time cost). Every 15 years, they will replace the artificial turf at a cost of $ Plant services will pay $ each year to mow and water the plastic grass. At a 4% annual cost of capital, how much should they ask of the donor, for the honor of putting his name on the stadium?