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Perpetuity (Capitalized Cost)

Perpetuity (Capitalized Cost). 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 relationship is A = P( i )

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Perpetuity (Capitalized Cost)

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  1. Perpetuity (Capitalized Cost) • 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 relationship is A = P( i ) • This concept is also called capitalized cost (where CC = P).

  2. 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.

  3. Perpetuity Problem • Given: • A = 10 000 per year, every year after Year 5 • n = 8 payments @ 6 mo. intervals, starting @ 6 mo. • i = 6%, cpd semi-annually • Find Amount of Initiating payments (Ai ):

  4. Perpetuity Problem • Given: • A = 10 000 per year, every year after Year 5 • n = 8 payments @ 6 mo. intervals, starting @ 6 mo. • i = 6%, cpd semi-annually • Find Amount of Initiating payments (Ai ):

  5. 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 (= CCPart 1) • 2.) finding the Annual Equivalent of one cycle of all the recurring cash flows, and then computing P (= CCPart 2) from the perpetuity relationship A = P(i) • 3.) summing (1.) and (2.) to find the total capitalized cost: • CCTotal = CCPart 1 + CCPart 2

  6. Capitalized Cost Example The SD School of Minds wants to build a soccer stadium. It will cost $ 5 000 000 to construct, and $ 7 000 each year to clean. In 20 years, the contractor will return to tighten all the bolts on the stadium structure, and they will charge $ 90 000 (one time cost). Every 15 years, they will replace the artificial turf at a cost of $ 50 000. Plant services will pay $ 80 000 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?

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