1. Perpetuity (Capitalized Cost) The relationship is A = P( i )
Engineering Economy
7/17/2019
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).
Copyright (c) , D.H. Jensen & K.D. Douglas

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: Find Amount of Initiating payments (Ai ):
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 (Ai ):

4. 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

5. 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 artificial turf.
At a 4% annual cost of capital, how much should they ask of the donors, for the honor of putting their name on the stadium?