Question

Bob, a philanthropist, is not sure what rate of return his gifts may realize once donated to his favorite charity. Determine the capitalized cost of $10,000 every 5 years forever, starting 5 years from now at an interest rate of 8% per year.

Answer 1

First we find the equivalent uniform annual worth of $10000 after 5 years

EUAW=10000*(P/F,8%,5)*(A/P,8%,5)

Now we calculate the interest factors

(P/F,8%,5)=1/(1+8%)^5=0.680583

EUAW=10000*0.680583*0.250456=1704.5610

So, A gift of $10000 every 5 years is equivalent to a gift of $1704.5610 per year.

It is similar to perpetuity of $1704.5610 per year at the interest rate of 8% per year.

Capitalized cost will be equal to PW of this perpetuity.

Capitalized Cost=EUAW/i=1704.5610/8%=$21307.01