What is the Annual Rate of Return for a Charitable Foundation's Donation?

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In summary, a charitable foundation received a $4 million donation from a wealthy building contractor and specified that $200,000 would be awarded each year for 5 years to a university conducting research on layered composite materials. After the initial 5 years, grants equal to the amount of interest earned would be given. Assuming the grants in subsequent years are expected to be $1 million per year, the annual rate of return for the foundation is estimated to be 15%.
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cs23
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Homework Statement



A charitable foundation received a donation from a wealthy building contractor in the amount of $4 million. It specifies that $200,000 is to be awarded each year for 5 years starting now (i.e., 6 awards) to a university engaged in research pertaining to the development of layered composite materials. Thereafter, grants equal to the amount of interest earned each year are to be made. If the size of the grants from year 6 into the indefinite future is expected to be $1,000,000 per year, what annual rate of return is the foundation earning?


Homework Equations



PWd=PWr

The Attempt at a Solution



PWd= PWr
4=0.2 + 0.2(P/A,i,5) + 1(P/A,i,infinity)
3.8 = 0.2(P/A,i,5) + 1(P/A,i,infinity)
3.8=0.2(1/i) +1(1/i)
3.8 = 1.2(1/i)+(1/i)
i= 31.57%

it seems too high, any help would be appreciated


i= 31.57%
 
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  • #2
If you assume the rate of return is the same the entire time (i.e. during the initial 6-year period and thereafter), what you have is a uniform series (I think that's the right term) for 6 years such that the future value of that series will have interest of exactly $1M per year. I believe the solution needs to be obtained iteratively and should be around 15%.
 

FAQ: What is the Annual Rate of Return for a Charitable Foundation's Donation?

1. What is the formula for finding the annual rate of return?

The formula for finding the annual rate of return is: [(Ending Value - Beginning Value) / Beginning Value] * 100.

2. Why is it important to calculate the annual rate of return?

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3. Can the annual rate of return be negative?

Yes, the annual rate of return can be negative if the ending value is less than the beginning value. This indicates a loss on the investment.

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5. Is the annual rate of return the same as the average rate of return?

No, the annual rate of return and the average rate of return are not the same. The annual rate of return is the rate of return earned in a single year, while the average rate of return is the average of the rate of return over multiple years.

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