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

[cs23]

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%

 

[hotvette]

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%.