321.2
You are endowing a scholarship and you want the first scholarship of $10,000 to be paid 3 years from today. After that you want the amount of the scholarship to grow by 3% and you can earn a nominal return of 9% on your money, what will it cost to endow the scholarship today? (3 pts)
Draw a cash flow diagram:
0
1
2
3
4 …
10,000
10,300 …
The value IN YEAR 2 of this growing perpetuity is
(First Cash Flow)/(r-g), which is 10000/(.09-.03) = 166,666.67
The value TODAY = 166,666.67/(1.09)^2 = 140280
Does delaying the start of the scholarship to year 3 positively or negatively impact the cost? WHY?
It decreased the cost by allowing us to wait before funding the scholarship. That is, we could invest less than $166,666.67 today in order to start funding a perpetual scholarship starting in year 3 because our investment would grow for 3 years before any money is withdrawn.
Does making the scholarship grow positively or negatively impact the cost? WHY?
This part increased the cost. Anytime you go from a level series of cash flows to a constantly increasing series, it becomes more expensive to create.