Oakridge College plans to create an endowment that will fund a merit-based…
MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
Oakridge College plans to create an endowment that will fund a merit-based scholarship in perpetuity. The first scholarship payment of 50,000 will be awarded exactly one year from today. Each subsequent annual payment is expected to be 2% larger than the preceding payment, continuing indefinitely. The college assumes its endowment portfolio will earn a constant annual effective return of 6%. Assume all cash flows occur at discrete one-year intervals and ignore taxes and management fees.
(a) Derive an explicit algebraic expression for the present value P, today's value, of the entire infinite stream of scholarship payments in terms of the given numerical parameters.
(b) Evaluate P numerically to the nearest dollar.
(c) Suppose the portfolio's expected return falls to 5% while the scholarship growth rate remains 2%. Determine the new present value Pnew and calculate the percentage increase in required principal relative to the value found in part (b). Round the percentage increase to one decimal place.
(d) Briefly explain, in the context of long-term endowment planning, why even a small change in the assumed portfolio return can have a large impact on the required initial principal.