Question

Bolzano Ltd has decided to provide an annual prize in perpetuity for a local university student who demonstrates outstanding leadership. The initial prize, to be awarded in exactly one year's time, will have a value of $500. The value of the prize will be increased in line with inflation, which can be assumed to be 2.75%. The university will invest funds today to provide for this scholarship, and the return on this investment fund is 5.25%. To set up the fund there is an initial administration cost of $100. As well, each year there is an administration cost of 1% of the value of that year's prize. Bolzano Ltd is responsible for these costs. For the scholarship to go ahead, Bolzano Ltd must provide the university with all funds today. How much does Bolzano Ltd need to provide today to the university so that the prize can be initiated?

Answer 1

The total prize money is growing by the rate of inflation i.e. 2.75%. Hence, we can calculate the total amount by discounting these prize money amounts by a discount rate. We observe that the return on investment fund is 5.25% bu there is also a 1% fees. Hence, it will grow annually by 4.25%. Therefore, this will be our discount rate. So, now we can use the Gordon growth formula to calculate the initial investment required.

Amount = 500 x (1+g)/(r-g) = 500 x 1.0275/(0.0425 -0.0275) = 34250.

Also, we add the initial administration cost of $100. So, the total amount becomes $34350.