Question

King T'Challa of Wakanda wants to create ten youth centers in and around Oakland, California, to improve the living conditions of Black kids in the area. He is considering two options to go about this project:

Option 1 Build all ten centers now, at a cost of $250,000,000

Option 2 Build four centers now for $100,000,000, three more after four years at a cost of $90,000,000, and three more eight years from now at a cost of $120,000,000

In either case, each youth center requires $150,000 (adjusted for inflation) to run every year once it is built. You can assume the investment for each youth center is paid in full at the beginning of the year and that operating costs are due at the end of every year starting with year one. If the average expected inflation is 2% and the interest rate is 9%, which option makes the most economic sense?

Answer 1

In order to figure out the feasibility of the 2 options we will calculate the present value of both the options and see which one comes out to be lower

As regards to option 1

Since the recurring cost is adjusted for inflation we have the present value in millions as:

250 + (0.15/1.09 +0.15/1.09^2+.....+ 0.15/1.09^10)*10

= 250 + 1.5*(1-(1/1.09)^10)/0.09 = $259.63 million

Considering option 2

The inflation adjusted rate of return is 1.09/1.02-1 = 6.86%

The present value of the construction of youth centers will be

100 + 90/1.0686^3 + 120/1.0686^7 = $249.17

We take 3 and 7 as years since the construction happens in the beginning of the year.

The recurring costs are given as:

0.6*(1-(1/1.09)^10)/0.09 + 0.45*(1-(1/1.09)^6)/(0.09*1.09^4) + 0.45*(1-(1/1.09)^2)/(0.09*1.09^8)

= $ 5.68 million

Hence the total present value of option 2 is $254.85

Since the present value of option 2 is less than option 1 the second option makes mre economic sense.