Question

A mine is for sale for 240,000. It is believed the mine will produce a profit of 65,000 the first year, but the profit will decline 5000 a year after that, eventually reaching zero, whereupon the mine will be worthless. What rate of return would this 240,000 investment produce for the purchaser of the mine? DO NOT USE EXCEL OR A FINANCIAL CALCULATOR

Answer 1

ANSWER:

SINCE EACH YEAR THE PROFIT IS REDUCING BY 5,000 , THE MINE WILL LAST 13 YEARS AS IT WILL BE DETERMINED AS THE PROFIT IN INITIAL YEAR / DECLINE IN PROFIT PER YEAR THAT IS 65,000 / 5,000 = 13 AND THEREFORE BY THE END OF THE 14TH YEAR THE PROFIT FROM THE MINE WILL BE ZERO.

IN ORDER TO FIND THE IRR WE WILL HAVE TO EQUATE THE PW TO ZERO.

Pw = initial cost + profit in year 1(p/a,i,n) + ..... + profit in year 13(p/a,i,n) + profit in year 14 (p/a,i,n)

where n = 1 to 14

and i will be found out by trial and error method.

and pw = 0

0 = -240,000 + 65,000(p/a,i,1) + 60,000(p/a,i,2) + .....+ 5,000(p/a,i,13) + 0(p/a,i,14)

240,000 = 65,000(p/a,i,1) + 60,000(p/a,i,2) + .....+ 5,000(p/a,i,13) + 0(p/a,i,14)

solving by trial and error method for i , we get i = 15.91%