Question

An investment project will require development costs of $150 million at time zero and $80 million at the end of second year from time zero with incomes of $25 million per year at the end of years 1, 2 and 3 and incomes of $60 million per year at the end of years 4 through 10 with zero salvage value predicted at the end of year 10. Calculate the rate of return for this project.

Please explain your work in details.

Answer 1

development cost at time 0 . d1 = $ 150 million

development cost at time 2 , d2 = $80 million

let the rate of return for this project = r

cash flow at the end of year 1 , c1 = $25 million

cash flow at the end of year 2 , c2 = $25 million

cash flow at the end of year 3 , c3 = $25 million

cash flow at the end of year 4 , c4 = $60 million

cash flow at the end of year 5 , c5 = $60 million

cash flow at the end of year 6 , c6 = $60 million

cash flow at the end of year 7 , c7 = $60 million

cash flow at the end of year 8 , c8 = $60 million

cash flow at the end of year 9 , c9 = $60 million

cash flow at the end of year 10, c10= $60 million

we can find r by solving the following equation

d1 =[c1/(1+r)]+[(c2-d2)/(1+r)²] + [c3/(1+r)³] + [c4/(1+r)⁴] + [c5/(1+r)⁵] +[c6/(1+r)⁶] + [c7/(1+r)⁷] +[c8/(1+r)⁸] + [c9/(1+r)⁹] + [c10/(1+r)¹⁰]

150 = [25/(1+r)] + [(25-80)/(1+r)²] + [25/(1+r)³] + [60/(1+r)⁴] + [60/(1+r)⁵] + [60/(1+r)⁶] + [60/(1+r)⁷]+ [60/(1+r)⁸] + [60/(1+r)⁹] + [60/(1+r)¹⁰]

By trial and error , we find that the value of r that satisfies the above equation is 0.1623

thus the rate of return , r = 0.1623 or 16.23%