Question

XYZ Manufacturing decides to build a new plant. The plant will cost $20 million today and is expected to have a useful life of 20 years. At the end of year 5, 10 and 15, there will be major renovation expenses of $K each time. The plant will produce level returns of $2.5 million at the end of each year for the first 10 years and $5 million at the end of each year for the second 10 years. Find the maximum value of K that XYZ could pay so that the internal rate of return on its investment is at least 12%. (Round your answer to integer)

ANS 3005010 Show all works, and please calculate it with math formula instead of financial calculator!! Thank you!

Answer 1

Let all cashflows be in million $

NPV = -20+(2.5/1.12+2.5/1.12^2+...+2.5/1.12^10) +(5/1.12^9+5/1.12^10+...+5/1.12^20) - (K/1.12^5+K/1.12^10+ K/1.12^15)

For maximum value of K, NPV = 0

=> -20+(2.5/1.12+2.5/1.12^2+...+2.5/1.12^10) +(5/1.12^9+5/1.12^10+...+5/1.12^20) - (K/1.12^5+K/1.12^10+ K/1.12^15) = 0

=> -20+2.5/0.12*(1-1/1.12^10)+ 1/1.12^10* 5/0.12*(1-1/1.12^10)- 1.072096*K = 0

=> 3.221661 = 1.072096*K

=> K = 3.00501

So, maximum value of K is $3.00501027 million or $3,005,010.27