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)

Answer 1

The answer is "$ 3,005,010.27".

Step-by-step explanation:

Let those cash flows be in millions of dollars

`NPV = -20+(\fatc{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)))`

`\ max \ value \ of \ K \ so, \ NPV = 0\\\\ \Rightarrow -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`

`\Rightarrow -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 \\\\\Rightarrow 3.221661 = 1.072096*K \\\\\Rightarrow K = 3.00501 \\`

The value of k = "$ 3,005,010.27".