Question

Consider the investment projects given in the table below. Assume that MARR = 13% in the following questions. EEClick the icon to view the net cash flows for the projects. Click the icon to view the interest factors for discrete compounding when MARR = 13% per year. (a) Compute i" for each investment. If the problem has more than onei", identify all of them. Compute i for Project 1. Select the correct choice below and, if necessary, fill in the the answer box(es) to complete your answer. O A. Project 1 has a unique positive i* of O B. Project 1 has two positive i* values: C. Project 1 has no positive i* value. %. (Round to one decimal place.) % and %. (Round to one decimal place. Enter values in ascending order.) A More Info Click to select and enter your n 0 1 Net Cash Flow Project 1 Project 2 - $1,000 - $1,000 2,100 1,860 - 820 1,090 Project 3 -$1,000 1,600 - 200 5 parts

Answer 1

Let i* for project 1 be r. Then

1,000 = [2,100 / (1 + r)] - [820 / (1 + r)²]

If (1 + r) = R,

1,000 = (2,100 / R) - (820 / R²)

1,000R² = 2,100R - 820

50R² = 105R - 41 [dividing by 20]

50R² - 105R + 41 = 0

Solving this quadratic equation using online solver,

R = 1.582 and R = 0.52

When R = 1.582,

1 + r = 1.582

r = 0.582 = 58.2%

When R = 0.52,

1 + r = 0.52

r = - 0.48 = - 48%

So (A) there is a unique positive i* of 58.2%.