Question

Consider the following streams of cash flows TOL projects A and B Yr 0 Yr 1 Yr 2 Yr 3 -$ 180,000 $ 70,000 $ 70,000 $ 70,000 - 435,000 120,000 200 200,000 250,000 A: B: 1. Calculate the Net Present Value and the Profitability Index for Project B if the required return on the project is 12%. Would you accept this project under etc criterion? Why or why not? (18 pt)

please solve by hand showing work

Answer 1

1). NPV = sum of present value (PV) of all cash flows

Project B NPV = -435,000 + 120,000/(1+12%) + 200,000/(1+12%)^2 + 250,000/(1+12%)^3 =

-435,000 + 109,090.91 + 165,289.26 + 187,828.70 = 27,208.87

Profitability index (PI) = sum of PV of all future cash flows/initial cash flow = (109,090.91 + 165,289.26 + 187,828.70)/435,000 = 1.06

Project B is acceptable as it has a positive NPV and PI of more than one, meaning that it is profitable.

2). IRR is the return at which the NPV becomes zero. So,

0 = -180,000 + 70,000*PVIFA(r, 3)

PVIFA(r, 3) = 180,000/70,000 = 2.5714

(1-(1+r)^-3)/r = 2.5714

1 - (1+r)^-3 = 2.5714r

This is a polynomial equation and requires advanced mathematics to solve. So, a trial and error method is used by trying a few values close to the discount rate of 12% and seeing which one is closest.

For 12%, PVIFA(12%,3) is 2.40 so r has to be less than 12%.

It comes out to be 8.12%. (Note: Please use a financial calculator and IRR function to calculate the exact IRR.)