Question

You are an intern for the corporate finance office of SCF, Inc. and have been tasked to evaluate the following potential investment projects:

Project A: Initial cash outflow of $96 million followed by cash inflows of $23 million per year for the next 10 years.

Project B: Initial cash outflow of $22 million followed by cash inflows for the next 10 years, starting at $5 million next year and growing at an annual rate of 3%. Project C: Initial cash outflow of $20 million followed by cash inflows of $3 million per year forever.

Project D: Initial cash outflow of $10 million followed by cash inflows grow at 3% per year indefinitely, starting from $2 million next year.

The window of opportunity to invest in these projects is closing and SCF, Inc. currently only has $100 million available for new projects. Also, the return required on these projects is 10%. Your supervisor is a strong advocate of the Profitability Index (PI) as an investment analysis tool because he argues that the PI indicates a project’s “bang for the buck” and is the most relevant information for decision-making in this context as investment funds are limited.
(a) Given SCF, Inc.’s resource constraints, using the PI would lead the firm to undertake which project or combination of projects?
(b) Do you agree with your supervisor that the PI is the best rule on which to base your investment decision under the firm’s current circumstances? Discuss and substantiate your answer numerically.   

(c) Explain why financiers are willing to provide more capital under the second arrangement in parts (a) and (b).

(c) Consider a one-period project with conventional cash flows of –C0 and C1 at the beginning and end of the period respectively. Denote the return required on this project as WACC.

(i) Express the project’s internal rate of return (IRR) in terms of its cash flows.

(ii) Express the project’s PI in terms of its cash flows and required return.

(iii) Using your answers to parts (c)(i) and (c)(ii), express the project’s PI in terms of its IRR.

(iv) Establish whether the relation between a project’s PI and IRR in part (c)(iii) for a one-period project holds for Project D, a multi-period project.    

Answer 1

a) The formula for profitability index is (PI) = 1 + [Net Present Value / Initial Investment]

We first calculate the NPV of the project as =

NPV of project A = - 96 + [ 23 / 1.11 +  23 / 1.12 + 23 / 1.13 + 23 / 1.14 + 23 / 1.15 + ...... + 23 / 1.110 ] = 45.35 million

NPV of project B = -22 + [ 5 / 1.1 + 5(1.03) / 1.12 + 5(1.03)2 + 1.13  + ...... + 5(1.03)9 / 1.110 ] = 21.39 milliom

NPV of project C = -20 + [ 3 / 10% ] = 10 million

NPV of project D = - 10 + [ 2 / 1.1 + 2(1.03) / 10% ] = 12.42 million

In project C and D we take 10% and not 1+r because the cash flows are received throughout perpetuity.

PI for project A is = 1 + 45.35/ 96 = 1.472

PI for project B is = 1 + 21.39/22.= 1.972

PI for project C is = 1 + 10/20 = 1.5

PI for project D is = 1+ 12.42/10 = 2.242

Based on PI the firm should undertake projects B, C, D and a part of project A such that the total investment in these projects is equal to 100 million.

b) No I do not agree with the supervisior that PI is the better indicator of the investment return. A better indicator of return on investmenty from such projects is the NET PPRESENT VALUE. The problem associated with PI is that a project can have the same profitability index with different investments and the vast difference in absolute dollar return.

c) Since the PI for all the four projects are more than 1 that is all the projects are profitable hence the financers are willing to provide more finance in the above projects.

d) 1) IRR is the rate of return where the NPV is 0.

Hence by the above two cashflows IRR= NPV = -CF0 + CF1 / IRR

2) Projects PI = 1 + NPV / Initial Investment, NPV = -CF0 +  CF1 /1+wacc