FIN 301 – Porter 4/22/09

Terms:

Independent Projects Normal CF stream

IRR Nonnormal CF stream

Mutually Exclusive Projects NPV Method

MIRR Payback Period

  1. If I were to buy a new shirt and a gallon of milk, and buying one would have no influence on purchasing the other, then these are Independent projects.
  2. IRR is the discount rate that makes a project’s NPV equal zero and to accept or reject a project, compare this number to the WACC.
  3. A cash flow stream with only one change in sign (ie. Begins negative and turns positive) is called a Normal cash flow stream.
  4. If I were in the grocery store and was going to buy rice krispies to make Scotch-O-Roos or apples to make an apple pie, but I wasn’t going to make both desserts, this would be a Mutually Exclusive project.
  5. MIRR is the discount rate where the present value of a project’s cost is equal to the present value of its terminal value, where the terminal value is found as the sum of the future values of the cash inflows, compounded at the firm’s cost of capital.
  6. If a project begins with a large and negative investment, becomes positive, but then has additional negative costs to end the project, this is an example of a Nonnormal cash flow stream.
  7. Payback Period is the amount of time it takes for an investment’s revenue to cove its initial costs.
  8. The way to rank projects based upon the present value of their future cash flows, discounted at the cost of capital, and you accept the project if it is greater then zero is called the NPV Method.

Concepts:

Method / Ind. Or M.E. / Accept or Reject / If / <, >, =
NPV / Independent / Accept / If / NPV / 0
NPV / Mutually Exclusive / Accept / Largest NPV
NPV / Independent / Reject / If / NPV / 0
NPV / Mutually Exclusive / Reject / Smallest NPV
IRR / Independent / Accent / If / IRR / WACC
IRR / Mutually Exclusive / Accept / Largest IRR
IRR / Independent / Reject / If / IRR / WACC
IRR / Mutually Exclusive / Reject / Smallest IRR

Problems:

9.  Project A costs $55,125 and has expected net cash inflows of $10,000 per year for 6 years, and its WACC is 11%. What is the project’s NPV? Should you accept this project based on NPV?

CF0= -55,125

Enter, down

CF1= 10,000

Enter, down

F1=6

Enter, down

NPV, I=11

Enter, down

NPV CPT=-12,819.62 DO NOT accept NPV < 0

10.  What is the IRR for problem 9?

CF0= -55,125

CF1-6= 10,000

IRR CPT= 2.476% DO NOT accept, IRR < WACC

11.  What is the MIRR for problem 9?

Professional:

Hit down again after IRR

RI= 11%

Enter, down

MOD CPT= 6.21

Student:

Calculate the PV first by bringing all the cash flows the time 6 using the following equation CFn* (1 + wacc )n, (where n is the number of periods it is moving forward) and adding them up.

CF6 = 10,000 because it doesn’t move back at all

CF5 = 10,000(1.11)1 = 11,100

CF4 = 10,000(1.11)2 = 12,321

CF3 = 10,000(1.11)3 = 13,676.31

CF2 = 10,000(1.11)4 = 15,180.70

CF1 = 10,000(1.11)5 = 16,850.58

Total: PV=79,128.59.

Then go to cash flow register and do the following:

CF0=-55,125

CF1=0 F1=5

CF2=79,128.59

IRR, CPT= 6.21

12.  A project costs 60,000 and its expected net cash inflows are 12,000 for the first 3 years, and 15,000 for the next 4 years. Its WACC is 12%. What is the project’s payback?

0 1 2 3 4 5 6 7

CF: -60 12 12 12 15 15 15 15

Total: -48 -36 -24 -9 6 21 36

Professional:

Hit NPV and the down arrow until you see “PB” hit compute.

Student:

Payback=

Yr B4 positive + (cumulative amount in the yr B4 going positive)/CF in the year of becoming positive

= 4 + (9000/15000)

=4.6 years

13.  What is the discounted payback for a project that costs $45,000 and then has cash flows of $12,000 for 3 years, and cash flows of 15,000 for 4 years, with a WACC of 12%?

Professional:

Hit NPV and down until you see DPB, hit compute

Student:

CF 1: 12,000/(1.12)1= 10,714,29

CF2: 12,000/(1.12)2 = 9,566.33

CF3: 12,000/(1.12)3 = 8,541.36

CF4: 15,000/(1.12)4 = 9,532.77

CF5: 15,000/(1.12)5 = 8,511.40

CF6: 15,000/(1.12)6 = 7,599.47

CF7: 15,000/(1.12)7 = 6,785.24

That is how much each of these cash flows are worth at time 0.

Year 0 / Year 1 / Year2 / Year3 / Year4 / Year5 / Year6 / Year7
Disc. CF / 10,714.29 / 9,566.33 / 8,541.36 / 9,532.77 / 8,511.40 / 7,599.47 / 6,785.24
Cumulative / -45,000 / -34,285.71 / -24,719.38 / -16,178.02 / -6,645.25 / +1,866.15

4+(6645.25/8511.40)=4.78 years

14.  A firm with a 12% WACC is evaluating 2 projects for this year’s capital budget. After tax cash flows, including depreciation are as follows:

Time / 0 / 1 / 2 / 3 / 4 / 5
Project A / -5,000 / 2,000 / 2,000 / 2,000 / 2,000 / 2,000
Project B / -18,000 / 5,600 / 5,600 / 5,600 / 5,600 / 5,600

Calculate NPV and IRR for each project. Which would you accept if the projects are independent? Which would you accept if the projects are mutually exclusive?

FIN 301 – Porter 4/22/09

Project A:

NPV:

CF0=-5,000

Enter, down

CF1= 2,000

Enter, down

F1=5

Enter, down

NPV

I=12

Enter down

CPT NPV= $2,209.55

IRR

IRR CPT: 28.65%

Project B:

NPV:

CF0= -18,000

Enter, down

CF1= 5,600

Enter, down

F1=5

Enter, down

NPV

I= 12

Enter, down

CPT NPV= $2,186.75

IRR

IRR CPT: 16.79%

FIN 301 – Porter 4/22/09

You would choose A and B if they were independent, and A if they were mutually exclusive b/c it is higher on both measures

FIN 301 – Porter 4/22/09