Capital Budgeting Iii

CAPITAL BUDGETING III

Objective: Focus on interrelationship between a firm’s Internal Rate of Return, Net Present Value, and various discount rates.

I. Investments

A. Simple investments

1. Involves an initial cash out‑flow followed by a series of cash in‑flows.

2. Graphical illustrations given

B. Non‑simple investments

1. Involves at least one change of sign in cash flows

2. Graphical illustrations given

C. Pure investments

1. Project balance negative until completion of project

D. Mixed investments

1. Project balance at least one time is zero

II. Net Present Value Profile

A. Example is given

1. Factors

a. Original Expected Expected

Project Cost Annual Return Life

A $10,000 $2,000 10 years

B $26,000 $3,000 15 years

b. Percentages of 1%, 2%, 6%, 8%, 24, and 16% are used

c. Plot results on a Net Present Value profile for both projects

2. Results

a. Project A ‑‑ a positive NPV until approximately 15%, which is this projects Internal Rate of Return.

b. Project B ‑‑ a positive NPV until approximately 8%, which is this projects Internal Rate of Return.

c. Based only upon Internal Rate of Return, Project A is preferred, however, this does not consider cost of capital.

d. Assuming a cost of capital of 3%, project B is desirable because at this point its NPV is greater.

e. Assuming a cost of capital of 7%, project A is desirable because at this point its NPV is greater.

f. Assuming a cost of capital between 8% ‑ 15%, project A is desirable because it has a positive NPV.

g. Assuming a cost of capital greater than 15%, neither project

is desirable.

h. Net Present Value Profile:

20 ‑

16 ‑

12 –

8 ‑

4 ‑

Discount

0 _________________________________________ rate (%)

2 4 6 8 10 12 14 16 Project A

4 ‑

8 ‑ Project B

III. Capital Budgeting Incorporating Risk

A. Expected return maximization

1. Determine projects.

2. Look at states of nature and assign probabilities totaling to one.

3. Determine returns for each project for each state of nature.

4. Calculate expected returns.

5. Project with the highest expected value is most desirable.

Period Cash Flow

0 -1800

1 450

2 450

3 450

4 450

5 450

6 450

7 450

8 450

9 450

10 450

11 450

12 450

13 450

14 450

15 450

16 -6750

Discount Annuity Fn Single Pmt Clean-up Net

Rate Factor Times Factor Times Present

15 Periods Factor 16 Periods Factor Value

0.0% ERR ERR 1.00 -6750 -1800

1.0% 13.87 6239 0.85 -5757 -1304

2.0% 12.85 5782 0.73 -4917 -917

3.0% 11.94 5372 0.62 -4206 -616

4.0% 11.12 5003 0.53 -3604 -385

5.0% 10.38 4671 0.46 -3092 -211

6.0% 9.71 4371 0.39 -2657 -82

7.0% 9.11 4099 0.34 -2286 11

8.0% 8.56 3852 0.29 -1970 75

9.0% 8.06 3627 0.25 -1700 117

10.0% 7.61 3423 0.22 -1469 140

11.0% 7.19 3236 0.19 -1271 149

12.0% 6.81 3065 0.16 -1101 146

13.0% 6.46 2908 0.14 -955 135

14.0% 6.14 2764 0.12 -830 118

15.0% 5.85 2631 0.11 -721 96

16.0% 5.58 2509 0.09 -628 70

17.0% 5.32 2396 0.08 -547 41

18.0% 5.09 2291 0.07 -478 11

19.0% 4.88 2194 0.06 -417 -20

20.0% 4.68 2104 0.05 -365 -51

21.0% 4.49 2020 0.05 -320 -82

22.0% 4.32 1942 0.04 -280 -113

23.0% 4.15 1869 0.04 -246 -144

24.0% 4.00 1801 0.03 -216 -174

25.0% 3.86 1737 0.03 -190 -203

26.0% 3.73 1677 0.02 -167 -231

27.0% 3.60 1620 0.02 -147 -257

28.0% 3.48 1568 0.02 -130 -283

29.0% 3.37 1518 0.02 -115 -308

30.0% 3.27 1471 0.02 -101 -331

IRR 1 = 6.86%

IRR 2 = 18.37%

Multiple Rates of Return

0.2 –

0.1 –

0 –

-0.1 –

-0.2 –

-0.3 –

-0.4 –

-0.5 –

-0.6 –

-0.7 –

-0.8 –

-0.9 –

-1 –

-1.1 –

-1.2 –

-1.3 –

-1.4 –

-1.5 –

-1.6 –

-1.7 –

-1.8 –

0% 4% 8% 12% 16% 20% 24% 28%

Discount Rate

QUESTIONS

True and False

1. Simple investment involves at least one change of sign in cash flows.

2. Lower Internal Rate of Return is preferable to higher.

3. A non‑simple investment may graphically have two internal rates of return.

4. The project with the maximum expect return may not necessarily be the best project.

Matching

1. Simple investment A. Project balance negative until

completion of project.

2. Non‑simple investment B. Involves an initial cash out‑flow

followed by a series of cash in‑

3. Pure investment flows.

C. Project balance at least one

4. Mixed investment balance is zero.

D. Involves at least one change of

sign as far as cash flows.