Finance Chapter 12 With Financial Calculator Enter The Cash Inflow

c.

NPV (Millions of Dollars)

Crossover Rate = 11.7%

A

B

125

100

75

Answers and Solutions: 12 – 21

10

15

50

20

25

30

12-16 Plane A: Expected life = 5 years; Cost = $100 million; NCF = $30 million;

COC = 12%.

Plane B: Expected life = 10 years; Cost = $132 million; NCF = $25 million;

COC = 12%.

Enter these values into the cash flow register: CF0 = –100; CF1-4 = 30; CF5 = –70; CF6-

10 = 30. Then enter I/YR = 12, and press the NPV key to get NPVA = $12.764 million.

Enter these cash flows into the cash flow register, along with the interest rate, and press

the NPV key to get NPVB = $9.256 million.

Project A is the better project and will increase the company’s value by $12.764

million.

The EAA of plane A is found by first finding the PV: N = 5, I/YR = 12, PMT = 30, FV

Answers and Solutions: 12 – 22

12-17 0 1 2 3 4 5 6 7 8

A: | | | | | | | | |

-10 4 4 4 4 4 4 4 4

–10

–6

Machine A’s simple NPV is calculated as follows: Enter CF0 = –10 and CF1-4 = 4. Then

enter I/YR = 10, and press the NPV key to get NPVA = $2.679 million. However, this

Machine A is the better project and will increase the company’s value by $4.51 million.

The EAA of Machine A is found by first finding the PV: N = 4, I/YR = 10, PMT =

4, FV = 0; solve for PV = $12.679. The NPV is $12.679 − $10 = $2.679 million. We

10%

Answers and Solutions: 12 – 23

10%

12-18 Cash flow time line for Machine 190-3:

0 1 2 3

| | | |

-190,000 87,000 87,000 87,000

Using a financial calculator, input the following data: CF0 = -190000; CF1-3 = 87000;

I/YR = 14; and solve for NPV190-3 = $11,982 (for 3 years).

Cash flow time line for Machine 360-6:

0 1 2 3 4 5 6

| | | | | | |

-360,000 98,300 98,300 98,300 98,300 98,300 98,300

Using a financial calculator, input the following data: CF0 = -360000; CF1-6 = 98300;

I/YR = 14; and solve for NPV360-6 = $22,256 (for 6 years).

14%

Answers and Solutions: 12 – 24

12-19 a. The project’s expected cash flows are as follows (in millions of dollars):

Time Net Cash Flow

0 ($ 4.4)

We can construct the following NPV profile:

Discount Rate NPV

0% ($1,700,000)

9 (29,156)

10 120,661

50 2,955,556

100 3,200,000

NPV (Millions of Dollars)

Maximum

NPV at 80.5%

3

2

1

Answers and Solutions: 12 – 25

b. If r = 8%, reject the project since NPV < 0 as shown in the project’s NPV profile. But

if r = 14%, accept the project because NPV > 0 as shown in the project’s NPV profile.

c. Other possible projects with multiple rates of return could be nuclear power plants

d. Here is the MIRR for the project when r = 8%:

PV costs = $4,400,000 + $25,000,000/(1.08)2 = $25,833,470.51.

Output = 7.61

MIRR = 7.61%.

At r = 14%, MIRR for the project is calculated as follows:

PV costs = $4,400,000 + $25,000,000/(1.14)2 = $23,636,688.21.

Answers and Solutions: 12 – 26

Now, MIRR is that discount rate which forces the PV of the TV of $31,578,000 over 2

years to equal $23,636,688.21:

$23,636,688.21 = $31,578,000(PVIFr,2).

12-20 a. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow

stream must include both cash inflows and outflows.

b. The PV of costs for the conveyor system is ($911,067), while the PV of costs for the

12-21 a. Payback A (cash flows in thousands):

Annual

Period Cash Flows Cumulative

0 ($25,000) ($25,000)

1 5,000 (20,000)

Payback B (cash flows in thousands):

Annual

Period Cash Flows Cumulative

0 ($25,000) ($25,000)

b. Discounted Payback A (cash flows in thousands):

Annual Discounted @10%

Period Cash Flows Cash Flows Cumulative

0 ($25,000) ($25,000.00) ($25,000.00)

Discounted Payback B (cash flows in thousands):

Annual Discounted @10%

Period Cash Flows Cash Flows Cumulative

0 ($25,000) ($25,000.00) ($25,000.00)

c. NPVA = $12,739,908; IRRA = 27.27%.

NPVB = $11,554,880; IRRB = 36.15%.

Answers and Solutions: 12 – 28

d. At a discount rate of 5%, NPVA = $18,243,813.

At a discount rate of 5%, NPVB = $14,964,829.

f. Project ∆ =

Year CFA – CFB

0 $ 0

1 (15)

g. Use 3 steps to calculate MIRRA @ r = 10%:

Step 1: Calculate the NPV of the uneven cash inflow stream, so its FV can then be

calculated. With a financial calculator, enter the cash inflow stream into the

Step 3: Calculate MIRRA as follows:

Enter N = 4, PV = –25000000, PMT = 0, and FV = 55255000 to solve for

I/YR = 21.93%.

Use 3 steps to calculate MIRRB @ r = 10%:

Step 1: Calculate the NPV of the uneven cash inflow stream, so its FV can then be

Answers and Solutions: 12 – 29

Step 2: Calculate the FV of the cash flow stream as follows:

Enter N = 4, I/YR = 10, PV = -36554880, and PMT = 0 to solve for FV =

$53,520,000.

12-22 a. NPV of termination after Year t:

NPV0 = -$22,500 + $22,500 = 0.

Using a financial calculator, input the following: CF0 = –22500, CF1 = 23750, and I/YR

= 10 to solve for NPV1 = –$909.09 ≈ -$909.

The firm should operate the truck for 3 years, NPV3 = $1,307.

Answers and Solutions: 12 – 30

SOLUTION TO SPREADSHEET PROBLEM

12-23 The detailed solution for the problem is available in the file Solution for Ch12 P23 Build

a Model.xls at the textbook’s Web site.

Answers and Solutions: 12 – 31

MINI CASE

You have just graduated from the MBA program of a large university, and one of your

favorite courses was “Today’s Entrepreneurs.” In fact, you enjoyed it so much you have

decided you want to “be your own boss.” While you were in the master’s program, your

grandfather died and left you $1 million to do with as you please. You are not an inventor

You have narrowed your selection down to two choices; (1) Franchise L, Lisa’s Soups,

Salads, & Stuff and (2) Franchise S, Sam’s Fabulous Fried Chicken. The net cash flows

shown below include the price you would receive for selling the franchise in Year 3 and the

forecast of how each franchise will do over the three–year period. Franchise L’s cash flows

another.

Here are the net cash flows (in thousands of dollars):

Expected Net Cash Flows

Year Franchise L Franchise S

0 ($100) ($100)

1 10 70

2 60 50

3 80 20

Depreciation, salvage values, net working capital requirements, and tax effects are all

included in these cash flows.

Mini Case: 12 – 32

a. What is capital budgeting?

Answer: Capital budgeting is the process of analyzing additions to fixed assets. Capital

budgeting is important because, more than anything else, fixed asset investment

decisions chart a company’s course for the future. Conceptually, the capital budgeting

b. What is the difference between independent and mutually exclusive projects?

Answer: Projects are independent if the cash flows of one are not affected by the acceptance of

the other. Conversely, two projects are mutually exclusive if acceptance of one impacts

c. 1. Define the term net present value (NPV). What is each franchise’s NPV?

Answer: The net present value (NPV) is simply the sum of the present values of a project’s cash

flows:

Mini Case: 12 – 33

Franchise L’s NPV is $18.79:

0 1 2 3

| | | |

(100.00) 10 60 80

9.09

c. 2. What is the rationale behind the NPV method? According to NPV, which

franchise or franchises should be accepted if they are independent? Mutually

exclusive?

Answer: The rationale behind the NPV method is straightforward: if a project has NPV = $0,

then the project generates exactly enough cash flows (1) to recover the cost of the

investment and (2) to enable investors to earn their required rates of return (the

c. 3. Would the NPVs change if the cost of capital changed?

Answer: The NPV of a project is dependent on the cost of capital used. Thus, if the cost of capital

10%

Mini Case: 12 – 34

d. 1. Define the term internal rate of return (IRR). What is each franchise’s IRR?

Answer: The internal rate of return (IRR) is the discount rate that forces the NPV of a project to

equal zero:

Expressed as an equation, we have:

IRR:

∑

=

+

N

0t t

t

)IRR1(

CF

= $0 = NPV.

Note that the IRR equation is the same as the NPV equation, except that to find the IRR

Franchise L’s IRR is 18.1%:

0 1 2 3

| | | |

18.1%

Mini Case: 12 – 35