12-1 Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, I/YR = 12, and then

solve for NPV = $7,486.68.

12-2 Financial calculator solution: Input CF0 = -52125, CF1-8 = 12000, and then solve for

IRR = 16%.

12-3 MIRR: PV costs = $52,125.

FV inflows:

PV FV

0 1 2 3 4 5 6 7 8

| | | | | | | | |

12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000

13,440

15,053

16,859

18,882

21,148

23,686

26,528

52,125 MIRR = 13.89% 147,596

Financial calculator solution: Obtain the FVA by inputting N = 8, I/YR = 12, PV = 0,

PMT = 12000, and then solve for FV = $147,596. The MIRR can be obtained by

inputting N = 8, PV = -52125, PMT = 0, FV = 147596, and then solving for I/YR =

13.89%.

12-4 Since the cash flows are a constant $12,000, calculate the payback period as:

$52,125/$12,000 = 4.3438, so the payback is about 4 years.

12-5 Project K’s discounted payback period is calculated as follows:

Annual Discounted @12%

Period Cash Flows Cash Flows Cumulative

0 ($52,125) ($52,125.00) ($52,125.00)

1 12,000 10,714.29 (41,410.71)

2 12,000 9,566.33 (31,844.38)

3 12,000 8,541.36 (23,303.02)

4 12,000 7,626.22 (15,676.80)

12%

1.12

(1.12)2

(1.12)3

(1.12)4

(1.12)5

(1.12)6

(1.12)7

5 12,000 6,809.12 (8,867.68)

6 12,000 6,079.57 (2,788.11)

7 12,000 5,428.19 2,640.08

8 12,000 4,846.60 7,486.68

The discounted payback period is 6 +

$2,788 . 11$5,42 8 .19 years, or 6.51 years.

12-6 a. Project A: Using a financial calculator, enter the following:

CF0 = -25, CF1 = 5, CF2 = 10, CF3 = 17, I/YR = 5; NPV = $3.52.

Change I/YR = 5 to I/YR = 10; NPV = $0.58.

Change I/YR = 10 to I/YR = 15; NPV = -$1.91.

Project B: Using a financial calculator, enter the following:

CF0 = -20, CF1 = 10, CF2 = 9, CF3 = 6, I/YR = 5; NPV = $2.87.

Change I/YR = 5 to I/YR = 10; NPV = $1.04.

Change I/YR = 10 to I/YR = 15; NPV = -$0.55.

b. Using the data for Project A, enter the cash flows into a financial calculator and

solve for IRRA = 11.10%. The IRR is independent of the WACC, so it doesn’t

change when the WACC changes.

Using the data for Project B, enter the cash flows into a financial calculator and

solve for IRRB = 13.18%. Again, the IRR is independent of the WACC, so it

doesn’t change when the WACC changes.

c. At a WACC = 5%, NPVA > NPVB so choose Project A.

At a WACC = 10%, NPVB > NPVA so choose Project B.

At a WACC = 15%, both NPVs are less than zero, so neither project would be

chosen.

12-7 a. Project A:

CF0 = -6000; CF1-5 = 2000; I/YR = 14.

Solve for NPVA = $866.16. IRRA = 19.86%.

MIRR calculation:

0 1 2 3 4 5

| | | | | |

-6,000 2,000 2,000 2,000 2,000 2,000

2,280.00

2,599.20

2,963.09

3,377 .92

13,220 .21

Using a financial calculator, enter N = 5; PV = -6000; PMT = 0; FV = 13220.21;

and solve for MIRRA = I/YR = 17.12%.

Payback calculation:

0 1 2 3 4 5

| | | | | |

-6,000 2,000 2,000 2,000 2,000 2,000

Cumulative CF:-6,000 -4,000 -2,000 0 2,000 4,000

Regular PaybackA = 3 years.

Discounted payback calculation:

0 1 2 3 4 5

| | | | | |

-6,000 2,000 2,000 2,000 2,000 2,000

Discounted CF:-6,000 1,754.39 1,538.94 1,349.94 1,184.16 1,038.74

Cumulative CF:-6,000 -4,245.61-2,706.67-1,356.73 -172.57 866.17

Discounted PaybackA = 4 + $172.57/$1,038.74 = 4.17 years.

Project B:

CF0 = -18000; CF1-5 = 5600; I/YR = 14.

Solve for NPVB = $1,255.25. IRRB = 16.80%.

1.14

(1.14)2

(1.14)3

(1.14)4

MIRR calculation:

0 1 2 3 4 5

| | | | | |

-18,000 5,600 5,600 5,600 5,600 5,600

6,384.00

7,277.76

8,296.65

9,458 .18

37,016 .59

Using a financial calculator, enter N = 5; PV = -18000; PMT = 0; FV = 37016.59;

and solve for MIRRB = I/YR = 15.51%.

Payback calculation:

0 1 2 3 4 5

| | | | | |

-18,000 5,600 5,600 5,600 5,600 5,600

Cumulative CF:-18,000-12,400 -6,800 -1,200 4,400 10,000

Regular PaybackB = 3 + $1,200/$5,600 = 3.21 years.

1.14

(1.14)2

(1.14)3

(1.14)4

Discounted payback calculation:

0 1 2 3 4 5

| | | | | |

-18,000 5,600 5,600 5,600 5,600 5,600

Discounted CF:-18,000 4,912.28 4,309.02 3,779.84 3,315.65 2,908.46

Cumulative CF:-18,000-13,087.72-8,778.70-4,998.86-1,683.211,225.25

Discounted PaybackB = 4 + $1,683.21/$2,908.46 = 4.58 years.

Summary of capital budgeting rules results:

Project A Project B

NPV $866.16 $1,225.25

IRR 19.86% 16.80%

MIRR 17.12% 15.51%

Payback 3.0 years 3.21 years

Discounted payback 4.17 years 4.58 years

b. If the projects are independent, both projects would be accepted since both of their

NPVs are positive.

c. If the projects are mutually exclusive then only one project can be accepted, so the

project with the highest positive NPV is chosen. Accept Project B.

d. The conflict between NPV and IRR occurs due to the difference in the size of the

projects. Project B is 3 times larger than Project A.

13-2 a. Project cash flows: t = 1

Sales revenues $10,000,000

Operating costs 7,000,000

Depreciation 2,000,000

Operating income before taxes $ 1,000,000

Taxes (40%) 400,000

Operating income after taxes $ 600,000

Add back depreciation 2,000,000

Project cash flow $ 2,600,000

b. The cannibalization of existing sales needs to be considered in this analysis on an

after-tax basis, because the cannibalized sales represent sales revenue the firm

would realize without the new project but would lose if the new project is accepted.

Thus, the after-tax effect would be to reduce the project’s cash flow by

$1,000,000(1 – T) = $1,000,000(0.6) = $600,000. Thus, the project’s cash flow

would now be $2,000,000 rather than $2,600,000.

c. If the tax rate fell to 30%, the project’s cash flow would change to:

Operating income before taxes $1,000,000

Taxes (30%) 300,000

Operating income after taxes $ 700,000

Add back depreciation 2,000,000

Project cash flow $2,700,000

Thus, the project’s cash flow would increase by $100,000.

13-3 Equipment’s original cost $20,000,000

Depreciation (80%) 16,000,000

Book value $ 4,000,000

Gain on sale = $5,000,000 – $4,000,000 = $1,000,000.

Tax on gain = $1,000,000(0.4) = $400,000.

AT net salvage value = $5,000,000 – $400,000 = $4,600,000.