Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three-year cutoff for projects. The required return is 11 percent.

Kaleb Konstruction, Inc., has the following mutually exclusive projects available. The company has historically used a three-year cutoff for projects. The required return is 11 percent.

Year	Project F		Project G
0	–$	139,000	–$	209,000
1		58,000		38,000
2		52,000		53,000
3		62,000		92,000
4		57,000		122,000
5		52,000		137,000

Required:

(a)	Calculate the payback period for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	Payback period
Project F	years
Project G	years

(b)	Calculate the NPV for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	Net present value
Project F	$
Project G	$

(c)	Which project should the company accept?
	Project G

Explanation:

(a)

The payback period for each project is:

F:     2 + ($29,000 / $62,000) = 2.47 years

G:    3 + ($26,000 / $122,000) = 3.21 years

The payback criterion implies accepting project F because it pays back sooner than project G. Project G does not meet the minimum payback of three years.

(b)

The NPV for each project is:

F:     NPV = – $139,000 + $58,000 / 1.11 + $52,000 / 1.112 + $62,000 / 1.113 + $57,000 / 1.114

+ $52,000 / 1.115

NPV = $69,197.62

G:    NPV = – $209,000 + $38,000 / 1.11 + $53,000 / 1.112 + $92,000 / 1.113

+ $122,000 / 1.114 + $137,000 / 1.115

NPV = $97,187.84

The NPV criterion implies we should accept project G because project G has a higher NPV than project F.

(c)

Even though Project G does not meet the payback period of three years, it does provide the largest increase in shareholder wealth, therefore, choose Project G. Payback period should generally be ignored in this situation.

    

Calculator Solution:

 

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

   

Project F		Project G
CFo	–$139,000	CFo	–$209,000
C01	$58,000	C01	$38,000
F01	1	F01	1
C02	$52,000	C02	$53,000
F02	1	F02	1
C03	$62,000	C03	$92,000
F03	1	F03	1
C04	$57,000	C04	$122,000
F04	1	F04	1
C05	$52,000	C05	$137,000
F05	1	F05	1
I = 11		I = 11
NPV CPT		NPV CPT
$69,197.62		$97,187.84

Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 19 percent. Year Project M Project N 0 –$140,000 –$355,000 1 63,500 152,500 2 81,500 180,000 3 72,500 137,500 4 58,500 110,000

Kerron Company is presented with the following two mutually exclusive projects. The required return for both projects is 19 percent.

Year	Project M	Project N
0	–$140,000	–$355,000
1	63,500	152,500
2	81,500	180,000
3	72,500	137,500
4	58,500	110,000

Required:
(a)	What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	IRR
Project M	%
Project N	%

(b)	What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	NPV
Project M	$
Project N	$

(c)	Which, if either, of the projects should the company accept?
	Project M

Explanation: (a)

The IRR for each project is:

M:	$140,000 = $63,500 / (1 + IRR) + $81,500 / (1 + IRR)2 + $72,500 / (1 + IRR)3 + $58,500 / (1 + IRR)4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 34.47%

N:	$355,000 = $152,500 / (1 + IRR) + $180,000 / (1 + IRR)2 + $137,500 / (1 + IRR)3 + 110,000 / (1 + IRR)4

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 24.61%

The IRR decision rule implies we accept project M because the IRR for M is greater than the IRR for N.

(b)

The NPV for each project is:

M:	NPV = – $140,000 + $63,500 / 1.19 + $81,500 / 1.192 + $72,500 / 1.193 + $58,500 / 1.194
	NPV = $43,108.55

N:	NPV = – $355,000 + $152,500 / 1.19 + $180,000 / 1.192 + $137,500 / 1.193 + $110,000 / 1.194
	NPV = $36,709.17

The NPV criterion implies we accept project M because project M has a higher NPV than project N.

(c)

Accept project M since the NPV is higher. IRR cannot be used to rank mutually exclusive projects.

   

Calculator Solution:

 

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

    

Project M
CFo	–$140,000	CFo	–$140,000
C01	$63,500	C01	$63,500
F01	1	F01	1
C02	$81,500	C02	$81,500
F02	1	F02	1
C03	$72,500	C03	$72,500
F03	1	F03	1
C04	$58,500	C04	$58,500
F04	1	F04	1
CPT IRR		I = 19
34.47%		NPV CPT
		$43,108.55

   

Project N
CFo	–$355,000	CFo	–$355,000
C01	$152,500	C01	$152,500
F01	1	F01	1
C02	$180,000	C02	$180,000
F02	1	F02	1
C03	$137,500	C03	$137,500
F03	1	F03	1
C04	$110,000	C04	$110,000
F04	1	F04	1
CPT IRR		I = 19
24.61%		NPV CPT
		$36,709.17

Problem 8-9 Calculating NPV [LO 4] Consider the following cash flows: Year Cash Flow 0 –$ 32,000 1 14,200 2 17,500 3 11,600

Problem 8-9 Calculating NPV [LO 4]

Consider the following cash flows:

Year	Cash Flow
0		–$	32,000
1			14,200
2			17,500
3			11,600

Requirement 1:

What is the NPV at a discount rate of zero percent? (Do not round intermediate calculations.) Net present value $   Requirement 2: What is the NPV at a discount rate of 10 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Requirement 3: What is the NPV at a discount rate of 20 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Requirement 4: What is the NPV at a discount rate of 30 percent? (Do not round intermediate calculations. Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)   Net present value $   Explanation: 1: The NPV of a project is the PV of the outflows plus the PV of the inflows. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is:   NPV = – $32,000 + 14,200 + 17,500 + 11,600 NPV = $11,300   2: The NPV at a 10 percent required return is:   NPV = – $32,000 + $14,200 / 1.10 + $17,500 / 1.102 + $11,600 / 1.103 NPV = $4,087.15   3: The NPV at a 20 percent required return is:   NPV = – $32,000 + $14,200 / 1.20 + $17,500 / 1.202 + $11,600 / 1.203 NPV = –$1,300.93   4: And the NPV at a 30 percent required return is:   NPV = – $32,000 + $14,200 / 1.30 + $17,500 / 1.302 + $11,600 / 1.303 NPV = – $5,441.97   Notice that as the required return increases, the NPV of the project decreases. This will always be true for projects with conventional cash flows. Conventional cash flows are negative at the beginning of the project and positive throughout the rest of the project.     Calculator solution:   Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.    CFo  –$32,000 CFo  –$32,000 C01  $14,200 C01  $14,200 F01  1 F01  1 C02  $17,500 C02  $17,500 F02  1 F02  1 C03  $11,600 C03  $11,600 F03  1 F03  1   I = 0%   I = 10%   NPV CPT   NPV CPT   $11,300.00   $4,087.15     CFo  –$32,000 CFo  –$32,000 C01  $14,200 C01  $14,200 F01  1 F01  1 C02  $17,500 C02  $17,500 F02  1 F02  1 C03  $11,600 C03  $11,600 F03  1 F03  1   I = 20%   I = 30%   NPV CPT   NPV CPT   –$1,300.93   –$5,441.97

Problem 8-7 Calculating NPV and IRR [LO 3, 4] A project that provides annual cash flows of $2,800 for nine years costs $9,200 today. Requirement 1: At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Problem 8-7 Calculating NPV and IRR [LO 3, 4]

A project that provides annual cash flows of $2,800 for nine years costs $9,200 today.

Requirement 1:

At a required return of 11 percent, what is the NPV of the project? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 2:

At a required return of 27 percent, what is the NPV of the project? (Do not round intermediate calculations. A negative amount should be indicated by a minus sign. Round your answer to 2 decimal places (e.g., 32.16).)

NPV

$

Requirement 3:

At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

Discount rate

%

Explanation:

1:

The NPV of a project is the PV of the outflows plus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 11 percent required return is:

NPV = – $9,200 + $2,800(PVIFA11%, 9)

NPV = $6,303.73

At an 11 percent required return, the NPV is positive, so we would accept the project.

2:

The equation for the NPV of the project at a 27 percent required return is:

NPV = – $9,200 + $2,800(PVIFA27%, 9)

NPV = –$36.22

At a 27 percent required return, the NPV is negative, so we would reject the project.

3:

We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is:

0 = – $9,200 + $2,800(PVIFAIRR, 9)

IRR = .2686, or 26.86%

   

Calculator Solution:

 

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

  

CFo	–$9,200	CFo	–$9,200	CFo	–$9,200
C01	$2,800	C01	$2,800	C01	$2,800
F01	9	F01	9	F01	9
I = 11%		I = 27%		IRR CPT
NPV CPT		NPV CPT		26.86%
$6,303.73		–$36.22

We are evaluating a project that costs $690,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

We are evaluating a project that costs $690,000, has a five-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 71,000 units per year. Price per unit is $75, variable cost per unit is $50, and fixed costs are $790,000 per year. The tax rate is 35 percent, and we require a 15 percent return on this project.

   

a-1	Calculate the accounting break-even point.

Break-even point

units

   

a-2	What is the degree of operating leverage at the accountin g break-even point? (Round your answer to 3 decimal places. (e.g., 32.161))

   

DOL

   

b-1	Calculate the base-case cash flow and NPV. (Round your NPV answer to 2 decimal places. (e.g., 32.16))

Cash flow	$
NPV	$

b-2	What is the sensitivity of NPV to changes in the sales figure? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))

ΔNPV/ΔQ

$

  

c.	What is the sensitivity of OCF to changes in the variable cost figure? (Negative amount should be indicated by a minus sign.)

  

ΔOCF/ΔVC

$

Explanation: a.

To calculate the accounting breakeven OCF, we first need to find the depreciation for each year. The depreciation is:

Depreciation = $690,000/5

Depreciation = $138,000 per year

   

And the accounting breakeven is:

QA = ($790,000 + 138,000)/($75 – 50)

QA = 37,120 units

   

To calculate the accounting breakeven, we must realize at this point (and only this point), the OCF is equal to depreciation. So, the DOL at the accounting breakeven is:

DOL = 1 + FC/OCF = 1 + FC/D

DOL = 1 + [$790,000)/$138,000)]

DOL = 6.725

b. 

We will use the tax shield approach to calculate the OCF. The OCF is:

  

OCFbase = [(P – v)Q – FC](1 – T) + TD

OCFbase = [($75 – 50)(71,000) – $790,000](0.65) + 0.35($138,000)

OCFbase = $688,550

Now we can calculate the NPV using our base-case projections. There is no salvage value or NWC, so the NPV is:

NPVbase = –$690,000 + $688,550(PVIFA15%,5)

NPVbase = $1,618,126.39

  

To calculate the sensitivity of the NPV to changes in the quantity sold, we will calculate the NPV at a different quantity. We will use sales of 76,000 units. The NPV at this sales level is:

OCFnew = [($75 – 50)(76,000) – $790,000](0.65) + 0.35($138,000)

OCFnew = $769,800

  

And the NPV is:

NPVnew = –$690,000 + $769,800(PVIFA15%,5)

NPVnew = $1,890,488.99

  

So, the change in NPV for every unit change in sales is:

ΔNPV/ΔS = ($1,618,126.39 – 1,890,488.99)/(71,000 – 76,000)

ΔNPV/ΔS = +$54.473

  

If sales were to drop by 500 units, then NPV would drop by:

NPV drop = $54.473(500) = $27,236.26

You may wonder why we chose 76,000 units. Because it doesn’t matter! Whatever sales number we use, when we calculate the change in NPV per unit sold, the ratio will be the same.

c.

To find out how sensitive OCF is to a change in variable costs, we will compute the OCF at a variable cost of $51. Again, the number we choose to use here is irrelevant: We will get the same ratio of OCF to a one dollar change in variable cost no matter what variable cost we use. So, using the tax shield approach, the OCF at a variable cost of $51 is:

OCFnew = [($75 – 51)(71,000) – 790,000](0.65) + 0.35($138,000)

OCFnew = $642,400

So, the change in OCF for a $1 change in variable costs is:

ΔOCF/ΔVC = ($688,550 – 642,400)/($50 – 51)

ΔOCF/ΔVC = –$46,150

If variable costs decrease by $1 then, OCF would increase by $46,150

You are evaluating two different silicon wafer milling machines. The Techron I costs $222,000, has a three-year life, and has pretax operating costs of $57,000 per year. The Techron II costs $390,000, has a five-year life, and has pretax operating costs of $30,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $34,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines.

You are evaluating two different silicon wafer milling machines. The Techron I costs $222,000, has a three-year life, and has pretax operating costs of $57,000 per year. The Techron II costs $390,000, has a five-year life, and has pretax operating costs of $30,000 per year. For both milling machines, use straight-line depreciation to zero over the project’s life and assume a salvage value of $34,000. If your tax rate is 35 percent and your discount rate is 9 percent, compute the EAC for both machines. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

	EAC
Techron I	$
Techron II	$

Which do you prefer?

Techron II

Explanation:

We will need the aftertax salvage value of the equipment to compute the EAC. Even though the equipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:

Aftertax salvage value = $34,000(1 − 0.35) = $22,100

To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:

OCF = −$57,000(1 − 0.35) + 0.35($222,000/3) = −$11,150

NPV = −$222,000 − $11,150(PVIFA9%,3) + ($22,100/1.093) = −$233,158.68

EAC = −$233,158.68 / (PVIFA9%,3) = −$92,110.45

And the OCF and NPV for Techron II is:

OCF = −$30,000(1 − 0.35) + 0.35($390,000/5) = $7,800

NPV = −$390,000 + $7,800(PVIFA9%,5) + ($22,100/1.095) = −$345,297.24

EAC = −$345,297.24 / (PVIFA9%,5) = −$88,773.31

The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.

Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.49 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,010,000 in annual sales, with costs of $705,000. The tax rate is 34 percent and the required return on the project is 16 percent. What is the project’s NPV?

Keiper, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.49 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $2,010,000 in annual sales, with costs of $705,000. The tax rate is 34 percent and the required return on the project is 16 percent. What is the project’s NPV? (Round your answer to 2 decimal places. (e.g., 32.16))

NPV

$

Explanation:

Using the tax shield approach to calculating OCF (Remember the approach is irrelevant; the final answer will be the same no matter which of the four methods you use.), we get:

OCF = (Sales − Costs)(1 − T) + T(Depreciation)

OCF = ($2,010,000 − 705,000)(1 − 0.34) + 0.34($2,490,000/3)

OCF = $1,143,500

Since we have the OCF, we can find the NPV as the initial cash outlay plus the PV of the OCFs, which are an annuity, so the NPV is:

NPV = −$2,490,000 + $1,143,500(PVIFA16%,3)

NPV = $78,174.69