A new computer system will require an initial outlay of $22,500, but it will increase the firm’s cash flows by $4,500 a year for each of the next 6 years.

The following are the cash flows of two projects:

 

Year	Project A	Project B
0	−$270	−$270
1	150	170
2	150	170
3	150	170
4	150

 

a.	If the opportunity cost of capital is 12%, calculate the NPV for both projects. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

 

Project	NPV
A	$
B

 

b.	Which of these projects is worth pursuing?
	Both

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

NPVA = −$270 + [$150 × Annuity factor (12%, 4 periods)]

NPVB = −$270 + [$170 × Annuity factor (12%, 3 periods)]

b.

Both projects are worth pursing as they are independent projects with positive NPV values.

  

Calculator computations:

a.

CF0 = −270

CO1 = 150              FO1 = 4

I = 12

NPV CPT = 185.60

b.

CF0 = −270

CO1 = 170              FO1 = 3

I = 12

NPV CPT = 138.31

The following are the cash flows of two projects:

Year	Project A	Project B
0	−$380	−$380
1	210	280
2	210	280
3	210	280
4	210

a.	Calculate the NPV for both projects if the discount rate is 11%. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Project	NPV
A	$
B

b.	Suppose that you can choose only one of these projects. Which would you choose?
	Project B

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

NPVA = −$380 + [$210 × Annuity factor (11%, 4 periods)]

NPVB = −$380 + [$280 × Annuity factor (11%, 3 periods)]

b.

Since you can only choose one project, select the one with the higher positive NPV.

Calculator computations:

a.

CF0 = −380

CO1 = 210              FO1 = 4

I = 11

NPV CPT = 271.51

b.

CF0 = −380

CO1 = 280            FO1 = 3

I = 11

NPV CPT = 304.24

The following are the cash flows of two projects:

Year		Project A					Project B
0		–	$	260			–	$	260
1				140					160
2				140					160
3				140					160
4				140

If the opportunity cost of capital is 11%, what is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Project	Profitability index
A
B

Is the project with the highest profitability index also the one with the highest NPV?

Yes

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

  

NPVA = −$260 + [$140 × Annuity factor (11%, 4 periods)]

NPVB = −$260 + [$160 × Annuity factor (11%, 3 periods)]

The profitability indexes are as follows:

Project A: $174.34 / $260 = .6705

Project B: $130.99 / $260 = .5038

Profitability index = NPV / Initial investment

In this case, with equal initial investments, both the profitability index and NPV give projects the same ranking. This is an unusual case, however, since it is rare for the initial investments to be equal.

The following are the cash flows of two projects:

 

Year	Project A	Project B
0	−$340	−$340
1	170	240
2	170	240
3	170	240
4	170

 

What is the payback period of each project? (Round your answers to 2 decimal places.)

 

Project	Payback Period
A	years
B	years

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

Project A has a payback period of $340 / $170 = 2.00 years

Project B has a payback period of $340 / $240 = 1.42 years

A project that costs $3,400 to install will provide annual cash flows of $1,000 for each of the next 6 years.

Calculate the NPV if the discount rate is 14%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

NPV

$

Is this project worth pursuing?

Yes

How high can the discount rate be before you would reject the project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Discount rate

%

rev: 09_17_2015_QC_CS-25813, 11_18_2015_QC_CS-34132, 05_12_2016_QC_CS-51588

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

Solving for IRR = 19.11%

At a discount rate of 14%, the project has a positive NPV and should be pursued. If the discount rate rises above the IRR of 19.11% the project is no longer attractive since the NPV would now become negative.

Calculator computations:

CF0 = −3,400

CO1 = 1,000            FO1 = 6

I = 14

NPV CPT = 488.67

CF0 = −3,400

CO1 = 1,000            FO1 = 6

IRR CPT = 19.11

A new computer system will require an initial outlay of $22,500, but it will increase the firm’s cash flows by $4,500 a year for each of the next 6 years.

a.	Calculate the NPV and decide if the system is worth installing if the required rate of return is 8%. What if it is 13%? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Rate of Return		NPV	Worth Installing
8%	$		No
13%	$		No

b.	How high can the discount rate be before you would reject the project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Maximum discount rate

%

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

NPV8% = −$22,500 + [$4,500 × Annuity factor (8%, 6 periods)]

NPV13% = −$22,500 + [$4,500 × Annuity factor (13%, 6 periods)]

b.

IRR = discount rate (r), which is the solution to the following equation:

[Using a financial calculator, enter PV = (−)22,500; PMT = 4,500; FV = 0; n = 6, compute i.]

The project will be rejected for any discount rate above this rate.

ere are the cash flows for a project under consideration:

C0				C1				C2
−	$	8,010		+	$	5,940		+	$	20,160

a.	Calculate the project’s net present value for discount rates of 0, 50%, and 100%. (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to the nearest whole dollar.)

Discount rate	Net present value
0%	$
50%	$
100%	$

b.	What is the IRR of the project? (Do not round intermediate calculations. Enter your answer as a whole percent.)

IRR

%

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

r = 0%  NPV = −$8,010 + $5,940 + $20,160 = $18,090

r = 50%  NPV =	−$8,010 +	$5,940	+	$20,160	= $4,910
		1.50		1.502

r = 100%  NPV =	−$8,010 +	$5,940	+	$20,160	= $0
		2.00		2.002

b.

IRR = 100%, the discount rate at which NPV = 0.

Calculator computations:

CF0 = −8,010

CO1 = 5,940        FO1 = 1

CO2 = 20,160      FO2 = 1

I = 0	I = 50	I = 100	CPT IRR = 100
NPV CPT = 18,090	NPV CPT = 4,910	NPV CPT = 0

Consider projects A and B with the following cash flows:

		C0				C1				C2				C3
A		−	$	32		+	$	16		+	$	16		+	$	16
B		−		57		+		32		+		32		+		32

a-1.	What is the NPV of each project if the discount rate is 12%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Project	NPV
A	$
B	$

a-2.	Which project has the higher NPV?
	Project B

b-1.	What is the profitability index of each project? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Project	Profitability index
A
B

b-2.	Which project has the higher profitability index?
	Project B

c-1.	Which project is most attractive to a firm that can raise an unlimited amount of funds to pay for its investment projects?
	Project B

c-2.	Which project is most attractive to a firm that is limited in the funds it can raise?
	Project B

rev: 03_16_2015_QC_CS-10561

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

NPVA = −$32 + [$16 × Annuity factor (12%, 3 periods)]

NPVB = −$57 + [$32 × Annuity factor (12%, 3 periods)]

Thus Project B has the higher NPV if the discount rate is 12%.

b.

PIA = NPVA / Initial investment = $6.43 / $32 = .20

PIB = NPVB / Initial investment = $20 / $57 = .35

Project B has the higher profitability index.

c-1.

For a firm with unlimited funds, the preferred project is the project with the highest NPV.

c-2.

For a firm with limited funds, the preferred project is the project with the highest PI that the firm can afford. In this case, we are assuming the firm can afford either project.

ere are the expected cash flows for three projects:

	Cash Flows (dollars)
Project	Year:	0			1			2			3			4
A		−	6,900		+	1,475		+	1,475		+	3,950			0
B		−	2,900			0		+	2,900		+	2,950		+	3,950
C		−	6,900		+	1,475		+	1,475		+	3,950		+	5,950

a.	What is the payback period on each of the projects?

Project	Payback period
A	years
B	years
C	years

b.	If you use a cutoff period of 2 years, which projects would you accept?
	Project B

c.	If you use a cutoff period of 3 years, which projects would you accept?
	Projects A, B, and C

d-1.	If the opportunity cost of capital is 12%, calculate the NPV for projects A, B, and C. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Project	NPV
A	$
B	$
C	$

d-2.	Which projects have positive NPVs?
	Project B and Project C

e.	"Payback gives too much weight to cash flows that occur after the cutoff date." True or false?
	False

 

Explanation:

Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

b.

Only Project B satisfies the 2-year payback criterion.

c.

All three projects satisfy a 3-year payback criterion.

d.

NPVA = −$6,900 +	$1,475	+	$1,475	+	$3,950	= −$1,595.64
	1.12		(1.12)2		(1.12)3

NPVB = −$2,900 +	$2,900	+	$2,950	+	$3,950	= $4,021.91
	(1.12)2		(1.12)3		(1.12)4

NPVC = −$6,900 +	$1,475	+	$1,475	+	$3,950	+	$5,950	= $2,185.69
	1.12		(1.12)2		(1.12)3		(1.12)4

Projects B and C have a positive NPV.

e.

False. Payback gives no weight to cash flows after the cutoff date.