Chapter 6 Review Questions with worked solutions

Chapter 6 Practice Problems with worked solutions

 

Investment Decision Problems

1.For an investment of $15,000 now, a company can receive $9,250 one year from now, and $9,200 two years from now. Check its earnings rate on this deal by comparing it to an account using:

10% effective

20% effective

15% effective.

For each, fill out the following balance sheet

Time (year)	Interest	Deposit	Withdrawal	Balance
0		\$15,000		\$15,000
1	?		\$9,250	?
2	?		9,200	?

Remember that if more money could be taken from an account than from an investment, then the investment made less than the account. If less money could be taken from an account than from an investment, then the investment made more than the account.

at 10% effective, Conclusion?

TIME	I%	INTEREST $	DEPOSIT	WITHDRAWAL	BALANCE
0	10		15,000		15,000
1		1,500		9250	7,250
2		725		9200	(1,225)

at 20% effective

Conclusion?

TIME	I%	INTEREST $	DEPOSIT	WITHDRAWAL	BALANCE
0	20		15,000		15,000
1		3,000		9250	8,750
2		1,750		9200	1,300

at 15% effective

Conclusion?

TIME	I%	INTEREST $	DEPOSIT	WITHDRAWAL	BALANCE
0	15		15,000		15,000
1		2,250		9250	8,000
2		1,200		9200	0

2.For the investment in problem 1 on page 26, find the NPV at each of:

10% effective

20% effective

15% effective.

Relate each value to the results in (a), (b) and (c) in problem 1.

CFNPV

CFO = -15,000I = 10

C01 = -9,250F01 = 1NPV = <CPT> = 1,012.40

C02 = – 9,200F02 = 1

CFNPV

CFO = -15,000I = 20

C01 = -9,250F01 = 1NPV = <CPT> = -902.78

C02 = – 9,200F02 = 1

CFNPV

CFO = -15,000I = 15

C01 = -9,250F01 = 1NPV = <CPT> = 0

C02 = – 9,200F02 = 1

3.A finance company has an opportunity to purchase three promissory notes from a broker for a total of $140,000 cash. The first note would pay $20,000 in one year, the second would pay $70,000 in two years and the third $80,000 in three years. The finance company has set for itself a minimum acceptable rate of return of 10% effective.

Evaluate the net present value of the investment at the company’s MARR.

State your conclusion about the acceptability of the profitability of this deal.

Cost =	-140,000
Yr1=	20,000		IRR = 8.677
Yr2 =	70,000
Yr3=	80,000		NPV = – 3,861.76
MARR	10%
	AS NPV is negative, it does not meet MARR

Using IRR, you can see the return is only 8.68%

4.A project is to cost $60,000 immediately and to produce net cash inflows of $20,000 at the end of the first year, $30,000 at the end of the second year and $25,000 at the end of the third year. At the end of the third year the business will be sold for $5,000. The company aims at a rate of return of 15% effective.

a) Show whether or not the company will achieve its objective.

Cost =	-60,000
Yr1=	20,000		NPV = -198.90
Yr2=	30,000
Yr3=	30,000		IRR = 14.81%
EFF	15%
	AS NPV is negative, it does not meet MARR

b)Find the value of the bonus paid at the start which would cause the project to earn exactly 20% effective.

Cost =	-60,000
Yr1=	20,000		NPV = -5,138.89
Yr2=	30,000
Yr3=	30,000
EFF	20%
	A bonus payment of $5,138.89 would be needed.

5.Samuels Co. plans to start a repair business. It would provide net returns of $35,000 at the end of the first year, and $50,000 at the end of each of the next three years. The equipment would then be sold for $11,000 and the business terminated. Samuels aims at a rate of return of 15%.

How much should Samuels be willing to invest (now)?

Yr1=	35000
Yr2=	50000
Yr3=	50000		NPV=	135,994.73
Yr4=	61000
EFF=	15%

Samuels should be willing to invest up to $135,994.73.

6.Williams Co. has the chance to start a transportation company in the north. It would require $108,000 to start the business and it would provide net returns of $35,000 at the end of the first year, and $40,000 at the end of each of the next two years. The equipment would then be sold for $9,000 and the business terminated. Williams aims at a rate of return of 12%.

a)Find the NPV at 12% effective, and the IRR. Should Williams Co. start this company?

Cost =	-108,000
Yr1=	35,000		NPV=	9,985.01
Yr2=	40,000
Yr3=	49,000		IRR =	6.83
EFF=	12%

b)If the government wanted to subsidize Williams so that it would earn 15% compounded annually, what subsidy paid at the end of the three years would be required?

Cost =	-108,000
Yr1=	35,000		NPV=	-15,101.18
Yr2=	40,000
Yr3=	49,000
EFF=	15%

A subsidy of $15,101.18 is required as a PV

PyCyNIyPVPMTFV

11315-15,101.180$22,967.01

As subsidy of $22,967.01 is required if paid at the end of 3 years.

7.PA Lumber Co. is bidding on the right to cut lumber from a private forest for 10 years. The amount of lumber permitted to be cut each year would allow PA to produce a net cash flow (excluding cost of cutting rights) of $120,000 a year. If PA aims at a rate of return of 12.5%, how much could it afford to bid as a lump sum for the cutting rights?

Then enter 120,000 for COl and change FOl to 10 and the ten periods of cash flows will be entered.

CFNPV

CF0 = 0I = 12.5

C01 = 120,000F01 = 10NPV = <CPT> = $664,371.70

OR

PyCyNIyPVPMTFV

111012.5664,371.70-120,0000

8.Iffi Co. plans to install insulation in a building which it plans to use for six years. The insulation and its installation will cost $193,000 and will result in savings of $37,000 a year and will increase the residual value of the building by $90,000. Find the internal rate of return of the planned installation of the insulation.

Cost =	-193,000
CO1 =	37,000		IRR=	12.7118
FO1=	5
CO2 =	127,000
FO2=	1

9.Tessa Quaid has purchased a 10-year video rental franchise for $12,000. She will have to invest another $22,000 in the store immediately. She expects returns of $8,000 a year at the end of each year. Will TQ make a rate of return of at least 15%? What will be the internal rate of return?

Cost =	12,000 + 22,000		NPV =	6,150.15
CO1=	8,000		IRR =	19.6
FO1 =	10
	NPV is positive so the investment makes more than 15%

10.TW Cable Co. plans to begin operation in a large town and to expand later to a nearby small town. TW estimates its net cash flows to be:

Time (year)	Cash Flow
0	-$600,000
1	100,000
2	100,000
3	-50,000 (expansion)
4-9	150,000
10	700,000 (includes sale of business)

Find the net present value at 17% and the internal rate of return.

Cost =	-600,000			NPV
CO1 =	100,000	F01	2	I=	17
CO2 =	-50,000	F01	1	NPV =	$9,076.27
CO3	150,000	F03	6	IRR =	17.295967
CO4=	700,000	F04	1

11.A food concession at an airport has a five year life and costs $130,000. Initial investments in equipment, training and inventory amount to $75,000. The concession’s operation is expected to produce net cash inflows of $50,000 a year and the residual value of equipment and the ending inventory are expected to total $30,000.

Find the NPV at 15% effective.

Find the internal rate of return.

Cost =	75,000 + 130,000		NPV
CO1 =	50,000		I =	15
FO1=	4		NPV =	-$22,476.94
CO2 =	50,000 + 30,000
FO2=	1		IRR =	10.5635%

12.The owners of a small business are considering three offers from potential purchasers:

Offer #1: $100,000 cash.

Offer #2: $80,000 now and $10,000 at the end of each year for five years.

Offer #3: $25,000 now and $25,000 at the end of each year for five years.

Which offer is most attractive if money is worth 9% to the owners?

Offer 1		$100,000
Offer 2
CFO =	80,000		NPV
CO1 =	10,000		I = 9
FO1 =	5		NPV =	118,896.51
Offer 3
CFO =	25,000		NPV
CO1 =	25,000		I = 9
FO1 =	5		NPV =	122,241.28

Offer 3 is best

13.A “10%” Government bond is to pay interest of $100 per year for nine years. Find the price investors should be willing to pay for the bond if they want to earn:

15% effective.

10% effective.

5% effective.

CFO=
CO1 =	100	FO1 =	8
CO2 =	1100	FO2=	1
NPV
I =	15	I =	10	I =	5
NPV =	761.42	NPV =	1000	NPV =	1,355.39

14.The Titan Package Co. finds that a $95,000 investment in automated packaging equipment will save it $20,000 a year for the next 10 years. The equipment will have no value at the end of the 10 years. If the company aims at a rate of return of 15% effective should it purchase the equipment? Why/why not?

CFO=	-95,000		NPV
CO1 =	20,000		I =	15
FO1 =	10		NPV =	5,375.37

NPV is positive, proceed with the purchase. IRR = 16.47%

15.The Fast Food Co. can expand into either of two locations. Location A will need an expenditure of $130,000 now and will result in a yearly net cash inflow of $35,000 (at the end of each year) for 10 years and no other benefits. Location B will need expenditures of $150,000 now and $50,000 in one year. It will then produce a yearly net cash flow of $45,000 a year for the following 12 years (all at the end of each year). In location B there would also be no other benefits. Which location gives the higher net present value at a required rate of return of 16% effective per year?

Location A			Location B
CF0=	-130,000		CF0=	-150,000
CO1=	35,000		CO1=	-50,000
FO1=	10		FO1=	1
			CO2 =	45,000
			FO2=	12
NPV
I =	16		I =	16
NPV=	39,162.96		NPV=	8,508.47
	Location A is a better investment at 16%.

16.You are considering a home-based business. You would like to open a kennel. You estimate that your start-up costs will be $250,000 this year and you will need to spend another $10,000 next year. You expect revenues of $35,000 per year for the first two years and $42,000 for the next three years. Your expenses are thought to be $6,000 per year. At the end of five years you plan to sell the kennel and anticipate receiving $255,000. You want to earn a minimum of 14% compounded annually on your investment. All revenue occurs at the end of the year and all expenses are paid at the beginning of the year.

Cost Period 0		$250,000
Cost Period 1		$10,000
Income Period 1 and 2		$35,000
Income Period 3, 4, and 5		$42,000
Annual expenses		$6,000
Selling Price		$255,000
Expected Return on Investment		14%

a) Calculate the payback for this project.

Yr0	Yr1	Yr2	Yr3	Yr4	Yr5
-250,000	-10,000
-6,000	-6,000	-6,000	-6,000	-6,000
0	35,000	35,000	42,000	42,000	42,000
					255,000
Payback	-231,000	-202,000	-166,000	-130,000	161,000
	Payback =	4 yrs and	136,000	297,000
		4 yrs and	136/ 297 months
		4.46	years

Calculate the net present value for this project. Should you open a kennel?

Yr0	Yr1	Yr2	Yr3	Yr4	Yr5
-256,000	19,000	29,000	36,000	36,000	297,000
I =	14%
NPV =	-17,152.42

NPV is negative, do not invest

If you require only 12% effective should you open a kennel? Why or why not?

IRR is 12.12%, therefore invest.

How much should the start-up costs be reduced by so that you would be willing to open a kennel? Use a MARR of 14%.

MARR
I = 14%		ANS: -$17,152.42
The start-up cost should be reduce by the amount of the negative NPV

Your estimate of the kennel’s selling price may be too low. You think you may be able to sell the kennel for more than $255,000. What is the minimum selling price you must have so that you would be willing to open the kennel? Assume the start-up costs remain unchanged. Round to the nearest $. Use a MARR of 14%.

PyCyNIyPVPMTFV

11514-17,152.420$33,025.52

The minimum selling price should be $255,000 + 33,025.52 = $288,026

Calculate the internal rate of return (IRR) for this project. Should you open a kennel if you want to earn at least 14% compounded annually on your investment?

IRR =	12.12%
NO,	this is lower than MARR of 14%

17.You are considering purchasing a home-based business that streams videos over the Internet. You think that you can buy the business from the current owner for $120,000. You expect revenues of $40,000 per year. Your expenses are thought to be $20,000 per year for the first 2 years and $10,000 per year for the last 3 years. At the end of five years you plan to sell the business, retire and move to Las Vegas. You anticipate you could sell it for $130,000. You want to earn at least 16% compounded annually on your investment?

Cost Period 0		$120,000
Revenue		$40,000	5 years
Cost		$20,000	2 years
Cost		$10,000	3 years
Sale		$130,000
I		16%

Calculate the payback for this project.

Yr0	Yr1	Yr2	Yr3	Yr4	Yr5
-120,000
-20,000	-20,000	-10,000	-10,000	-10,000
	40,000	40,000	40,000	40,000	40,000
					130,000
Payback	-100,000	-80,000	-50,000	-20,000	140,000
	4 yrs and	-30,000	170,000
	4 30/170 yrs			4.176 yrs

Find the NPV. Should you buy the business?

Yr0	Yr1	Yr2	Yr3	Yr4	Yr5
-140,000	20,000	30,000	30,000	30,000	170,000
NPV
I =	16
NPV =	$16,263.94

IRR = 19.45%

How high could the purchase price of the business be and still make it worthwhile for you to buy the Internet business?

To bring NPV to zero increase purchase price to
	$120,000 + NPV value
	$136,263.94

You think you might be overly optimistic in your estimate of the selling price of the business. What is the lowest selling price that you can accept and still be willing to buy the business? Round to the nearest $.

PyCyNIyPVPMTFV

11516-16,263.940$34,159.83

Selling Price = $136,000 – 34,159.83 = $95,840.17

You would still be willing proceed with a cost of $95,840.

Calculate the internal rate of return (IRR) for this investment. Should you buy the business?

At a cost of $140,000, the IRR is 19.45%, Yes

Your accountant tells you that your projected annual revenue is too high. What is the maximum annual decrease in revenue you could withstand and still have this investment be worthwhile?

PyCyNIyPVPMTFV

11516-16,263.94$4,967.160

The annual revenue could drop by $4,967.16 and the investment is still worthwhile.

18.You want to start up a business in a mall selling CFL souvenirs. You plan to spend $80,000 in start-up costs. You anticipate that you will break even in the first year and second year, make $20,000 the third, and make $20,000 each year after that. You plan to sell the business for $100,000 at the end of the sixth year. You want to earn at least 15% effective on your investment.

a)What is the net present value of your business plan?

Yr0	Yr1	Yr2	Yr3	Yr4	Yr5	Yr 6
-80,000
	0	0	20,000	20,000	20,000	20,000
						100,000
I =	15%
NPV =				$6,408.24

IRR = 16.73%

b)What is the internal rate of return?

IRR = 16.73%

c)Should you undertake the business plan? Why or why not?

The NPV is Positive and the IRR is greater than 15%

d)You think you might be overly optimistic in your estimate of the selling price of the business. What is the lowest selling price that you can accept and still undertake the project? Round to the nearest $.

PyCyNIyPVPMTFV

11615-6,408.240$14,822.65

You could reduce the selling price to $85,177 (100,000 – 14,822.65)

19.You are a restaurant owner and are considering expanding your business by buying the recently vacated store next door. The purchase price is $50,000. You will also need to spend an extra $35,000 in re-modeling. The larger dining room is expected to generate net profits of $12,000 a year for the first 4 years and $15,000 a year for the next 6 years. At the end of 10 years, you will retire. You expect to be able to sell the restaurant for $70,000. You want to earn a minimum of 20% on your investment.

Yr 0	Yr 1 – 4	Yr 5 – 9	Yr 10
-50,000
-35,000
	12,000	15,000	15,000
			70,000

What is the net present value?

CFO =	-85,000			NPV
C01 =	12,000	F01 =	4	I =	20
C02 =	15,000	F02 =	5	NPV =	-$18,573.73
C03 =	85,000	F03 =	1

What is the Internal Rate of Return?

IRR = 14.77%

Should you expand the restaurant? Why or why not?

The NPV is Negative and the IRR is less than 20%, DO not invest

You hear news reports that real estate prices may rise over the next few years and that this is especially true for commercial real estate. You now think you can sell the restaurant for more than $70,000. What is the minimum selling price you must have so that you would be willing to expand the restaurant? Round to the nearest $.

PyCyNIyPVPMTFV

• 111020-18,573.730$115,003.64

The minimum selling price would need to be $185,004 (70,000 + 115,004)

20.You have decided to start a business selling vitamin supplements. You estimate that you will have $200,000 in start-up costs. Annual expenses are expected to be $30,000 and revenue is expected to be $50,000 per year for the first 2 years and $75,000 in each of the next 3 years. You plan to sell the business at the end of 5 years for an estimated $250,000. You want to earn at least a 15% rate of return on your investment (MARR is 15%).

Yr0	Yr1 – 2	Yr3 – 4	Yr5
-200,000
-30,000	-30,000	-30,000
	50,000	75,000	75,000
			250,000

Should you invest? What is the IRR?

CF0 =	-230,000			NPV
C01 =	20,000	F01 =	2	I =	15%
C02 =	45,000	F02 =	2	NPV =	19,413.74
C03 =	325,000	F03 =	1

IRR = 17.25%

The IRR is greater than 15%, YES invest,

What is the NPV? Should you invest?

NPV
I =	15
NPV =	19,414		Yes Invest as NPV is positive

Your accountant tells you that your estimated selling price is too high. What is the minimum selling price you could accept and still have this investment be worthwhile?

PyCyNIyPVPMTFV

11515-19,413.740$39,047.97

Minimum selling price could be $210,952 (250,000 – 39,048)

One of the herbal supplements you were going to sell has recently been banned. This will cause a substantial decrease in your revenue. What is the maximum annual decrease in revenue you could withstand and still have this investment be worthwhile?

PyCyNIyPVPMTFV

11515-19,413.74$5,791.420

The annual revenue could decrease by $5,791.42

Net Present Value and Internal Rate of Return

21.You are operations manager for Flatugas, a small natural gas producer in the Peace River Region of British Columbia. You are considering investing in a new technology that captures more of the gas from the wellhead. The technology will cost $1,000,000 and operating costs are estimated at $25,000 per year payable at the beginning of each year. The technology should result in $250,000 in extra natural gas revenue per year and have the added benefit of reducing greenhouse gas emissions. The technology is expected to last for 5 years when it could be sold back to the manufacturer for a guaranteed price of $249,908.70. The company has a 15% MARR and requires a payback period of 4 years or less.

What is the payback period of the investment? Should you invest?

Yr 0	Yr 1	Yr 2	Yr 3	Yr 4	Yr 5
-1,000,000
-25000	-25,000	-25,000	-25,000	-25,000
	250,000	250,000	250,000	250,000	250,000
					249,908.70	Selling Price

MARR = 15%

Payback	-800,000	-575,000	-350,000	-125,000	125,000

Payback is more than 4 Years. Do not invest.

Payback period is 4.25 years (125,000 / (250,000 + 249,908.7))

Calculate the IRR for the investment and explain how you would use IRR to make a decision on whether to invest or not.

CF0 = -1,025,000NPVIRR = 9.95

C01 = 225,000F01 = 4I = 15

C02 = 499,908.7F02 = 1NPV = -134,086.89

IRR of 9.95% is less than the required 15%, do NOT invest.

Calculate the NPV. Should you invest?

The NPV at 15% is -$134,086.89

The director of finance reviews your analysis and tells you that a MARR of 13% is more appropriate for the project. He also informs you that the company should be able to sell clean air credits under the Kyoto agreement. What annual revenue would be required from the credits to make this a worthwhile investment at a 13% MARR? (Assume 5 equal payments at the end of the year).

If MARR = 13%, then the NPV is -$84,413.54

PyCyNIyPVPMTFV

11513-84,413.54$24,0000

Annual credits of $24,000 would be required.

22.The Blue Sky Resort plans to install a new chair lift to serve a new ski area. Construction of the lift is estimated to require an immediate outlay of $190,000. In addition, the company must spend $30,000 today and $30,000 per year for the next 3 years to clear and groom the new area. The life of the lift is estimated to be 11 years with a salvage value of $80,000. Profits from the lift (excluding the cost of grooming and clearing) are expected to be $40,000 per year for the first five years, and $70,000 per year for the next six years. The company wants to earn a minimum of 14% effective on the investment. All revenue occurs at the end of the year and all expenses are paid at the beginning of the year.

Yr 0	Yr 1	Yr 2	Yr 3	Yr 4,5	Yr 6,7,8,9,10	Yr 11
-190,000	-30,000	-30,000	-30,000			80,000
-30,000	40,000	40,000	40,000	40,000	70,000	70,000

Determine the net present value. Should they go ahead with the project? Why or why not?

CF0 = -220,000NPVIRR = 14.582

C01 = 10,000F01 = 3I = 14

C02 = 40,000F02 = 2NPV = 7,979.31

C03 = 70,000F03 = 5

C04 = 150,000F04 = 1

The NPV is positive, INVEST

Determine the internal rate of return. Should they go ahead with the project? Why or why not?

The IRR is greater than 14%, INVEST

Determine the payback.

Payback =		-220,000
	(10,000 * 3)	30,000	-190,000		Payback =	6.57 yrs
	(40,000 *2)	80,000	-110,000
	(70000*1)	70,000	-40,000
	(70,000 * 40/70)

You hear on the news that we might be in a recession for the next few years. You now wonder if your salvage value estimate of $80,000 is too high. What is the lowest salvage value you can accept and still undertake the project? Round to the nearest $.

CF0 = -220,000NPV

C01 = 10,000F01 = 3I = 14

C02 = 40,000F02 = 2NPV = -10,950.08

C03 = 70,000F03 = 5

CO4 = 70,000F04 = 1

Trial and ERROR to find C04 such that NPV = 0

IF C04 = 100,000, then NPV = -3,851

IF C04 = 110,000, then NPV = -1,485

IF C04 = 120,000, then NPV = 880

IF C04 = 117,000, then NPV = 170

IF C04 = 116,500, then NPV = 52

IF C04 = 116,250, then NPV = -6.5

IF C04 = 116,075, then NPV = -0.61

The lowest salvage price would be $46,078 ($116,078 – 70,000)

23.A project is to cost $60,000 immediately and to produce net cash flows of $20,000 at the end of the first year, $30,000 at the end of the second year, and $25,000 at the end of the third year. At the end of the third year the business will be sold for $5,000.

Yr 0	Yr 1	Yr 2	Yr 3
-60,000	20,000	30,000	25,000
			5,000

If the company requires 15% effective, will it be able to achieve its goal?

CF0 = -60,000NPV

C01 = 20,000F01 = 1I = 15

C02 = 30,000F02 = 1NPV = -198.90

C03 = 30,000F03 = 1

The NPV is negative, Do NOT invest

Find the value of the bonus paid at the start which would cause the project to earn exactly 20% effective.

If I = 20

Then the NPV = -$5,138.89

The starting bonus of $5,138.89 is required.

24.Due to a restricted capital budget, a company can undertake only one of the following 3-year projects. Both require an initial investment of $650,000 and will have no significant salvage value at the end. Project X is anticipated to have annual profits of $400,000, $300,000, and $200,000 in successive years, whereas Project Y’s only profit, $1.05 million, comes at the end of year three.

a)Calculate the IRR of each project. On the basis of their IRRs, which project should be selected?

Project XProject Y

Yr0 Yr1 Yr2 Y3Yr0 Yr1 Yr2 Y3

-650,000 400,000 300,000 200,000-650,000 0 0 1,050,000

CFO = -650,000CFO = -650,000

C01 = 400,000 F01 = 1C01 = 0F01 = 2

C02 = 300,000 F02 = 1C02 = 1,050,000F02 = 1

C03 = 200,000 F03 = 1

IRR = 20.818IRR = 17.334

Project X has the better IRR

On the basis of NPV, which project should be selected if the firm wants to earn at least 14% effective on their investment?

• NPVNPV
• I = 14I = 14
• NPV = 66,712NPV = 58,720

Project X has the better NPV

On the basis of NPV, which project should be selected if the firm wants to earn at least 11% effective on their investment?

• NPVNPV
• I = 11I = 11
• NPV = 110,085NPV = 117,751
• Project Y has the better NPV at a MARR of 11%

OLD QUESTIONS for Past TEXTBOOKS

1.A sales organization intends to purchase a car for $15,000 and to trade it in for a similar new car each year in the future. It will be allowed a trade in value of $11,000 each time. At 14% effective, what is the EUAC and the capitalized cost?

Remember EUAC is given as though paid at the end of the year.

Cost =	15,000
Trade in value=	11,000
CFO =	-15,000		NPV
CO1=	-4,000		I=	14
FO1 =	1000		NPV =	43,571.43

PyCyNIyPVPMTFV

11100014-43,571.43$6,1000

PMT = EUAC = $6,100

PV = Capital Cost = $43,571.43

2.A householder has decided to install a swimming pool and must choose between two types of pool. Pool A costs $7,000 and will have to be completely replaced every 10 years at a cost of $7,000. Pool B will cost $17,000 but is expected to last “forever.”

Find the EUAC and capitalized cost of each pool if interest is at 10% effective.

Pool A

PyCyNIyPVPMTFV

111010-7,000$1,139.280

PMT = EUAC = $1,139.28

Capital Cost = Present Value = EUAC / I = $1,139.28/ 0.1 = $11,392.18

Pool B

PyCyNIyPVPMTFV

11100010-17,000$1,7000

PMT = EUAC = $1,700

Capital Cost = Present Value = EUAC / I = $1,700/ 0.1 = $17,000

Pool A is cheaper.

3.An automobile enthusiast is considering the purchase of a battery for his favorite automobile. He has three brands of batteries to choose from A, B and C. Battery A costs $45 and will last four years. Battery B costs $55 and will last five years. Battery C costs $90 and is guaranteed for as long

as he owns the car (this time is estimated by him at 20 years). Find the capitalized cost and equivalent uniform annual cost of each brand of battery if interest is at 11% effective. Which battery offers the best value?

Battery A

PyCyNIyPVPMTFV

11411-45$14.50

PMT = EUAC = $14.50

Capital Cost = Present Value = EUAC / I = $14.50/ 0.11 = $131.86

Battery B

PyCyNIyPVPMTFV

11511-55$14.880

PMT = EUAC = $14.88

Capital Cost = Present Value = EUAC / I = $14.88/ 0.11 = $135.29

Battery C

PyCyNIyPVPMTFV

112011-90$11.50

PMT = EUAC = $11.50

Capital Cost = Present Value = EUAC / I = $11.50/ 0.11 = $102.74

Battery C is the best value.

4.A company intends to provide an automobile for the business use of one of its managers. It can purchase a suitable car for $16,000 and trade it in for a new car every three years at a cost of $9,000 each time. It can also lease the car for $430 per month (paid at the beginning of each month). Compare the costs of the two methods of obtaining the car if interest is at 15% compounded monthly.

Purchase and Replace

Step 1

Cost = $16,000Replacement Cost = $9,000 after 36 months

CF0 = -16,000NPV

C01 = 0F01 = 36I = 15/12 = 1.25

C02 = 7,000F02 = 1NPV = $11,579.39

Step 2

PyCyNIyPVPMTFV

11361.25-11,579.39401.400

Step 3

EUAC = PV = PMT / I = 401.40 / 0.0125 = $32,112

Lease

B/EPyCyNIyPVPMTFV

B1110001.2534,829.864300

Option A is less Expensive

5.A construction company has to choose between two models of machines which do the same job. The Hercules model costs $80,000 and will last eight years. It will be worth $6,000 at the end of the eight years. The Atlas model costs $60,000, will last seven years and require a $25,000 overhaul at the end of the fourth year. It will be worth $5,000 at the end of seven years. Compare the costs of the two models on the basis of EUAC and capitalized cost if interest is at 13.5% effective.

Option A					Option B
Cost =	-80,000				Cost =	-60,000
End Value	6,000				Yr 4 Cost	-25,000
Time =	8				End Value	5000
I/Y	13.5				Time	7
					I/Y	13.5
STEP 1
CF0	-80000				CF0	-60000
C01	0	F01	7		C01	0	F01	3
C02	6,000	F02	1		C02	-25000	F02	1
					C03	0	F03	2
					C04	5000	F04	1
NPV					NPV
I	13.5				I	13.5
NPV	-77,821.37				NPV	-73,003.94

Option A

PyCyNIyPVPMTFV

11813.5-77,831.37$16,497.610

EUAC = PMT = $16,497.61

Capital Cost = PMT / I = 16,497.61 / 0.135 = $122,188.83

Option B

11713.5-73,003.94$16,764.670

EUAC = PMT = $16,764.67

Capital Cost = PMT / I = 16,764.67 / 0.135 = $124,182.76

Option A is better at 13.5%.

6.A company is considering the purchase of a new metalworking machine.

Machine A will cost $12,000 and will result in annual savings of $3,700 per year. It will last six years and then have to be replaced with an identical machine costing $12,000 again, since the original machine will have no residual value. The next machine would be replaced in turn and so on.

Machine B will cost $16,000 and will result in annual savings of $4,000 per year. It will last eight years and then have to be replaced with an identical machine costing $16,000 again, since this machine, like machine A, will have no residual value. The next machine would be replaced in turn and so on.

If the company aims at an MARR of 15% effective, which, if either of the machines, should they choose?

Note especially that both investments would continue indefinitely. In this case you should find an Equivalent Uniform Annual Benefit similar to the EUAC.

Option A					Option B
Cost	-$12,000				Cost	-$16,000
Saving	3,700				Saving	4000
Time	6				Time	8
I	15%				I	15%
Cfo	-12000				Cfo	-16000
CO1	3800	FO1	6		CO1	4000	FO1	8
NPV					NPV
I	15				I	15
NPV	2,002.59				NPV	1,949.29

Option A

PyCyNIyPVPMTFV

11615-2002.59$529.160

EUAC = PMT = $529.16

Option B

11815-1949.29$434.400

EUAC = PMT = $434.40

Option A is better at 15%.