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4-1. The following table presents cash flows for four investments (A, B, C, D) over a five-year period. Projects Cash Flow ($)
N [year]	A	B	C	D
0	-$2,000	-$4,000	-$3,500	-$2,600
1	0	2,000	-1,500	-1,500
2	-1,000	2,500	-500	2,100
3	0	3,700	4,200	2,400
4	6,700	2,300	4,400	1,700
5	1,000	500	2,000	0

1. What is the payback period of each project? Present your answer to the 0.1 year.

Answer: A= 3.5; B=1.8; C= 3.3; D= 2.8

2. What is the discounted payback period for an interest rate of 12% compounded annually for each project? Again, present your answer

Answer: A=3.6; B=2.1; C=3.8; D=3.5

What is the present worth of a project that requires an investment of $125,000 today and produces revenues of $35,000 per year for six years at an interest rate of 14%, compounded annually?

Answer: $11,103.36

To increase production, your company is trying to decide whether to purchase a new machine for $300,000. An additional $26,000 is needed for preparation and installation. The company believes that the increased production will lead to increased revenues of $87,000 per year for seven years, after which the machine is expected to have a salvage value of $68,000. You have been asked to determine if the purchase would be justified at an interest rate of 11% (compounded annually) based on NPW analysis. What is the NPW? Is the purchase justified?

Answer: PW=$116,713.80, Yes, justified

A company is trying to decide between two machines to purchase for its factory. Based solely on net present value of costs over a 5-year period, which machine should be purchased if = 12%? Report net present cost of each. 2

Machine 1: Initial cost of $60,000 with a salvage value of $20,000. It will cost $9,000 annually to operate.

Machine 2: Initial cost of $40,000 with a salvage value $10,000. It will cost $11,000 annually to operate.

Answer: NPWcost (1) = $81,094.45, NPWcost(2) = $73,978.27; Purchase Machine 2

What is the future worth of the following investments at the end of 15 years, assuming an interest rate of 10% compounded monthly? Rank the investments in terms of desirability based on Future Worth considerations

( a) Deposit $7,000 now

Answer: $31,177.44

( b) Deposit $90 at the end of each month for 10 years and leave the accumulated funds in the account for the additional 5 years

Answer: $30,332.99

( c) Deposit $65 at the end of each month for 15 years

Answer: $26,940.57

( d) Deposit $20,000 at the end of year 10

Answer: $32,906.18

Answer: Ranking best to worst: (d), (a), (b), (c)

The Construction Company is evaluating a new bulldozer that will cost $100,000 upfront and has an annual maintenance cost of $5,000. There is also an additional tune-up cost of $10,000 once every 4 years. Assuming that the bulldozer will be operated with these costs for an infinite evaluation horizon, answer the following assuming i = 12% (compounded annually).

( a) What is the equivalent annual cost of the tune-ups?

Answer: $2,092.34

( b) What is the capitalized worth of the annual maintenance costs?

Answer: $41,666.67 3

( c) What is the total capitalized worth (cost) of the bulldozer?

Answer: $159,102.84

The annual upkeep costs for a large storage facility is $90,000. Assuming the facility will incur upkeep costs indefinitely and i= 6%, compounded monthly, compute the capitalized worth of the upkeep costs.

Answer: $1,459,196

A city is considering two alternatives for linking one of its suburbs with the downtown area. What are the capitalized costs of the two options assume i = 5%? Based solely on each options capitalized cost, which option is preferred?

Option 1: Construct a new road. The upfront cost will be $5M, and there is an additional $1M every 5 years that covers maintenance.

Option 2: Construct a light-rail system. The upfront cost will be $8M, and there is an additional $5M every 20 years that will be used to replace old equipment.

Answer: CW(1) = $8.62M, CW(2) = $11.02M, Option 1 would be preferred

Machine 1: Initial cost of $60,000 with a salvage value of $20,000. It will cost $9,000 annually to operate.

Machine 2: Initial cost of $40,000 with a salvage value $10,000. It will cost $11,000 annually to operate.

Answer: NPWcost (1) = $81,094.45, NPWcost(2) = $73,978.27; Purchase Machine 2

. What is the future worth of the following investments at the end of 15 years, assuming an interest rate of 10% compounded monthly? Rank the investments in terms of desirability based on Future Worth considerations

( a) Deposit $7,000 now

Answer: $31,177.44

( b) Deposit $90 at the end of each month for 10 years and leave the accumulated funds in the account for the additional 5 years

Answer: $30,332.99

( c) Deposit $65 at the end of each month for 15 years

Answer: $26,940.57

( d) Deposit $20,000 at the end of year 10

Answer: $32,906.18

Answer: Ranking best to worst: (d), (a), (b), (c)

The Construction Company is evaluating a new bulldozer that will cost $100,000 upfront and has an annual maintenance cost of $5,000. There is also an additional tune-up cost of $10,000 once every 4 years. Assuming that the bulldozer will be operated with these costs for an infinite evaluation horizon, answer the following assuming i = 12% (compounded annually).

( a) What is the equivalent annual cost of the tune-ups?

Answer: $2,092.34

( b) What is the capitalized worth of the annual maintenance costs?

Answer: $41,666.67 3

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