ACC 100 Lecture Notes - Lecture 8: Opportunity Cost, Net Present Value

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5 Mar 2021

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Net present value: difference between present value of its benefits and present value of its costs. Npv = pv (benefits_ - pv (costs) Npv rule: when choosing among investment alternatives, take the alternative with the highest npv. Choosing this alternative is equivalent to receiving its npv in cash today. Accepting this will be equivalent to receiving their npv in cash today. Accepting this will reduce the firm"s value. Rejecting negative npvs won"t have any cost/loss to the firm. If npv = 0, you won"t gain or loose anything by accepting/rejecting. Firm"s value wont reduce (good), but nothing will be added to the firm"s value (not so good) The discount rate that sets the npv of the cash flows to =0. States that you should accept a project/investment only if its cash flows pay back its initial investment, within a pre-specified period.

Related Questions

Least-Cost Investment Decision

You are considering the purchase of a new vehicle. There are twooptions for the auto acquisition: a traditional gas-powered auto ora hybrid auto. Based on the information provided below and usingnet present value (NPV), you will be evaluating the two options andmaking a recommendation. Note: this scenario is a least costdecision. Since the decision to buy a car will only involve costs,you will be choosing the option with the highest NPV (which in thiscase, will be the project with the LEAST negative NPV). The assumedWACC is 10%.

Traditional Gas-Powered Auto:

Project Life: The autos are going to bekept for 7 years before being sold.

Cost ofAuto: $18,000

Annual Maintenance Cost: Each year,maintenance costs will be a fixed $300.

Gas Cost:The cost of gas is estimated to be an average of $3.30 per gallonover the next 7 years. The auto gets an average of 30 miles to thegallon. The auto is to be driven 16,000 miles per year.

SalvageValue: The car has an estimated salvage value of$4,000 at the end of 7 years.

Hybrid Auto:

Project Life: The autos are going to bekept for 7 years before being sold.

Cost ofAuto: $24,000

Annual Maintenance Cost: Each year,maintenance costs will be a fixed $450 (hybrid maintenance costsare higher due to more complex technology).

Gas Cost:The cost of gas is estimated to be an average of $3.30 per gallonover the next 7 years. The auto gets an average of 55 miles to thegallon. The auto is to be driven 16,000 miles per year.

SalvageValue: The car has an estimated salvage value of$7,000 at the end of 7 years.

Tax Credit:The US government encourages the purchase of more fuel-efficientautos, and has offered a $1,000 tax credit in the year of purchaseof a qualifying vehicle. Note: The tax credit represents a cashinflow, as it represents cash saved on taxes. Assume the tax creditis taken at the END of the first year of ownership.

Required:

Calculate the NPV for both auto purchases.

Make a recommendation for which car you would purchase.

Assume gas prices rise to an average of $4.50 per gallon.Recalculate the NPVs and make a recommendation.


Traditional Gas-Powered Auto
		$ Amount	PV Factor	PV of Cash Flow*
	Cost of Auto
	Maintenance per Year
	Cost of Gas per Year
	Salvage Value

	Net Present Value			0




	* Remember to make cash outflows negative and inflowspositive



Hybrid Auto
		$ Amount	PV Factor	PV of Cash Flow*
	Cost of Auto
	Tax Credit
	Maintenance per Year
	Cost of Gas per Year
	Salvage Value

	Net Present Value			0

3. Gas at 4.50


Traditional Gas-Powered Auto
		$ Amount	PV Factor	PV of Cash Flow*
	Cost of Auto
	Maintenance per Year
	Cost of Gas per Year
	Salvage Value

	Net Present Value			0




	* Remember to make cash outflows negative and inflowspositive



Hybrid Auto
		$ Amount	PV Factor	PV of Cash Flow*
	Cost of Auto
	Tax Credit
	Maintenance per Year
	Cost of Gas per Year
	Salvage Value

	Net Present Value			0

salmonhyena170

Real Options

The assignment is to evaluate both parts, the traditional NPVcalculation as well as the Real Options approach.

Scenario: A company must decide whether to invest $100 millionin developing and implementing a new enterprise system in the faceof considerable technological and market (demand for product andmarket share) uncertainty. The firm's cost of capital is 10%.

Part 1.â¨

The probability of a successful project (or pilot) is now .7 andthe probability of an unsuccessful project is .3.

Good Result: The Free Cash flow perpetuity (Annual Benefits) inthe âgoodâ case is $15 million per year

Bad Result: The system proves to be more difficult to implementand improvements in management of the supply chain are less. Inaddition, the growth in market demand for the product is lower. TheFree Cash flow perpetuity (Annual Benefits) in the "bad" case isnow $1.5 million per year, not $2 million.

Given: Year 0 (now) cash flows: $-100 million for ERP purchaseand implementation.

The cost of capital is .1. Use this to calculate the PV of theâgoodâ perpetuity and the PV of the âbadâ perpetuity. Thencalculate the âgoodâ NPV and the âbadâ NPV. Finally calculate theExpected NPV and decide if you will invest.

Part 2.â¨

The real options alternative allows for flexibility and thedelay of the investment for 1 year. In this case, if we do a pilotproject we will be better able to evaluate ERP implementationcomplexities, achievable supply chain benefits, and the marketshare our products will achieve. However, the cost of the projectwill rise to $110 Million ($10 Million this year and $100 Millionnext year) with the one-year delay and additionally managementdecides to purchase and implement the financial module in year 1 ata cost of $10 Million (real option).

The results are slightly different:

Year 0 (now) cash flows: $10 million for the pilot project.

After year 1, if the conditions indicate a good result, the firmwill invest the $100 million for the ERP with expected benefits(cash flows) of $15 million annually (forever) beginning in year 2.Benefits in year one from the financial module are $1 million.

If a bad result is indicated, the firm makes no furtherinvestments beyond the financial module, which yield annualbenefits of $.5 million in year 1 and each year thereafter(forever).

Here the firm has flexibility and has exercised its option tomake no further investments based on better information andknowledge of expected future benefits.

Evaluate the expected NPV of this project using the describedreal option.

Consider that we have the opportunity to do a pilot program byinstalling the financial model only at a cost of $10 MM. A yearfrom now, we can decide whether to invest in the full plant or not.Analyze this case as follows: Find the good case NPV and the badcase NPV. Obviously, we won't exercise the option if we discoverthat we're in the Bad Case. So, we limit our loss to $10 MM lessthe present value of the bad case starting in Year 1.

Part 3.â¨

What is the expected NPV in each case? Compare the

expected NPV using the traditional NPV approach with theexpected NPV using real options. What do you recommend? Why? Whatdo you conclude in each case?

If you don't know the probability of success for the pilot, isthere a value that is critical to your recommendation? Is there aprobability of success above or below which you will recommendundertaking the pilot and below or above which you will recommend ago/ no go decision on the underlying project without undertaking apilot test? â¨â¨

Label your work as follows:

Part 1: NPV Analysisâ¨

1. PV of "Good" perpetuity:â¨

2. PV of "Bad" perpetuityâ¨

3. "Good" NPV:â¨

4. "Bad" NPV:â¨

5. Expected NPV: â¨

6. Invest or don't invest:

Part 2: Real Options Approachâ¨

1. Good case NPV by installing the financial module.â¨

2. Bad case NPV by installing the financial module.â¨

3. Expected NPV by installing the financial module.â¨

4. Should we go ahead with the financial module pilot project orthe full project? â¨

5. Should we undertake both the full project and the pilot"today"?

Part 3: Critical Probabilitiesâ¨

1. Probability to forget the Pilot and complete the Project. Wecan find that probability by equating the present values of thefull project and thepilot. â¨

2. Probability of going ahead with the Pilot. We can calculatethe critical probability for going ahead with the pilot by settingthe PV expression = 0 and solving for X.â¨

3. If there is no real option, breakeven probability for go/nogo.â¨

QUESTION 1

Which of the following statements is correct regarding thepayback method as a capital budgeting technique?

		The payback method considers the time value of money.
		An advantage of the payback method is that it indicates if aninvestment will be profitable.
		The payback method provides the years needed to recoup theinvestment in a project.
		Payback is calculated by dividing the annual cash inflows by thenet investment.

0.625 points

QUESTION 2

Taxes are not an important consideration indeveloping cash flow assessments.

True

False

0.625 points

QUESTION 3

USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT (2)QUESTIONS:

Parkways Inc. is considering the purchase of a new machine. Themachine will cost $60,000 to purchase and will generate $15,000 ofcash revenues per year for the next 8 years. The machine will cost$1,000 per year to operate & maintain. At the end of it'suseful life, it has an estimated salvage value of $5,000. Parkwaysrequires a minimum rate of return of 14% for this class of asset.Determine the Net Present Value of this investment proposal.

PV of $1 (14%, 8n) is .351; PVOA (14%, 8n) is 4.639

		$6,701
		$57,000
		$1,166
		$0

0.625 points

QUESTION 4

Sun Devil Corporation is adding a new product line that willrequire an investment of $138,000. The product line is estimated togenerate net cash flows of $25,000 the first year, $23,000 thesecond year, and $18,000 each year thereafter for ten more years.What is the payback period?

		7.26
		5.52
		7.00
		7.67

0.625 points

QUESTION 5

Sparky Company invested in an asset with a useful life of 5years. The companys required rate of return is 10% for this classof asset. The net cash flows are estimated to be $7,610 per yearfor the next 5 years and no salvage value is anticipated.

If the asset generates a positive net present value of $2,000,what was the amount of the original investment? (Roundyour answer to the nearest whole dollar. Do not use $signs or commas in recording youranswer. EXAMPLE: If you answer is $22,516,enter your answer as 22516).

Present Value of $1
Periods	10%	12%	14%
5	.621	.567	.519
8	.467	.404	.351
10	.386	.322	.270
Present Value of Ordinary Annuity
Periods	10%	12%	14%
5	3.791	3.605	3.433
8	5.335	4.968	4.639
10	6.145	5.650	5.216

0.625 points

QUESTION 6

Suppose Whole Foods is considering investing inwarehouse-management software that costs $500,000, has $60,000residual value and should lead to cash cost savings of $130,000 peryear for its five-year life. Determine the NPV of the investment ifmanagement uses a 12% discount rate. (Round to the nearest wholenumber for your final answer. When recording your answer, do notuse $ dollar signs or commas. EXAMPLE: If you answer is $12,251,enter 12251)

Present Value of $1
Periods	10%	12%	14%
5	.621	.567	.519
8	.467	.404	.351
10	.386	.322	.270
Present Value of Ordinary Annuity
Periods	10%	12%	14%
5	3.791	3.605	3.433
8	5.335	4.968	4.639
10	6.145	5.650	5.216

0.625 points

QUESTION 7

ABC, Corporation is looking to purchase a new piece of equipmentfor $121,505. The equipment has a useful life of 8 years and noexpected salvage value.

The minimum desired rate of return is 10%. ABC is uncertain asto the annual net cash flows the equipment will generate.

What is the minimum annual net cashflow ABC must achieve in order to justify the purchase of this newequipment?

(Round your answer to the nearest whole dollar. Do not use $dollar signs or commas when recording your answer.)

Present Value of $1
Periods	10%	12%	14%
5	.621	.567	.519
8	.467	.404	.351
10	.386	.322	.270
Present Value of Ordinary Annuity
Periods	10%	12%	14%
5	3.791	3.605	3.433
8	5.335	4.968	4.639
10	6.145	5.650	5.216

0.625 points

QUESTION 8

Sparky Company is considering the replacement of an old machinewith the purchase of a new piece of production equipment that willreduce labor and maintenance costs by $45,000 peryear. If Sparky purchases the new machine, the companywill sell the old equipment for an estimated $20,000 salvage value.Data related to the new machine follows:

InitialInvestment $300,000

UsefulLife 10years

Salvagevalue (newmachine) $30,000

HurdleRate 12%

Assume all cash flows occur at the end of the year and ignoreincome taxes. Calculate the net present value of theinvestment in the new machine. (Round your answer to the nearestwhole dollar. If you have a negative NPV, record youranswer using () parenthesis. EXAMPLE: If yourNPV is ($2,000), enter your answer as (2000).

Present Value of $1
Periods	10%	12%	14%
5	.621	.567	.519
8	.467	.404	.351
10	.386	.322	.270
Present Value of Ordinary Annuity
Periods	10%	12%	14%
5	3.791	3.605	3.433
8	5.335	4.968	4.639
10	6.145	5.650	5.216

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ACC 100 Lecture Notes - Lecture 8: Opportunity Cost, Net Present Value

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