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Quiz 2 solution sketches Quiz 2 solution sketches

Quiz 2 solution sketches - PowerPoint Presentation

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Quiz 2 solution sketches - PPT Presentation

1100 Lecture Version A Note for multiplechoice questions Choose the closest answer Internal Rate of Return Norah invests 1000 today and will receive 50 per year forever starting in 1 hour What is the internal rate of return on this investment ID: 364013

000 annual today rate annual 000 rate today year years 200 npv payments discount 262 460 return receive internal

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Slide1

Quiz 2 solution sketches

11:00 Lecture, Version A

Note for multiple-choice questions: Choose the closest answerSlide2

Internal Rate of Return

Norah invests $1,000 today and will receive $50 per year forever, starting in 1 hour. What is the internal rate of return on this investment?

-1000 + 50 + 50/IRR = 0

50/IRR = 950

IRR = 5.26%Slide3

Net Present Value

Jacqueline has been asked to determine the net present value of a business. The business has costs of $50,000 per year forever, starting six months from now. The business receives $40,000 in profits one year from today, and increases by 8% each year forever. What is the NPV of the business if the effective annual discount rate is 12%?Slide4

Net Present Value

PV

benefits

= 40000/(.12-.08) = $1,000,000

PV

costs

= 50000/.12*(1.12)

1/2

= $442,959

NPV = $559,041Slide5

Semi-annual Perpetuity

Valerie will receive $20,000 per year forever. However, the first payment will be made two years from today, and payments will be made every 6 months. (In other words, she will receive $10,000 every 6 months, starting 2 years from today.) If her effective annual discount rate is 10%, what is the PV of this stream of payments?Slide6

Semi-annual Perpetuity

6-month rate: (1.1)

1/2

– 1 = 4.880%

PV = 10,000/.0488 * 1/(1.1)

3/2

PV = $177,588Slide7

Less-Frequent-than-Annual Perpetuities

Harrison will receive $50,000 every four years forever, starting six years from now. The effective annual interest rate is 6%. Find the total present value of all payments.

4-year rate: (1.06)

4

– 1 = 26.2477%

FV

2

= 50,000/.262477 = $190,493

PV = 190,493/(1.06)

2

= $169,538Slide8

Equal Loan Payments

Jill Birdwell will borrow $50,000 on

July 1, 2014. She will make 10 equal yearly payment, on January 1 of years 2015-2024, to completely pay back the loan. How much will each payment be if the effect annual interest rate is 8%?Slide9

Equal Loan Payments

If payments were made on

July

1 of each year:

50,000 = C/.08 * [1 – 1/(1.08)

10

]

50,000 = 6.71008 * C

C = $7,451.47

Payments are actually on

January

1:

C’ = C/(1.08)

1/2

C’= $7,170.18Slide10

Equivalent Annual Cost

The

Lockyear

Machine can be purchased today for $500. It will incur maintenance costs of $200 two years from today and $500 five years from today. The machine lasts for 10 years. If the effective annual discount rate is 12%, what is the equivalent annual costs of the machine?Slide11

Equivalent Annual Cost

PV

costs

= 500 + 200/(1.12)

2

+ 500/(1.12)

5

= $943.15

EAC:

943.15 = C/.12 * [1 – 1/(1.12)

10

]

943.15 = 5.6502 * C

C = $166.92Slide12

Profitability Index

If you invest $5,000 today in a new invention, you will receive a positive cash flow of $800 in 8 months, followed by a positive cash flow of $800 every 12 months thereafter. What is the profitability index of this investment if the effective annual discount rate is 9%?Slide13

Profitability Index

PV

benefits

= 800/.09 * (1.09)

1/3

PV

benefits

= $9147.93

P.I. =

PV

benefits

/ Today’s cost

P.I. = 9147.93 / 5000 = 1.82959Slide14

Growing Perpetuity

Petey

will receive $500 today. He will receive 5% more each subsequent year. If his effective annual discount rate is 15%, what is the present value of this stream of payments?

PV = 500 + 525/(.15-.05) = $5,750Slide15

Long-Answer:

Internal Rates of Return

Rachel will be opening a gold mine this year. All of the gold will be extracted in one year, and she must close it in two years to meet environmental laws. This leads to the following cash flows: She knows that she must spend $200 million today, she will earn $460 million one year from today, and she must spend $262 million two years from today.Slide16

Long-Answer:

Internal Rates of Return

(a) Find all internal rates of return.

All numbers in $millions.

Let X = 1+IRR.

0 = -200 + 460/X – 262/X

2

0 = -200X

2

+ 460X – 262

X

X

X = 1.0381965, 1.2618035

IRR = 3.81965%, 26.18035%

 Slide17

Long-Answer:

Internal Rates of Return

(

b

) For what annual discount rates will this project have positive net present value? You must show examples to justify your answer and get full credit.

Pick a discount rate in each range:

r = 0%:

NPV = -200 + 460 – 262 = -2 < 0 NO

r = 10%:

NPV = -200 + 460/1.1 – 262/1.1

2

= 1.65

>

0 YES

r = 100%: NPV = -200 + 460/2 – 262/2

2

= -35.5 < 0 NOSlide18

Long-Answer:

Internal Rates of Return

(

b

) Pick a discount rate in each range:

r = 0%:

NPV = -200 + 460 – 262 = -2<0 NO

r = 10%:

NPV = -200 + 460/1.1 – 262/1.1

2

= 1.65>0 YES

r = 100%:

NPV = -200 + 460/2 – 262/2

2

= -35.5<0 NO

Positive NPV for r: 0.0381965<r<0.2618035