Quiz 3 solution sketches - PowerPoint Presentation

Slide1

Quiz 3 solution sketches

1:00 Lecture, Version A

Note for multiple-choice questions: Choose the closest answerSlide2

Finite PV

Someone tells you that there is a stock that will have an annual growth rate of dividend payments of 55%, and the annual discount rate for the stock is 40%. Which of the following statements is correct? (Assume that dividends are paid annually starting one year from today.)Slide3

Finite PV

A: The stock is finitely valued if we assume that dividends will be paid forever.

No (g>r means infinite PV of perpetuity)

B:

The stock is finitely valued if we assume that dividends will be paid

only for 100 years.

Yes (each PV is finite)Slide4

Finite PV

C

:

No stock can ever have dividend growth of 55% from one year to the next.

No, high growth rate is possible in any year

D

:

The PV of the stock is $0.

No, PV is positive since the dividend>0.

E

:

Both (A) and (B)

No, because (A) is false.Slide5

Sample Standard Deviation

A sample of 3 stocks has rates of return of 8%, 5%, and 2%. What is the standard deviation of this sample?

Avg

= (8 + 5 + 2)/3 = 5%

Variance

= 1/2*[(.08-.05)

2

+ (.05-.05)

2

+ (.02-.05)

2

]

= 1/2*[.0018] = .0009

S.D. = (.0009)

1/2

= .03

S.D. = 3%Slide6

Expected NPV

Mariah plans to open a new car dealership. She will buy a plot of land today for $900,000. She will have to spend $800,000 for cars today. Starting one year from today, she will have positive cash flows (undiscounted) of $200,000 every year. The last of these positive cash flows will be 10 years from today.Slide7

Expected NPV

There is a clause in the contract that 10 years from today, the land must be sold to a university. If economic times are good, the plot will sell for $2 million. If not, the plot must be sold for $900,000. If the effective annual discount rate is 5% and you believe the probability of good economic times is 50%, what is the NPV of this investment?Slide8

Expected NPV

(in $millions)

NPV = -0.9 – 0.8 + .2/.05 (1 – 1/1.05

10

) + 0.5 *2*(1/1.05

10

) + 0.5*0.9(1/1.05

10

)

NPV = 0.7345

NPV = $734,500Slide9

Semiannual Bond Coupons

A bond pays coupons of $60 annually, starting six months from today, until the bond matures (with the last coupon on the maturity date). The bond will mature 3½ years from today and pay a face value of $500. What is the PV of this bond if the appropriate effective annual interest rate for this bond is 8%?Slide10

Semiannual Bond Coupons

PV = 60/(1.08)

1/2

+ 60/(

1.08)

3/2

+

60/(

1.08)

5/2

+

560

/(

1.08)

7/2

PV = $588.46Slide11

Zero-Coupon Bond Value

A zero-coupon bond will mature 5 years from today. The promised payment at maturity is $10,000. The current market rate (as an effective annual interest rate) is 12%. What is the current value of owning this bond?

X * (1.12)

5

= 10,000

X = 10,000/(1.12)

5

X

= $5674.27Slide12

Change in Bond Value

You currently own a zero-coupon bond with maturity date in 18 months. The bond will pay $3,000 on the maturity date. The effective annual rate of return for this bond at the beginning of today is 9%. At the end of the day the rate drops to 8%. How much does the value of the bond change today?Slide13

Change in Bond Value

PV @ 9% = 3000/(1.09)

3/2

= $2,636.22

PV @

8%

= 3000/(

1.08)

3/2

= $

2,672.92

r decreases

 PV increases

Change in PV = 2672.92 – 2636.22

Change in PV = $36.70Slide14

Payback Period Method

Use the undiscounted payback period method, with the cutoff date 10 years, 4 months from now. (In other words, the payback period is 10 years, 4 months.) The effective annual discount rate is 37.934%. Which of the following offers should be picked if someone uses this method?Slide15

Payback Period Method

A:

A one-time payment of

$5,000

today

B

: $600 every year forever, starting 1 year from now

C: $1,100 every 2 years, starting today

D

: $8,000 every 10 years, starting 8 years from now

E: $20,000 every 20 years, starting 11 years from nowSlide16

Payback Period Method

Undiscounted future value at 10y 4m:

A: $5,000

B: $600 * 10 = $6,000

C: $1,100 * 6 = $6,600

D: $8,000

E: $0 (

first payment not until year

20)

Using the undiscounted payback period method, one should choose option DSlide17

Price-to-Earnings Ratio

Stocks A and B have the same annual discount rate, and would each pay the same dividend if they acted as cash cows. Stock A has no growth opportunities with positive NPV. Stock B has many growth

opportunities with positive NPV.

Which of the following statements is true if both companies maximize the value of their stock?Slide18

Price-to-Earnings Ratio

A: Stock A will have a lower price-to-earnings ratio than Stock B

B:

Stock A will have a

higher

price-to-earnings ratio than Stock B

C: Both stocks will have the same price-to-earnings ratio

D:

Stock

A will have a

higher

price-to-earnings ratio than Stock

B if the growth opportunities are small enough

E: None of the aboveSlide19

Price-to-Earnings Ratio

Price per share / Earnings per share

= 1/R + NPVGO/EPS

1/R is positive and the same for both

NPVGO is positive for B and zero for A

A’s P-E ratio < B’s P-E ratio, so the correct response is ASlide20

Growing Dividends

Goliath Galloping Ghost, Inc. will pay its first dividend two years from today, and will pay annually thereafter forever. The first dividend payment (in 2 years) is $5 per share. Each of the next two dividend payments will be 30% higher than the previous payment. After that, dividend payments will grow at 6% per year forever.Slide21

Growing Dividends

What is the PV of this stock if the effective annual interest rate is 13%?

Year 2: PV = 5/1.13

2

= $3.92

Year

3:

PV =

5*1.3/1.13

3

=

$4.50

Year

4:

PV =

5*1.3

2

/1.13

4

= 8.45/1.13

4

= $5.18

Years 5+: FV in year 4

= 8.45*1.06/(.13 – .06) = $127.96

Years 5+: PV = 127.96/1.13

4

= $78.48

Sum of PVs = $92.08