Solving problems

[DREK]

Hello,

I've been reading this forum for a long while since I'm interested in financial markets. The times I have spent here have been worth, for sure. I am attending one financial topic in my course, the professor asked us to solve some quizzes which will play a part in the final note. There were 30 questions but I am facing problems whith these ones.

1-Green Corporation has a dividend policy that calls for constant annual dividends of $3 per share. What is one share of this stock worth today if the market requires a 10% return on this stock for the next 3 years, an 11% return on this stock for the following 3 years, and a 12% return thereafter?

a. $39.79

b. $25.10

c. $22.20

d. $26.70

e. $27.46

2-As winner of a breakfast cereal competition you can choose one of the following prizes. If the interest rate is 12%, which is the most valuable prize?

a. $19,000 a year for 10 years

b. $180,000 at the end of five years

c. $100,000 now

d. $6,500 next year and increasing thereafter by 5 per cent a year forever
e. $11,400 a year forever

3-The interest-rate risk of a bond is:
I. The risk related to the possibility of bankruptcy of the bond's issuer.
II. The risk that arises from the uncertainty of the bond's return caused by changes in interest rates.
III. The unsystematic risk caused by factors unique in the bond.

a. I and II only

b. II only

c. I only

d. III only

e. I, II and III

4-A seven-year par value bond has an annual coupon rate of 9%, a duration of ___, and a modified duration of ___.
Seleccione uma resposta.

a. 5.49 years ; 3 years

b. 7 years ; 5.49 years

c. 7 years ; 5.03 years

d. 5.49 years ; 5.03 years

e. none of the above

5-Which of the following statements are true?
I. There is an inverse relationship between present values and interest rates.
II. The effective annual interest rate will be higher than the annualized rate for a loan that compounds interest monthly.
III. There is an inverse relationship between future values and the number of time periods.
IV. All else equal, the more frequently interest is compounded on a loan, the greater the total interest.


a. I, II and IV only

b. II, III, and IV only

c. I, II, III, and IV

d. III and IV only

e. I and II only

[KTP]

I stopped on question one because there is not enough information presented to determine the share value. How can you possibly know the value of the stock today if you have no information about the assets, net income, etc?

A stock could be worth $20, $200, or $2000 and still pay a $3 dividend and grow by 10%, 11% or 12% depending on it's assets and profits

[KTP]

Ok I think I just realized what they were asking in question one.

In 6 years the stock would have a value of $25/share since the market at that point will require that dividends be 12% of the value of a stock (3 / 0.12 = 25)

Since the market for the 3 years leading up to year 6 will only require that dividends be 11% of the share value this stock will be paying out more dividend than the market requires for these 3 years (since the dividend is fixed at $3 for eternity). So we have to value the share at more than $25 (note that at this point we have now ruled out answer c since it is less than $25). Also note that we can rull out answer a because the stock can't be worth more than $30 ever (since for today it pays out the bare minimum to meet market conditons at $3/0.10 = $30).

At this point I am still confused because there is no explanation of how the dividends will get re-invested. Will they purchase more shares of the same company at the present value at that time, then they also must compound? It really seems like either a very complicated problem or poorly worded.

[DREK]

I don't have also no clue about answer 1.

[toboramai]

There should be a formula in your finance book. It has been a few years since I was in school but it is similar to the formula on wikipedia. links below.

You have to break up the formula into parts. Not exact formula but the concept would be similar.

P (stock price) = time value of money of dividend for year 0 to 2 + time value of money of dividend for year 3 to 6 + time value of money of dividend in perpetuity.

Perpetuity - Wikipedia, the free encyclopedia
Stock valuation - Wikipedia, the free encyclopedia

You have to combine multiple formulas to get this question. Im guessing this is an intro finance class.

[Broken Arrow]

Yeah, was going to say it looks like somebody else needs help with their homework.

[cptacek]

2-As winner of a breakfast cereal competition you can choose one of the following prizes. If the interest rate is 12%, which is the most valuable prize?
e. $11,400 a year forever

FOREVER??? Really? Can you bequeath it to your decendents? For the next 5000 years? For the next 200 years? What does forever mean?

[disneysteve]

Originally Posted by cptacek

2-As winner of a breakfast cereal competition you can choose one of the following prizes. If the interest rate is 12%, which is the most valuable prize?
e. $11,400 a year forever

FOREVER??? Really? Can you bequeath it to your decendents? For the next 5000 years? For the next 200 years? What does forever mean?

My thought exactly. How do you calculate the value when you don't have a finite time period?

[simpletron]

here something to think about for 2:

getting one dollar in year 1 is equal to getting 1.12^99 or 74,573.45 dollars in year 100 because with interest the 1 dollar will become 74,573.45 in 99 years.

after an infinite number of years, they are all infinite, but one grew faster than the rest and that one is the answer. for example, which is more valuable: getting paid $1/year forever or getting paid $2/year forever?

[cptacek]

Ah. I didn't even see option d. For some reason I skipped immediately down to option e, and saw forever and thought "that's a pretty stupid question...that's not realistic!".

Of course, $6,500 next year and increasing thereafter by 5 per cent a year forever would be better for you if you lived another 45 years (about where I calculated that option d would be better than option e), but it would be better for your descendants in every case, if it really goes forever.

I still don't get the significance of 12% interest. Are they saying you put the money away and don't touch it ever? If so, what's the point?

[simpletron]

Originally Posted by cptacek

I still don't get the significance of 12% interest. Are they saying you put the money away and don't touch it ever? If so, what's the point?

it doesn't matter how much you spend because it doesn't affect the value of payment plan. So in effect yes, the calculations are just like you never spent any because it is easier to calculate.

which is more valuable if interest is 10%?
A) 100K this year or
B) 9K a year forever

the answer is A, because B will never catch to the interest payments of A. it doesn't matter how much you spend every year because A is always greater than B with any spending plan that follows the same pattern with the same amounts applied to each payment plan. spend 9K/year with B you're hitting at 0 constantly, with A you'll never drop below 100K for the end of the year.

[toboramai]

Originally Posted by cptacek

2-As winner of a breakfast cereal competition you can choose one of the following prizes. If the interest rate is 12%, which is the most valuable prize?
e. $11,400 a year forever

FOREVER??? Really? Can you bequeath it to your decendents? For the next 5000 years? For the next 200 years? What does forever mean?

Its called a perpetuity. Because the time value of money, at some point any amount will be worth $0 if the time horizon is large enough.

from wikipedia:
PV = {A \r}

Where PV = Present Value of the Perpetuity, A = the Amount of the periodic payment, and r = yield , discount rate or interest rate.

Concrete example of money being worth $0.

PV = ($100/10,000 years)
present value of $100 in 10,000 yrs is = .01 cents

taking #2 question it would be
PV = 11,400 / .12
PV = $95,000

[toboramai]

Originally Posted by simpletron

it doesn't matter how much you spend because it doesn't affect the value of payment plan. So in effect yes, the calculations are just like you never spent any because it is easier to calculate.

which is more valuable if interest is 10%?
A) 100K this year or
B) 9K a year forever

the answer is A, because B will never catch to the interest payments of A. it doesn't matter how much you spend every year because A is always greater than B with any spending plan that follows the same pattern with the same amounts applied to each payment plan. spend 9K/year with B you're hitting at 0 constantly, with A you'll never drop below 100K for the end of the year.

This is not exactly correct either. You have to discount the payments every year. All these formulas are in a basic finance book. Again, time value of money.

Formulas at wikipedia link.

Time value of money - Wikipedia, the free encyclopedia