Question 1

The interest rate is 9% and there is no inflation.A bond is available that can be redeemed either after one year or after two years.If it is redeemed after one year, the investor gets $109.If it is redeemed after two years, the investor gets $115.54.The investor gets no other payments than what she receives when she redeems the bond.In equilibrium, investors will be willing to pay more than $100 for this bond.

Accepted Answer

In equilibrium, the present value of the bond's future payments should equal the price paid. With a 9% interest rate, the present value of $109 in one year is $100, and the present value of $115.54 in two years is also $100. Therefore, investors would not be willing to pay more than $100 for the bond.

Question 2

If the interest rate is r and will remain r forever, then a bond that will pay 75 dollars a year forever, starting one year from now, is worth how much today?

Accepted Answer

The value of a perpetuity, which is a bond that pays a fixed amount forever, is calculated as the payment divided by the interest rate. Therefore, a bond that pays $75 a year forever, at an interest rate of r, is worth $75/r today.

Question 3

The amount people are willing to pay to drink a bottle of a certain vintage of wine when it is t years old is $2 + 3t.It costs $.50 a bottle per year to store this wine.The interest rate is 5%.If the annual cost of storing the wine rises to $1, what will be the effect on the price of this wine when it is consumed and on the length of time for which it is stored before it is consumed?

Accepted Answer

B

Question 4

A consumer who can borrow and lend at the same interest rate should prefer an endowment with a higher present value to an endowment with a lower present value, no matter how he plans to allocate consumption over the course of his life.

Accepted Answer

If the consumer can borrow and lend at the same interest rate, then the time value of money is equivalent for both borrowing and lending. Therefore, the consumer's preference is solely based on the present value of the endowment, regardless of how they allocate consumption over time.

Question 5

If the interest rate is 10%, then an asset that returns $1 a year forever is worth $1/1.1.

Accepted Answer

The correct formula to calculate the present value of a perpetuity (an asset that returns a fixed amount forever) is the annual payment divided by the interest rate. Therefore, an asset that returns $1 a year forever with an interest rate of 10% is worth $1/0.1, which equals $10, not $1/1.1.

Question 6

Suppose that the cost of cutting down a tree is zero and the tree grows on land that is useless for anything else, that the interest rate is constant, and that the price of lumber does not change.The optimal time to cut the tree is when the difference between its growth rate and the interest rate is maximized.

Accepted Answer

The optimal time to cut the tree is when its growth rate equals the interest rate, not when the difference between its growth rate and the interest rate is maximized. This is because the value of the tree must grow at the rate of interest to make holding onto the tree as valuable as selling it and investing the proceeds at the interest rate.

Question 7

You buy a painting for $1,280.Its market value will rise by $80 per year for the next 30 years.It is worth $80 a year to you to have it hanging on the wall.The interest rate is 10%.In how many years will you sell it?

Accepted Answer

The answer of You buy a painting for $1,280.Its market...

Question 8

The interest rate is 10% and there is no inflation.A bond is available that can be redeemed either after one year or after two years.If it is redeemed after one year, the investor gets $110.If it is redeemed after two years, the investor gets $117.70.The investor gets no other payments than what she receives when she redeems the bond.In equilibrium, investors will be willing to pay more than $100 for this bond.

Accepted Answer

Given the interest rate of 10% and no inflation, the present value of the bond's future payments should equal its face value for it to be a fair investment. For a $100 investment, receiving $110 after one year is exactly a 10% return, matching the interest rate. For the two-year option, a 10% annual interest rate compounded would result in a future value of $121 ($100 * 1.1 * 1.1), not $117.70. Therefore, in equilibrium, investors would not be willing to pay more than $100 for this bond, as its future payments do not exceed the returns of an alternative investment with a 10% interest rate.

Question 9

The interest rate is 10%.A certain piece of land can be used for a parking lot, in which case there are no construction costs and it will yield a net return of $5,000 per year forever starting one year from now.Or it can have a house built on it.Building a house would cost $50,000 now.If a house is built on the lot, it will yield a stream of net income equal to $12,000 per year starting one year from now.No other uses are contemplated.The theory of asset markets predicts that the lot will sell for

Accepted Answer

To determine the best use of the land, we need to compare the present value of future cash flows from each option.

Option 1: Use as a Parking Lot

The annual net return is $5,000 forever, starting next year. We can use the perpetuity formula to calculate its present value:

PV = Net Return / Interest Rate
PV = $5,000 / 0.10
PV = $50,000

Therefore, if the land is used as a parking lot, its present value is $50,000.

Option 2: Build a House

The house will cost $50,000 now and generate an annual net income of $12,000 starting next year. We can use the formula for a growing perpetuity to calculate its present value:

PV = Net Income / (Interest Rate - Growth Rate)
PV = $12,000 / (0.10 - 0)
PV = $120,000

However, we also need to subtract the construction cost of $50,000:

PV = $120,000 - $50,000
PV = $70,000

Therefore, if a house is built on the land, its present value is $70,000.

Comparing Options

Since $70,000 is greater than $50,000, it is better to build the house on the land. Therefore, the answer is choice C: $70,000 and a house will be built on it.

Question 10

Today is January 1.The interest rate is 8% and investors are convinced that it will stay at 8% for the next 10 years.A corporate bond comes on the market that for the next 7 years will pay $160 on December 31 to whoever owns the bond on that date.On January 1, 7 years from today, the issuer of the bond will redeem the bond by buying it back from the bondholder for $2,000.What should this bond sell for?

Accepted Answer

The answer of Today is January 1.The interest rate is...

Question 11

If everybody has the same information, then a well-functioning market for assets would, in equilibrium, leave no opportunities for arbitrage.

Accepted Answer

In a well-functioning market where everyone has the same information, all assets would be priced efficiently and there would be no price discrepancies to take advantage of through arbitrage. Therefore, there would be no opportunities for arbitrage in equilibrium.

Question 12

If the nominal interest rate is 80% and the rate of inflation is 50%, then the exact real rate of interest is

Accepted Answer

The exact real rate of interest can be calculated using the formula: (1 + nominal rate) / (1 + inflation rate) - 1. Plugging in the values: (1 + 0.80) / (1 + 0.50) - 1 = 0.20 or 20%.

Question 13

A certain wine costs $3 a bottle to produce.It improves in taste if stored properly for a period of time.When it is newly bottled, people are willing to pay only $2 a bottle to drink it.But the amount that people are willing to pay to drink a bottle of this wine will rise by $3 a year for the next 50 years.Storage costs, not including interest, are $.50 per year.If the interest rate is 5% and the wine is kept by rational investors, how old will it be when it is drunk and what will be its price at that time?

Accepted Answer

The optimal time to sell the wine is when the marginal increase in price due to aging equals the marginal cost of holding the wine for another year. The marginal cost includes both the storage cost and the opportunity cost of not selling the wine (interest). Initially, the wine increases in value by $3 per year, which must be compared to the annual cost of holding it. The formula to calculate the optimal time to sell (T) considering the interest rate (i), initial cost (C), annual increase in value (V), and storage cost (S) is derived from equating the marginal increase in value to the marginal cost of holding the wine for another year, including the opportunity cost. Solving this equation gives the optimal time to sell to maximize profit, which in this case is 16 years, with a selling price of $50.

Question 14

The interest rate will be 10% for one more year, but a year from now, it will fall to 5% and stay at 5% forever.What is the market value of an investment that is sure to pay $220 a year forever, starting two years from today?

Accepted Answer

The present value of the investment is the sum of the present values of the two cash flows: the $220 payment in two years and the perpetuity of $220 payments starting in three years. The present value of the first payment is $220/(1.1)^2 = $176.47. The present value of the perpetuity is $220/0.05 = $4,400. The total present value is $176.47 + $4,400 = $4,576.47.

Question 15

Art Dreck's paintings are terribly unpopular now.In fact nobody would pay a dime to have one of his paintings on the wall now.But experts believe that 10 years from now, there will be a craze for Dreck paintings.The craze will last for 2 years and then nobody will ever want to see a Dreck again.During this 2-year period, people will be willing to pay $1,100 a year to have an original Dreck on the wall.The interest rate is r.If the experts' belief is widely held among investors, today's market value of Dreck should be about

Accepted Answer

Using the formula for present value of an annuity, we can find the present value of the 2-year period where people are willing to pay $1,100 a year for an original Dreck painting:
PV = 1,100/(1+r) + 1,100/(1+r)^2
PV = 1,100/(1+r)(1+r) + 1,100/(1+r)(1+r)^2
PV = 1,100(1/(1+r) + 1/(1+r)^2)
PV = 1,100((1+r)/(1+r)^2 + 1/(1+r)^2)
PV = 1,100((1+r+1)/(1+r)^2)
PV = 1,100(1+r)/(1+r)^2
PV = 1,100/(1+r)

Then, the present value of the two-year period is divided by (1+r)² to represent the present value of Dreck's paintings 10 years from now:
PV = 1,100/(1+r)^3

Finally, the total present value is the sum of the present value of the two-year period and the present value of the paintings 10 years from now:
PV = 1,100/(1+r) + 1,100/(1+r)^3
PV = 1,100(1/(1+r) + 1/(1+r)^3)

This can be simplified as PV = 1,100/(1+r)(1+r²), which is equivalent to choice (D): 1,100/(1+(1+r)+(1+r²)).

Question 16

The interest rate will be 10% for one more year, but a year from now, it will fall to 5% and stay at 5% forever.What is the market value of an investment that is sure to pay $440 a year forever, starting two years from today?

Accepted Answer

The investment pays $440 starting in year 2. The present value of a perpetuity starting in year 2 with a 5% interest rate is $440/0.05 = $8,800. Discount this back one year at 10%: $8,800 / 1.10 = $8,000.

Question 17

Vincent Smudge's paintings are unappreciated now.Nobody is willing to pay anything to have them on the walls.In 5 years Smudge's work will gain enduring popularity.People will suddenly be willing to pay $1,000 a year to have an original Smudge on their walls and will continue to be willing to do so ever after.If investors realize that this is the case and if the interest rate is and always will be r, a painting by Smudge will currently be worth about

Accepted Answer

This problem requires the use of the formula for present value of a future cash flow, which is: PV = CF/(1+r)^n. In this case, the future cash flow is $1,000 per year, n is 5 years, and r is the interest rate. Using the formula, we can rewrite the expression as: PV = $1,000/(1+r)^5. Therefore, Smudge's painting will currently be worth approximately $(1,000/r)[1/(1+r)^5]. This matches choice A.

Question 18

In a perfect asset market, it is known with certainty that an asset will sell for $24 in one year.If the annual interest rate is 10%, then the asset will sell for $26.40 right now.

Accepted Answer

To calculate the present value of the asset, we use the formula:
Present Value = Future Value / (1 + interest rate)^time period

Here, the future value is $24, the interest rate is 10%, and the time period is 1 year.

So, Present Value = $24 / (1 + 0.10)^1 = $21.82

Therefore, the asset will sell for $21.82 right now, not $26.40.

Question 19

According to the theory of asset markets, if the interest rate is constant, then the competitive market price of a bottle of wine will rise at a constant rate per year until it is consumed, even if the amount that wine drinkers are willing to pay for it does not rise at a constant rate.

Accepted Answer

This is because the price of the wine must rise at the rate of interest to compensate the owner for not selling it earlier and investing the proceeds at the interest rate. This is a reflection of the opportunity cost of holding onto the wine instead of selling it and investing the money.

Question 20

If the interest rate is r and will remain r forever, then a bond that will pay 95 dollars a year forever, starting one year from now, is worth how much today?

Accepted Answer

The value of a perpetuity, which is a bond that pays a fixed amount forever, is calculated as the payment divided by the interest rate. Therefore, a bond that pays $95 a year forever, at an interest rate of r, is worth $95/r today.

Quiz 10: Asset Markets-Part A