# Present Value of the annuity

Fin 325, 9/10/2020                                                   QUIZ 1—in class version

30 pts. total

You will get this quiz paper back.  Please insert your note page(s) behind this page when done.  You MUST enter all your responses in writing (below) AND electronically in your iClicker.  (Remember to scroll forward to the next question, after entering each response.)

True/False (2 points for each question, 6 questions, 12 points total)

Indicate whether the sentence or statement is true (write “T” below) or false (“F”).  Choose “A” on your iClicker for True responses and “B” for False responses.

Question Block 1 Cash flow (1 of the 5 following questions, drawn at random)

1. The following event, from the corporation’s standpoint, will represent an increase in cash flow:

increase in dividends paid

1. The following event, from the corporation’s standpoint, will represent an increase in cash flow:

decrease in inventory

1. The following event, from the corporation’s standpoint, will represent an increase in cash flow:

decrease in A/P (accounts payable)

1. The following event, from the corporation’s standpoint, will represent an increase in cash flow:

increase in A/R (accounts receivable)

1. The following event, from the corporation’s standpoint, will represent an increase in cash flow:

increase in accrued wages

Question Block 2 Duration  (1 of the 2 following questions, drawn at random)

1. Bonds with higher coupon rates, all else equal, have longer duration than bonds with lower coupon rates.

1. Bonds with higher coupon rates, all else equal, have shorter duration than bonds with lower coupon rates.

1. Consider the following spreadsheet from Holden:

The following Excel formula will properly calculate the Present Value of the annuity displayed in this spreadsheet:  =(B4/B5)*(1-1/(1+B5)^B6)

1. The formula for the present value of a perpetuity (PV= C_1 / (r – g)) requires that g < r. The economic reason that g must be less than r is that a perpetuity with g >= r would have infinite value and that makes no economic sense.

1. Consider the below Beacon results, from a different class than yours.

It is very likely that Team Central had a much lower gross profit percentage than all of the other teams and that was the main reason it had such a large loss.

1. Consider homeowners who have financed their homes with long-term fixed rate mortgages.

If actual inflation is less than expected inflation, then–considering only their mortgages–homeowners will be better off due to their paying of a lower real interest rate.

Multiple Choice (3 points for each question, 6 questions, 18 points total)

Identify the letter of the choice that best completes the statement or answers the question.  For numerical problems, choose the response closest to the number you calculate.

Question Block–Delayed Perpetuity  (1 of the 2 following questions, drawn at random)

1. What is the value of a \$400 delayed perpetuity.  The payments are annual.  The interest rate is 6.0%.  The first payment occurs three years from now, i.e. at t = 3.

 a. 5,500 d. 5,800 b. 5,600 e. 5,900 c. 5,700

1. What is the value of a \$400 delayed perpetuity.  The payments are annual.  The interest rate is 6.0%.  The first payment occurs five years from now, i.e. at t = 5.

 a. 5,200 d. 5,500 b. 5,300 e. 5,600 c. 5,400

1. Which of the following organization forms for a business does NOT avoid double taxation?

 a. “S” corporation d. Limited partnership b. Limited liability company e. All of these organizational forms avoid double taxation. c. “C” corporation

1. Which of the following statements is FALSE?

 a. If the bond trades at a discount, an investor who buys the bond will expect to earn a return both from receiving the coupons and from receiving a face value that exceeds the price paid for the bond. d. At any point in time, changes in market interest rates affect a bond’s yield to maturity and its price. b. A coupon bond trades at a discount when its yield is less than its coupon rate. e. All of the other responses are TRUE. c. Most coupon bond issuers choose a coupon rate so that the bonds will initially trade at, or very near to, par.

1. [Difficult] Your business pays \$3,000 per month rent.  Your rent is due at the beginning of the month and you have a 12-month lease.

A global pandemic hits and your landlord gives you a two-month grace period on each of the remaining 12 payments.  The first payment, otherwise due today, is now due 2 months from now.  Each of the 12 lease payments can now be paid 2 months later.

Using a 12% APR (i.e. 1% per month) what is the change in present value of the cost of the lease due to the more favorable terms.  (Hint: the present value of the lease will decrease, so the change will be a negative number.)

 a. -\$400 d. -\$700 b. -\$500 e. -\$800 c. -\$600

1. Your daughter is currently eight years old. You anticipate that she will be going to college in 10 years. You would like to have \$100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account each year (i.e.ten payments, from t=1 to t=10) to ensure that you will have \$100,000 in 10 years?

 a. \$8,000 d. \$11,000 b. \$9,000 e. \$12,000 c. \$10,000

1. You need to find the value of a stock that will pay no dividends for the next five years.  However, exactly six years from now you expect the firm to pay a \$3.00/share dividend.  You also expect this dividend to grow by 3.0% per year thereafter.  You determine that a 9.0% discount rate is appropriate for this stock.  What is the value per share?
 a. \$27.50 d. \$25.00 b. \$30.00 e. \$35.00 c. \$32.50

Finance 325, Fa 20, Quiz 1

TRUE/FALSE

1. ANS:   F                      PTS:    1

1. ANS:   T                      PTS:    1

1. ANS:   F                      PTS:    1

1. ANS:   F                      PTS:    1

1. ANS:   T                      PTS:    1

1. ANS:   T                      PTS:    1

1. ANS:   F

A higher coupon rate returns a greater percentage of the bond’s present value earlier than bonds with lower coupon rates.

PTS:    1

1. ANS:   T

A higher coupon rate returns a greater percentage of the bond’s present value earlier than bonds with lower coupon rates.

PTS:    1

1. ANS:   T

PV = (PMT/r)*(1-1/(1+r)^N)

PMT is in B4

r is in B5

N is in B6

Also see Holden Ch. 2 spreadsheet.

PTS:    1

1. ANS:   T

If g =  r, then all the terms of the perpetuity have the same present value and then you are adding up the present values of an infinite number of such terms and that would give you an infinite present value.

If g>r, then you have the same situation only it’s worse as the present values of each of the terms are getting larger.  Also makes no economic sense.

If g<r, then the present value of each successive term is getting smaller.  This enables the infinite sum of these decreasingly-small present values to add up to a single number.  (In math terms that is called “convergence.”)

PTS:    1

1. ANS:   T

Team Central had no inventory remaining, i.e. they sold out.  They would have very likely sold out had their price been \$20/unit higher at \$90, to take a simple example.

With a \$20 higher price, they would have generated (\$20/unit)(333,333 units) \$6.67M more gross profit.

PTS:    1

1. ANS:   F

Homeowners will be worse off with lower inflation.

Keep in mind that in other areas of their life, homeowners may be hurt by inflation.  For example, if their wages do not increase as quickly as inflation then their real income will fall.  So the total net impact of changes in inflation should consider these effects.

PTS:    1

MULTIPLE CHOICE

1. ANS:   E

PV_2010 = (1193248.20/0.08)*(1-1/1.08^25) = \$12.737M

PV_2000 = \$12.737M/1.08^10 = \$5.9M

From ESPN: “The Mets famously bought out the final year of Bobby Bonilla’s contract in January 2000 and deferred the \$5.9 million deal into 25 payments of \$1,193,248.20 that began in 2011 and end in 2035. By deferring, Bonilla turned the \$5.9 million into \$29.8 million after negotiating an 8 percent interest rate on the deferral.”

Of course, there is some risk to Bonilla that the Mets will default before 2035.  But so far so good.

PTS:    1

1. ANS:   E

PV2 = 400 / 0.06 = 6667

PV0 = 6667 / (1.06)^2 = 5933

PTS:    1

1. ANS:   B

PV2 = 400 / 0.06 = 6667

PV0 = 6667 / (1.06)^4 = 5281

PTS:    1

1. ANS:   C                     PTS:    1

1. ANS:   B

MFL 3A, #5

PTS:    1

1. ANS:   D

Regular lease terms:

PV = \$3K plus an 11-month annuity of \$3k/month.

PV = 3 + (3/0.01)(1-1/1.01^11) = 34.102K

Alternatively, find the PV of an annuity due:

PV = 1.01*((3/0.01)(1-1/1.01^12)) = \$34.102K

Delayed lease terms:

Simply discount the PV of the regular lease terms by 2 months

PV = 34.102K/1.01^2 = 33.430

Change in PV = \$33,430 – \$34,102 = -\$671

PTS:    1

1. ANS:   B

FV = 100K

PV = 100K/1.03^10 = 74.409

You will make 10 annuity payments having a PV of 74.409K.  Need to solve for the payment:

74.409K = (PMT/0.03)(1 – 1/1.03^10)

PMT = 8.723K = \$8,723

PTS:    1

1. ANS:   C

This is a delayed, growing perpetuity.  At t=5, the value is \$3.00/(0.09 – 0.03) = \$50.00.  Discounting that by five years gives

\$50.00 / 1.09^5 = \$32.50.

PTS

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