Lab 7 Problems

A mix of TVM and bond problems:

  1. The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning system. The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance. What will be the outstanding balance after the third payment?

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a. / $60,000
b. / $20,865
c. / $45,788
d. / $50,866

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  1. What amount received at the end of 15 years is equivalent to $100 received at the end of each year for 15 years if the interest rate is 12%?
a. / $3,728
b. / $4,042
c. / $2,676
d. / 547
e. / 625
  1. A bank has agreed to lend you $10,000 at 11% for 5 years. You are required to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance. Determine the amount of these annual payments (to the nearest penny).
  1. You have borrowed $180,000 to buy a new home. You plan to make monthly payments over a 25-year period. The bank has offered you a 10% interest rate compounded monthly. Calculate the total amount of interest you will pay the bank over the life of the loan.
a. / $301,499
b. / $307,541
c. / $310,545
d. / $319,766
  1. You want to purchase a car for $40,000 when you graduate in two years. At that time you will take out a 5-year bank loan at 12% compounded monthly. Based on your estimated earnings, you think you’ll be able to afford loan payments of $750 per month. You plan to save up the difference between the cost of the car and the amount you’ll borrow by making quarterly deposits over the next two years in a bank account that pays 8% compounded quarterly. How large must those deposits be? (Round to the nearest dollar)
a. / $523
b. / $637
c. / $732
d. / $845
  1. Find the present value of a payment stream of $100 per year for the first fifteen years and $200 per year for the next five years, given a 12% discount rate.
a. / $813
b. / $1,402
c. / $953
d. / $887
e. / $712
  1. Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live to about 80, and wants to be able to withdraw $25,000 per year from the account on his 61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr. Moore.
a. / $212,850
b. / $23,449
c. / $2,164
d. / $8,514

Bond Problems

  1. J&J Manufacturing issued a bond with a $1,000 par value. The bond has a coupon rate of 7% and makes payments semiannually. If the bond has 30 years remaining and the annual market interest rate is 9.4%, what will the bond sell for today?

a. / $760.91
b. / $861.29
c. / $937.42
d. / $1,000.00
e. / $1,025.32
  1. Tom’s Underwear Emporium Inc. has a 15 year semiannual $1000 face value 8% coupon bond outstanding. The market currently requires a 7% return on bonds of this risk. What is TUE’s bond worth?
  1. I don’t know
  2. I don’t care
  3. Whatever
  4. All the above
  5. $1091.96
  1. Willamson Inc.’s bonds have a coupon rate of 12% and a par value of $1,000. The bonds have 15 years left to maturity. If Williamson’s bonds are currently selling for $1,430, calculate their yield to maturity. Assume semiannual coupon payments.

a. / 3.1%
b. / 5.3%
c. / 7.2%
d. / 9.8%
  1. Aurand Inc. has outstanding bonds with an 8% coupon paid semiannually. The bonds have a par value of $1,000, a current price of $904, and will mature in 14 years. What is their yield to maturity?

a. / 15.80%
b. / 10.47%
c. / 9.24%
d. / 7.90%
e. / 4.62%
  1. a. Addleson Corp. has a $1,000 par value annual coupon bond outstanding that was issued for 30 years 5 years ago at a coupon rate of 15%. The yield on similar bonds is now 12%. What is its price?

a. / $1,235.27
b. / $2,418.58
c. / $836.74
d. / $1,236.44

25.b. What is the current yield on the Addleson Corp. bond?

25.c. Assume one additional year has passed on the Addleson Corp. bond and nothing else has changed (still market required return of 12%, $1000 face value, and 15% coupon), What is the bond worth now?

25.d. What was the capital gain (loss) over the year that passed between 25a and 25c?

25.e. Check the sum of the current yield (25b) and capital gains yield (25d):

  1. If a 30-year, $1,000 bond has a 9% coupon and is currently selling for $826, its current yield is:

a. / $90
b. / 9.0%
c. / 10.9%
d. / 12.0%
  1. Alpha Inc. has a $1,000 par valuesemiannual coupon bond that was issued ten years ago for a 30-year term. Interest rates were very high at that time and the bond’s coupon rate is 22%. The relevant bond market interest rate is now 10%. All of Alpha’s bonds have a call feature. It allows the company to pay off the bond anytime after the first 15 years but requires that bondholders be compensated with an extra year’s interest at the coupon rate if such a payoff is exercised. What is the bond’s market price assuming investors expect it will be called as soon as possible?
  1. If a 30-year bond with a quoted price of $810 pays $40 interest semiannually, its current yield would be about:

a. / 8.0%
b. / 4.0%
c. / 5.5%
d. / 9.9%
  1. Find the yield to call on a semiannual coupon bond with a face value of $1000, a 10% coupon rate, 15 years remaining until maturity given that the bond price is $1175 and it can be called 5 years from now at a call price of $1100.
  1. A company has issued a $10,000 bond with zero coupon. It has 20 years remaining to its original 30-year maturity and the market is seeking a yield of 8%. Work this as an annual bond. The price (intrinsic value) of the bond today is:

a. / $2,145
b. / $2,083
c. / $6,667
d. / none of the above

Key Lab 7 Problems

  1. ANS:C

n=5, I=10, PV=100000, FV=0, compute PMT = $26,379.75

n-3, I=10, PV=100000, PMT=-26379.75, compute FV=$45,783.03

  1. ANS:A

Calculator steps: 100 PMT 12 I/Y 15 n Solve for FV = $3,727.97

  1. ANS:C

N=5, I= 11. PV=10000, FV=0, compute PMT=2705.70

  1. ANS:C

Calculator Steps: 180,000 PV .833 I/Y 300 n Solve for PMT = $1,635.66

Total Interest Paid: ($1,635.66  300) – $180,000 = $310,698

  1. ANS:C

Calculator Steps:

Loan value: – 750 PMT 60 n 1 I/Y Solve for PV = $33,716

Down Payment Needed = $40,000 – $33,716 = $6,284

Quarterly Saving: 6,284 FV 8 n 2 I/Y. Solve for PMT = $732

  1. ANS:A

Calculator steps:

-100 PMT 15 n 12 I/Y Solve for PV = $681.09

-200 PMT 5 n 12 I/Y Solve for PV = $720.96

-720.96 FV 15 n 12 I/Y Solve for PV = $131.72

$681.09 + $131.72 = $812.81

  1. ANS:C

N=20, I=10, PMT = 25000, FV = 0, compute NPV=212839.09

N=25, i=10, FV= 212839.09, PV=0. Compute PMT = 2164.16

Bond problems

  1. ANS:A

Calculator Steps: 1000 FV; 35 PMT; 60 n; 4.7 I/Y; PV = 760.91

  1. 1000 FV; 40 PMT; 30 n; 3.5 I/Y; PV = 1091.96
  2. ANS:C

Calculator Steps: 1000 FV; –1430 PV; 60 PMT; 30 n

Solve for I/Y = 3.625%  2 = 7.25%

  1. ANS:C

n = 28; PV = –904; PMT = 40; FV = 1000; I/Y = 4.6178%, YTM = 4.62%  2 = 9.24%

  1. a. ANS: A

25 n; 12 I; 150 PMT; 1000 FV; compute PV = 1235.29

25b. 150/1235.29 = 12.14%

25c. N=24; I=12; PV=?= -1233.53; PMT=150; FV=1000

25d. (1233.53 – 1235.29)/1235.29 = -1.76/1235.29 = - 0.14%

25e. CY + CGY = 12.14% - 0.14% = 12.00%

The sum of current yield and capital gains yield (loss in this case) is equal to the required rate of return.

  1. The current yield is: 90/826 = 10.9%
  2. n = 10; I = 5; compute PV = –1598.67; PMT = 110; FV = 1220
  1. ANS:D; 80/810 = 9.88%
  2. n = 10; PV = –1175; PMT = 50; FV = 1100; I/Y = 3.7166%, YTC = 3.7166% 2 = 7.43%
  3. ANS: A; 20 n; 8 I; 0 PMT; 10000 FV; compute PV = 2145.48

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