## Week 2 Problem Set

14 Mar

Week 2 Problem Set

Prepare a spreadsheet that shows your calculations for the following problems for time value and bonds.

Part 1:  Time Value of Money

1. The value of a house is estimated to be \$180,000 today.  (a) If it has increased in value by 4.5% per year for the past 10 years, what was the value 10 years ago? (b) If the house had increased in value by 40% over the entire 10-year period, what would have been the annual percentage increase?
• (a) = 115,907
• (b) = 3.422%

1. Mr. and Mrs. Smith are considering the purchase of a house.  They can budget a mortgage payment (P&I) of \$1,400 per month.   (a) If the current mortgage rate is 4.25% for a 30-year mortgage and they make a down payment of 20% of the purchase price, can they buy a house costing \$300,000?  (b) What is the maximum amount they can borrow?
• (a) = 1180.66 –> Yes
• (b) = 284,587

1. Mr. Jones bought a car 2.5 years ago and borrowed 25,284.72 from the credit union.  The interest rate was 3.49% for a 5 year loan.  (a) what is the monthly payment on the car?  (b)  What is the current outstanding principal balance on the car loan?
• (a) = 459.86
• (b) = 13,192.73

1. After graduation, you plan to work for Mega Corporation for 10 years and then start your own business.  You expect to save \$5,000 a year for the first 5 years and \$10,000 annually for the following 5 years, with the first deposit being made a year from today.  In addition, your grandfather just gave you a \$20,000 graduation gift which you will deposit immediately.  If the account earns 8% compounded annually, what how much will you have when you start your business 10 years from now?
• 144,944

1. You are interested in buying a duplex as an investment.  Your discount rate for evaluating cash flows is 12%.  A property you are considering is expected to produce the following cash flows:
 Year Cash Flow 1 5,500 2 6,500 3 8,500 4 12,500 5 179,000

What is the present value of these cash flows?

• 125,655

1. An income stream that has a negative flow of \$200 per year for 2 years, a positive flow of \$300 in the 3rd  year, and a positive flow of \$500 per year in Years 4 through 6.  The appropriate discount rate is 4% for each of the first 3 years and 5% for each of the later years.  Thus, a cash flow accruing in Year 6 should be discounted at 5% for some years and 4% in other years.  All payments occur at year-end.  Calculate the present value of the income stream.
• 1,099.96

1. Prepare an amortization schedule based on the following information:

You are purchasing a car for \$19,500 and you are getting a loan for the entire amount.  The interest rate from Honda Motor Finance Corporation is 9.9% per year.  Your loan in a unique one in that you only have to pay twice per year (at the end of every 6 months).  The loan has a 3-year term, but you plan to make a lump sum payment after 2 years in order to pay off the loan.  Find out what the ending balance on the loan will be after 2 years and complete an amortization table with the following columns filled in for periods 1-4:  Beginning Balance, Payment, Interest, Principal, Ending Balance.

• Ending Balance = 7,137.20

1. Upon graduation, you’ve decided you won’t accept a job unless the total compensation you receive has a present value of at least \$90,000.  You have determined that the appropriate interest rate is 6% per year (nominal).  You receive an offer from CBA Inc. where you get paychecks at the end of every 2 weeks (26 times per year).  The offer includes a signing bonus of \$5,000 that is paid immediately and a bonus of \$7,500 that is paid along with your final (26th) regular paycheck of the year.    How much must your regular paycheck be in order for you to accept CBA’s offer?
• \$3,091.83

Part 2:  Bond Valuation

• What is the price of a bond that pays \$40 every six months, matures in 20 years and has a yield to maturity of 6.65%? \$1,148.14

1. What is the price of a bond that pays \$20 every three months, matures in 20 years and has a yield to maturity of 6.65%? \$1,148.73

1. What is the coupon rate for a bond that is priced at \$917.87, has 5 years to maturity, has an interest rate of 7.5% and pays coupons semiannually? 5.0%

1. How long until maturity for a bond that is priced at \$556.84 with a yield to maturity of 5% and a \$1000 face value. The bond makes no interest payments (zero-coupon bond).  Assume annual compounding.  12 years

1. What is the yield to maturity for a bond priced at 1106.95 that pays coupons of \$13.75 every six months for the next 12.5 years? 1.79%

1. Bond X is a premium bond making annual payments. The bond has a coupon rate of 9%, a YTM of 7% and has 13 years to maturity.  Bond Y is a discount bond making annual payments.  The bond has a coupon rate of 7%, a YTM of 9% and has 13 years to maturity.

What are prices of the bonds today?

• X=1167.15, Y=850.26

If interest rates remain unchanged, what will the bond prices be in 1 year?  3 years? 5 years? 10 years? 13 years?  Discuss what is happening with the bond prices over time.

• X=1158.85, 1140.47, 1119.43, 1052.49 after 1,3,5, and 10 years respectively.
• Y=856.79, 871.65, 889.30, 949.37 after 1,3,5, and 10 years respectively.

1. There are two bonds that have identical 7% coupons, make semi-annual payments and are priced at par. Bond A has 4 years to maturity; Bond B has 20 years to maturity.

What are interest rates today?  7%

If interest rates increase by 2%, what will be the new price of the two bonds?  What is the percentage change in the prices?

• A=934.04, -6.6% change
• B=815.98, -18.4% change

Now assume that interest rates decrease by 2% from where they were originally.  Now that are the prices for the two bonds and what are the percentage changes in their prices?

• A=1071.7, +7.17% change
• B=1251.03, +25.10% change

Interest rate risk is a measure of how much a bond’s value changes when interest rates change.  Which of these bonds has the highest interest rate risk?

1. There are two bonds that both have 10 years to maturity and have a YTM of 8%. Bond Alpha has a 4% coupon rate (with semi-annual payments) and Bond Beta has a 12% coupon rate (with semi-annual payments).

What are prices of the bonds today?

Alpha=728.19; Beta=1271.81

If interest rates increase by 2%, what will be the new price of the two bonds?  What is the percentage change in the prices?

Alpha=626.13; Beta=1124.62

Now assume that interest rates decrease by 2% from where they were originally.  Now that are the prices for the two bonds and what are the percentage changes in their prices?

Alpha=851.23; Beta=1446.32

Interest rate risk is a measure of how much a bond’s value changes when interest rates change.  Which of these bonds has the highest interest rate risk?