Week 2 Problem Set

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

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**Part 1: Time Value of Money**

- 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%

- 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

- 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

- 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

- 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

- 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

- 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

- 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*

- 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*

- 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%*

- 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*

- 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%*

- 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.

- 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?

- 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?