Corporate Finance problem set

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%

2.  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

3.  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

4.  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

5. 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:

 What is the present value of these cash flows?

· 125,655

6.  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

7.  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

8.  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

1 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

2.  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

3.  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%

4.  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

5. 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%

6.  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.

7.  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?

8.  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?