Problem Set #2

Question 1
Assume that you are nearing graduation and have applied for a job with a local bank.  As part of the bank’s evaluation process, you have been asked to take an examination that covers several financial analysis techniques.  The first section of the test addresses time value of money analysis.  See how you would do by answering the following questions.

Draw time lines for (a) a $2000 lump sum cash flow at the end of year 4, (b) an ordinary annuity of $1000 per year for 5 years, and (c) an uneven cash flow stream of -$450, $1000, $650, $850 and $500 at the end of years 0 through 4.
What is the future value of an initial $1000 after 5 years if it is invested in an account paying 5% annual interest?
What is the present value of $1000 to be received in 4 years if the appropriate interest rate is 5%?
We sometimes need to find out how long it will take a sum of money (or anything else) to grow to some specified amount.  For example, if a company’s sales for 2020 is $1000 and expected to grow at a rate of 10% per year, how long will it take sales to double?
If you invested $10,000 in an investment account and you expect it to double in 4 years, what interest rate must it earn?
What is the future value of a 5-year ordinary annuity of $1000 if the appropriate interest rate is 5%? What is the present value of the annuity?
What is the future value of $1000 after 4 years under 10% annual compounding?  Semiannual compounding?  Quarterly compounding?  Monthly compounding?  Daily compounding
What is the effective annual rate (EAR or EFF%)?  What is the EFF% for a nominal rate of 5%, compounded semiannually?  Compounded quarterly?  Compounded monthly?  Compounded daily?
Construct an amortization schedule for a $1,000, 12% annual rate loan with 4 equal installments. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 2?
Suppose on January 1 you deposit $1000 in an account that pays a nominal, or quoted, interest rate of 12%, with interest added (compounded) daily.  How much will you have in your account on October 1, or 9 months later?
You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment?
While Mary Corens was a student at the University of Tennessee, she borrowed $20,000 in student loans at an annual interest rate of 5%. If Mary repays $200 per year, then how long (to the nearest year) will it take her to repay the loan?

Question 2
1. Jackson Corporation’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. The bonds have a yield to maturity of 10%. What is the current market price of these bonds?
2. Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 10 years, have a face value of $1,000, and a yield to maturity of 9%. What is the price of the bonds?
3. Wilson Wonders’s bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $900. What is their yield to maturity?
4. Heath Foods’s bonds have 10 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 9%. They pay interest annually and have a 10% coupon rate. What is their current yield?
5. Suppose Hillard Manufacturing sold an issue of bonds with a 12-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. 
 a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 5%. At what price would the bonds sell? 
b. Suppose that 2 years after the initial offering, the going interest rate had risen to 11%. At what price would the bonds sell?
c. Suppose that 2 years after the issue date (as in part a) interest rates fell to 5%. Suppose further that the interest rate remained at 5% for the next 10 years. What would happen to the price of the bonds over time?