Assume that you are nearing graduation and have applied for a job with a local bank. The bankâ€™s evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test asks you to address these discounted cash flow analysis problems:
1. What is the present value of the following uneven cash flow stream âˆ’$50, $100, $75, and $50 at the end of Years 0 through 3? The appropriate interest rate is 10%, compounded annually.
2. We sometimes need to find out how long it will take a sum of money (or something else, such as earnings, population, or prices) to grow to some specified amount. For example, if a companyâ€™s sales are growing at a rate of 20% per year, how long will it take sales to double?
3. Will the future value be larger or smaller if we compound an initial amount more often than annuallyâ€”for example, every 6 months, or semiannuallyâ€”holding the stated interest rate constant? Why?
4. What is the effective annual rate (EAR or EFF%) for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?
5. Suppose that on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months later?
Use the following information for Questions 6 and 7:
A firm issues a 10-year, $1,000 par value bond with a 10% annual coupon and a required rate of return is 10%.
6. What would be the value of the bond described above if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13% return? Would we now have a discount or a premium bond?
7. What would happen to the bondâ€™s value if inflation fell and rd declined to 7%? Would we now have a premium or a discount bond?
8. What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does a bond selling at a discount or at a premium tell you about the relationship between rd and the bondâ€™s coupon rate?
9. What are the total return, the current yield, and the capital gains yield for the discount bond in Question #8 at $887.00? At $1,134.20? (Assume the bond is held to maturity and the company does not default on the bond.)