Assume that you are nearing graduation and have applied for a job with a local bank. The bank’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 −$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 company’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 annually—for example, every 6 months, or semiannually—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 bond’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 bond’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.)

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