?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. PV=190.46 (SEE EXCEL FILE ATTACHED)
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? It would take about 3.801784 years before the sales double. (SEE EXCEL FILE ATTACHED)
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? It will be larger because it’s basically like adding on interest on top of interest as the frequency increases.
4. What is the effective annual rate (EAR or EFF %) for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily? EAR = (1 + Nominal Interest/Number of Period) ^Number of Period -1 SEMI ANNUALLY= (1+.12/2)^2-1=12.36%
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? OCT 1ST= 100*(1+.1133463/365) ^ (365*.75) = $108.87
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? PV= $837.21 (SEE EXCEL FILE ATTACHED)
It would be considered a discounted bond because the present value is less than its face value.
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? PV= $1210.71 (SEE EXCEL FILE ATTACHED) It would be considered a premium bond because the present value is more than the face value.
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? RATE = 11% for a bond that sells for $887 and the RATE = 7% for a bond selling for $1134.20
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.) The return for the $887 bond is 11% and the yield is 90/887 which equals 10.15%. The capital gain would be 11% – 10.15%= .85% The return for the $1134.20 bond is 7% and the yield is 90/1134.20 which equals 7.9%. The capital gain would be 7% – 7.9%= -.9%