Fin 534 Hw 2
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%
QUARTERLY= (1+.12/4)^4-1=12.55%
MONTHLY= (1+.12/12)^12-1=12.68%
DAILY= (1+.12/365)^365-1=12.75%
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
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%
QUARTERLY= (1+.12/4)^4-1=12.55%
MONTHLY= (1+.12/12)^12-1=12.68%
DAILY= (1+.12/365)^365-1=12.75%
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