accounts data bank
1. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?
a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.
The discount rate increases.
c. The riskiness of the investment’s cash flows decreases.
d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.
e. The discount rate decreases.
2.Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?
a. The periodic rate of interest is 2% and the effective rate of interest is 4%.
b. The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.
c. The periodic rate of interest is 4% and the effective rate of interest is less than 8%.
d The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
e. The periodic rate of interest is 8% and the effective rate of interest is also 8%.
3.Which of the following investments would have thehighest future valueat the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.
a Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).
4.You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?
5. Suppose the real risk-free rate is 2.50% and the future rate of inflation is expected to be constant at 3.05%. What rate of return would you expect on a 5-year Treasury security, assuming the pure expectations theory is valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
r = r* + IP + DRP + LP + MRP
r = 2.50% + 3.05% = 5.55%
6. Suppose the real risk-free rate is 3.50%, the average future inflation rate is 2.25%, and a maturity premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the years to maturity. What rate of return would you expect on a 1-year Treasury security, assuming the pure expectations theory is NOT valid? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic average.
r = r* + IP + DRP + LP + MRP
r = 3.50% + 2.25% + 0 + 0 + .10% = 5.85%
7. The real risk-free rate is 2.50%, inflation is expected to be 3.00% this year, and the maturity risk premium is zero. Taking account of the cross-product term, i.e., not ignoring it, what is the equilibrium rate of return on a 1-year Treasury bond?
(1 + r) = (1 + r*) ( 1+ IP)
(1+r) = (1.025) (1.03) = 1.05575 - 1 = 5.575%
<>8.Suppose the U.S. Treasury offers to sell you a bond for $3,000.No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000.What interest rate would you earn if you bought this bond at the offer price?
n = 10
i = ?
PV = -3000
PMT = 0
FV = 5000
Solve for "i" which will be 5.2410 %
9. Keys Corporation's 5-year bonds yield 6.50%, and T-bonds with the same maturity yield 4.40%. The default risk premium for Keys' bonds is DRP = 0.40%, the liquidity premium on Keys' bonds is LP = 1.70% versus zero on T-bonds, inflation premium (IP) is 1.5%, and the maturity risk premium (MRP) on 5-year bonds is 0.40%. What is the real risk-free rate, r*?
Simply subtract the IP of 1.50% and the MRP of .40% from the T-bond yield of 4.40% to arrive at 2.50%
10. The Carter Company's bonds mature in 10 years have a par value of $1,000 and an annual coupon payment of $80.The market interest rate for the bonds is 9%.What is the price of these bonds?