A company’s preferred stock will pay level annual dividends forever starting five years from now. Using an annual effective interest rate of 10%, the modified duration of the stock is D.

Calculate D

• 13.64
• 14.55
• 15.00
• 16.00
• 16.50

A firm has a liability cash flow of 100 at the end of year two and a second liability cash flow of 200 at the end of year three. The firm also has asset cash flows of X at the end of years one and five. Using an annual effective interest rate of 10%, calculate the absolute value of the difference between the Macaulay durations of the asset and liability cash flows.

• 0.018
• 0.020
• 0.022
• 0.024
• 0.026

You are given the following term structure of interest rates:

Calculate the one-year annual effective rate for the fifth year implied by this term structure.

• 9.0%
• 9.5%
• 10.0%
• 10.5%
• 11.5%

Determine which of the following expressions represents the modified duration for a zero-coupon bond that is currently priced at an annual effective yield rate i and an n-year maturity.

• [[math]]n[[/math]]
• [[math]]n(1+i)[[/math]]
• [[math]]n(1+i)^{-1}[[/math]]
• [[math]]\frac{\sum_{t=1}^nt(1+i)^{-t}}{\sum_{t=1}^n(1+i)^t}[[/math]]
• [[math]]\frac{\sum_{t=1}^nt(1+i)^{-t}}{\sum_{t=1}^n(1+i)^{-t}}[[/math]]

The table below shows the cash flows for a particular investment and the prevailing spot rates.

Calculate the present value of this investment at the start of year 1.

• 47.33
• 48.64
• 49.50
• 50.04
• 51.14

An investor purchases a 1200 face amount zero-coupon bond for a price of 1000. With respect to the bond’s annual effective yield rate, the Macaulay duration is four years and the modified duration is d years.

Calculate d.

• 3.33
• 3.82
• 3.86
• 4.00
• 4.19

An insurer has a liability that is expected to result in the following cash outflows.

The insurer uses an 8% annual effective interest rate to discount future cash flows.

Calculate the Macaulay duration of this liability.

• 3.1 years
• 3.2 years
• 3.4 years
• 3.5 years
• 3.6 years

An investor pays 4000 today for a three-year investment that returns cash flows of 1400 at the end of each year. The cash flows can be reinvested at the positive annual effective interest rate of i. Using an annual effective rate of interest of 4%, the net present value of this investment is 0.

Calculate i.

• 2.5%
• 3.0%
• 3.5%
• 4.0%
• 7.0%

A company has liabilities of 1000 and 300 due at the end of years two and four, respectively. The company develops an investment program that produces asset cash flows of X and Y at the end of years one and three, respectively. The investment portfolio is constructed to match the present value and duration of the company’s payment obligations based on an annual effective rate of interest of 5%.

Calculate X/Y.

• 2.14
• 2.75
• 3.42
• 4.05
• 4.91

The table below defines available zero-coupon bonds and their prices:

A company chooses to purchase 15 one-year zero-coupon bonds; 20 two-year zero- coupon bonds; and 30 three-year zero-coupon bonds.

Calculate the Macaulay duration of this portfolio

• 1.97
• 2.11
• 2.16
• 2.20
• 2.23