:please help me answer the following questions.

Question 1:

Financial institution has the following balance sheet structure:

Assets

Liabilities

Cash$1,000

Certificate of deposit$10,000

Bond10,000

Equity1,000

Total assets$11,000

Total liabilities and equity$11,000

The bond has a ten-year maturity and a fixed-rate coupon of 10 per cent. The certificate of deposit has one-year maturity and a 6 per cent fixed rate of interest. The FI expects no additional asset growth.

(a) What will be the net interest income at the end of the first year?

(b) If at the end of year 1 market interest rates have increased 100 basis points (1 per cent), what will be the net interest income for the second year? Is this result caused by reinvestment risk or refinancing risk?

(c(c) Assuming that market interest rates increase 1 per cent, the bond will have a value of $9446 at the end of year 1. What will be themarket value of equity for the FI?

(d) If market interest rates had decreased 100 basis points by the end of year 1, would the market value of equity be higher or lower than $1000? Why?

(e) What factors have caused the changes in operating performance and market value for this firm?

Question 2:

A bank has invested $50 million in a two-year asset paying 10 per cent interest per annum and simultaneously issued a $50 million, one-year liability paying 8 per cent interest per annum. What will the impact on the bank%u2019s net interest income if at the end of the first year all interest rates have increased by 1 per cent100 basis points)?

Question 3:

Evaluate the prices of the following pure discount (zero-coupon) bonds:

(a) $1000 face value received in five years yielding an annual rate of 8 per cent.

(b) $10,000 face value received in three years yielding an annual rate of 6 per cent.

(c)$100,000 face value received in 10 years yielding an annual rate of 13 per cent.

(d) $1,000,000 face value received in two years yielding an annual rate of 7 per cent.

(e) $1,000,000 face value received in six months yielding an annual rate of 7 per cent.

Question 4:

Calculate the percentage price changes for each of the bonds in Question 3 if all yields increase by 1 per cent.

Question 5:

ABC Ltd (in thousands of dollars)

Assets

Liabilities

Two-year treasury bond$175

One-year CD$135

15-year corporate bond$165

Five-year deposit$160

Notes: All securities are selling at par (equal to book value). The two-year Treasury bonds yield 5 per cent; the 15-year corporate bonds yield 9 per cent; the one-year CD issue pays 4.5 per cent; and the five-year deposit pays 8 per cent. Assume that all instruments have annual coupon payments.

(a) What is the value of ABC Ltd%u2019s equity?

(b) What is the weighted average maturity of the FI%u2019s assets?

(c)What is the weighted average maturity of the FI%u2019s liabilities?

(d) What is the FI%u2019s maturity gap?

(e) What does your answer in part (d) imply about the interest rate risk exposure on ABC Ltd?

(f)Calculate the values of all four securities on ABC Ltd%u2019s balance sheet if all interest rates increase by 2 per cent.

(g) What is the impact on the equity of ABC Ltd? Calculate the percentage change in the value of equity.

(h) What would be the impact on ABC Ltd%u2019s interest rate risk exposure if its liabilities paid interest semi-annually as opposed to annually?

Question 6

What is the price of a newly tendered five-year Treasury bond with a coupon of 7 per cent and a yield of 7.05 per cent? (All treasury notes and bonds pay interest semi-annually)

Question 7:

(a) What are all of the promised cash flows on a $1000 one-year loan yielding 10 per cent p.a. that pays interest and principal quarterly?

(b) What is the present value of the loan if interest rates are at 10 per cent p.a.?

(c)What is the present value of the loan if interest rates are at 8 per cent p.a.?

Question 8:

Calculate the duration of a two-year Euro-note with $100,000 par value and an annual coupon rate of 10 per cent if todays yield to maturity is 11.5 per cent. What would the duration be if todays yield was 5.5 per cent? (Interest is to be paid annually.)

Question 9:

Use the following information about a hypothetical government security dealer named XYZ Ltd to answer parts (a) through (e) (Market yields are in parentheses.)

XYZ Ltd (in millions of dollars)

Assets

Liabilities

Cash$10

Overnight interbank borrowing (7.00%)$170

T-notes: 30-day (7.05%)75

Subordinated debt:

T-notes: 91-day (7.25%)75

Seven-year, fixed at (8.55%)150

T-bonds: two-year (7.50%)50

Equity15

T-bonds: 10-year (8.96%)100

Corporate bonds:25

5-year quarterly floating rate (8.20%)

(a) What is the repricing or funding gap if the planning period is 30 days? 91 days? Two years?

(b) What is the impact over the next 30 days on net interest income if all interest rates rise by 50 basis points?

(c)If the duration of assets is 3.41 years and the duration of liabilities is 3.5 years, what is XYZ Ltd%u2019s duration gap?

(d) What conclusions regarding XYZ Ltd%u2019s interest rate exposure can you draw from the duration gap in your answer to part (c)? From the repricing or refunding gap (30 days%u2019 planning period) in your answer to part (a)?

(e) Approximately how will the market value of the Treasury note portfolio change if all interest rates increase by 50 basis points?

1. This question is about fixed Income securities and stocks [25 marks] Use discrete compounding of interest rates and assume that bond coupons are annual throughout this question. a) [5 marks] Consider three bonds with face value $100. The coupons are paid annually. Bond 1 is a three-year 10% coupon bond, bond 2 is a two-year 10% bond, and bond 3 is a two-year 15% bond. These three bonds have yields to maturity 8.5118%, 8.3105%, and 8.2479%, respectively. What are the prices of these bonds and discount factors d,, da, and dy? What is the term structure of interest rates? b) [6 marks] The one-year spot rate is r,=2%. Let ry denote the unknown spot rate between years t and 1+T in the future. Investors have the following expectations. They believe that in is equally likely to be 2% or 3%, whereas on, will be 3% with probability 0.25 and 5% with probability 0.75. Suppose, the expectations theory of the term structure holds, What are the spot rates ra and r? c) [5 marks] Consider an insurance company that needs to pay $10 million in each of the years 3, 4, and 5 from now. The term structure is flat at r=2%, What are the present value and Macaulay duration of the company's liabilities? The company has $28 million in cash that it wants to invest In bonds to immunize its liabilities. How many units of 3-year and 5-year zero-coupon bonds with face value $100 does the company need to buy to immunize its liabilities with respect to interest rate risk? d) [4 marks] Consider the same insurance company as in part c). Determine by how much the net worth of the company changes when the flat term structure shifts from 2% to 1.5% and the company does not immunize its liabilities. Determine by how much the net worth of the company changes for the same change in the term structure when the firm immunizes its liabilities as in part c). In both cases, calculate the exact net worth rather than approximations. Explain the intuition for your results, e) [5 marks] Company ABC is stable, has earnings per share (this is the same as net income per share) of $10, PVGO per share of $7.5, and ROE=20%. Its shares are traded at $70. What are the expected return / and the plowback ratio p of this company? Assume that the company has an infinite horizon