Question

Part A. Suppose your firm has an obligation to pay an annuity with 18 annual payments of $80,000. The first payment is due two years from today. Assume all interest rates are 11.5%. Write down the information requested on your answer sheet. What is the present value of the obligation? Round and express your answer to the nearest whole dollar (i.e., nearest integer). Do not include a dollar sign.

Part B. What is the duration of the obligation? Please carry out intermediate steps further but in your final answer be accurate to and express your FINAL answer as accurate to the nearest 4 decimal places. Please do NOT answer MORE than 4 decimal places...round your answer to the nearest 4 decimal places.

Part C. Suppose the firm wishes to use a portfolio consisting of two different bonds to fully fund and immunize the obligation. Bond A is a 4-year, zero-coupon bond. Bond B is a 20-year, 4% annual coupon bond with a duration of 11.5 years. Using your final, rounded answers to 17-18 when performing calculations, what should be the total par value (or face value), in dollars, of the firm’s total investment in Bond B? Round and express your final answer to the nearest whole dollar (i.e., nearest integer) and do not include a dollar sign in your answer.

Do not calculate using excel. Show entire work.

Answer 1

Part A

First arrear annuity payment of $80,000 to be paid 2 years from now and total of 18 payments are to be made

if the present time (let) be 0

then first annual payment occur at 2 years time

and so on till the last payment at 19th year

interest rate (i)=11.5% or 0.115

discount or present value factor (v)=1/1+i = 1/1.115

present value of obligation = 80,000 x ( v² +v³+v⁴.....+v¹⁹)

= 80,000 x v x ( v+ v² +v³....+v¹⁸)

    =80,000 x v x ( (1-v¹⁸)/i) (By sum of GP r<1)

   = 80,000 x 6.699

   =535966.69
=535967 approx