Question

SHOW ALL WORK PLEASE

QUESTION: An insurance company must make payments to a customer of $10 million in 5 years and $25 million in 30 years. The yield curve is flat at 8%.

A) What is the present value of its obligation?

B) What is the duration of its obligation?

C) If it wants to fully fund and immunize its obligation to this customer by buying a single issue of a zero-coupon bond, what face value the bond must have?

D) Suppose you buy a zero-coupon bond with value and duration equal to your obligation, and that rates immediately increase to 9%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation?

PLEASE SHOW WORK TO ALL PARTS AND MAKE SURE YOU CLEARLY LABEL THE ANSWER TO EACH PART

FOR EXAMPLE -

PART A= x

PART B=x

PART C=x

PART D=x

Answer 1

Liabilities(L)	Term(t)	PV=L x 1.08^(-n)	n x PV
10	5	6.81	34.03
25	30	2.48	74.53
Total		9.29	108.56

PART A

PV=L x r^(-n)

L- Liability amount

r - Rate of interest

n - Number of years

The present value of the obligations = $ 9.29 million

PART B

Duration = (n*PV) / PV

Duration = 108.56 / 9.29 = 11.69 years

Maturity of the zero coupon bond (ZCB) = duration of the liabilities calculated = 11.69 years

PART C

Face value of the ZCB that you will buy = PV * ( 1 + r )^d

Face value of the ZCB that you will buy = 9.29 x (1 + 8%)11.69 = $22.84

PART D

When YTM changes to 9%;

PV of the bonds = 22.84 / (1 + 9%)11.69 =   8.34

nd the PV of the obligations = 10 / (1 + 9%)5 + 25 / (1 + 9%)30 = 6.50 + 1.88 = 8.38

Hence, the net position = 8.34 - 8.38 = - $ 0.04 million

Thus the net position is a loss (reduction in value of) of $ 0.04 million.

Thank You....