ACTS 4308. AU 2017. HOMEWORK 8 Use the cash flow matching to determine how many

Question

ACTS 4308. AU 2017. HOMEWORK 8 Use the cash flow matching to determine how many of each investments will cover these liabilities and calculate the total price of assets. Problem 6 A Company has liabilities that require payments of 2000 six months from now and 3000 one year from now. The following investments are available to the company: Maturity Effective Yield | Par Value Coupon Rate (years) (semi-annual) 6.00% 8.00% semi-annual 5% 5% 0.5 1000 1000 Calculate the amount of each bond to purchase and the total cost of the bonds needed to match the liability cash flows exactly. Problem7

Explanation / Answer

We will first start with matching the 1 year liability of 3000. The bond available is the 1 year bond with 1000 par value and 6% semi-annual coupon. Let x be the number of bonds to be purchased.We will receive a coupon of 30 every six months.

3000 = x (1000 + 30)

x = 2.91

In order to match the 2000 liability we will use the six month bond with 1000 par value and 5% coupon. Note that we will receive 30 * 2.91 = 87.3 coupon from the 1 year bonds. Let y be the number of six month bonds to be purchased.

2000 = y (1000 + 25) = 87.3

y = 1.87

Total amount = 2.91(1000) + 1.87 (1000) = 4780

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