The following information applies to Problems 56

first we have to calculate price of both bonds.(how ever it is not required for calculation of portion of each bond to invest but how much to be(in dollars) invested in each bond)

price is present value of future cash flows discounted at YTM

Price of 6-month bond:

coupon = 1000 * 8% / 2 = 40

Redemption value = 1000

YTM = 6% / 2 = 3%

Price = (1000 + 40) / (1+3%)

= 1009.71

Price of one-year bond :

here number of coupons = 2

coupon payments = 1000*5% / 2 = $25

redemption price = $1000

YTM = 7% / 2 = 3.5%

price = 25 / (1+3.5%) + (1000+25) / (1+3.5%)^2

= $981

cash flow at the end of 6 - months = $40 coupon payment and redemption value of $1000 (total $1040) for 6month bond and $25 coupon payments for one year bond

cash flow at the end of one -year period = $25 coupon and $1000 redemption value for one year bond

let X = portion to be invested in 6 - month bond

Y = portion to be invested in one year bond

we want $1000 at the end of 6-months

so , 1000 = 1040X + 25Y...........(i)

another $1000 at the end of one year

so , 1000 = 1025Y.............(ii)

From (ii) Portion to be invested in one - year bond (Y) = 1000 / 1025 = 0.97561

substitute value of Y in equation (i) we get ,

1000 = 1040X + 25*(0.9756)

Portion of amount to be invested in 6 - month bond (X) = 0.93809

value of 6 - month bond to be purchased = 1009.71*0.93809 = $947.19

Value of one year bond to be purchased = 981 * 0.97561 = $957.08

Total = 947.19 + 957.08 = $1904.27