Leland Price must pay $5,000 six months from now and $10,000 one year from now.

Question

Leland Price must pay $5,000 six months from now and $10,000 one year from now. He wishes to purchase bonds so that together they form a portfolio of assets that exactly match his liabilities. Available bonds are a six-month zero-coupon $1,000 bond that has a 3.0225% annual yield and a one-year $1,000 par-value 6% bond with semiannual coupons and a 4% nominal yield (convertible semiannually). How much must Leland pay to purchase the bonds? Assume that he may buy any quantity he wishes of each bond.

Explanation / Answer

a.Price of a zero coupon bond = F/(1+r)^t

where F = face value = 1000

r = 3.0225 = 1.51125% = 0.0151125 and t = 1 (since 1 six month period)

Hence Price = 1000/1.0151125 = 985.1124 = $985.11

b. For the coupon bond:

Price is given by =pv(rate,nper,pmt,fv) in excel where rate = 0.04/2, nper = 2, pmt = 60/2 = 30 and fv =1000

So price of the coupon bond =pv(0.04/2,2,30,1000) = $1,019.42

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