Company XYZ has a liability of $60,000 that is due in 3 years. The company can invest x in the 1-year zero coupon bond, and y in the 5-year zero coupon bond. The PV of the cash flow of assets and liabilities is
P (i) = x (1.05) ^1 *(1 + i) ^-1 + y (1.05) ^5 *(1 + i) ^-5 - 60,000*(1 + i) ^ -3
Therefore
P’ (i) = [- (1)*(1.05) ^1*(1 + i) ^-2] - [(5)* y (1.05) ^5 *(1 + i) ^-6] + [(3)* 60000 *(1 + i) ^-4]
We solve for x and y in the equations P (0.05) = 0 and P’ (0.05) = 0,
x + y = (60000) * (1.05) ^-3 = 51830.26
And 1x + 5y = (180000) *(1.05) ^-3 = 155490.77
4 y = 103,660.51
Therefore,
Y = 25,915.13
And x = $ 51,830.26 - $25,915.13
= $25,915.13
Company XYZ should invest $25,915.13 in Bond X.
A company is a legal entity formed by a group of individuals to conduct and operate a commercial or industrial business. A company may be organized in various ways for tax and financial liability purposes, depending on the corporate law of its jurisdiction.
Etymology. The English word company comes from the old French term Compagnie (first mentioned in 1150), meaning "company, friendship, intimacy". Lex Salica (English: Salic Law) (c.
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