Answer:
Duration of liability (perpetual) = (1 + y) / y
= (1 + 17.5%) / 17.5%
= 6.71
Value of liability = Cash Flow / yield
= $3.5 million / 17.5%
= $20 million
a. Assume you invest w in 5-year bond and 1-w in 25-year bond such that the duration of the portfolio is 6.71
6.71 = w x 4 + (1 - w) x 16
w = (16 - 6.71) / (16 - 4)
w = 77% in 5-year bond
1 - w = 28% in 25 year bond
Market Value of 5 year bond = 77% * $20 million = $15.4 million
Market Value of 20 year bond = 23% * $20 million = $4.6 million
b. Market Price of 20 year bond can be calculated using PV function on a calculator
N = 25, I/Y = 17.5%, PMT = 9, FV = 100
Price = Present Value (25,17.5%, 9 ,100)
Price = 52.29042644
Price = $52.30
Par Value of 25 year bond = Market Value /% Price
Par Value of 25 year bond = $4.6 million / 50.83%
Par Value of 25 year bond = $9,049,774
