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A bank has an obligation of $750 at the end of the first period and $550 at the end of the second period.It also has $1,528.93 to invest and can choose between zero-coupon bond or the coupon bond.The coupon bond matures in two years, pays an annual coupon of $100, and has a balloon payment of $1,400.The zero-coupon bond has a balloon payment of $1,610 at the end of the second year.The default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
-What is the present value of the bank's equity?
A)$1,528.93
B)$1,500.00
C)$1,300.00
D)$1,136.36
E)$392.57

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A bank has an obligation of $750 at the end of the first period and $550 at the end of the second period.It also has $1,528.93 to invest and can choose between zero-coupon bond or the coupon bond.The coupon bond matures in two years, pays an annual coupon of $100, and has a balloon payment of $1,400.The zero-coupon bond has a balloon payment of $1,610 at the end of the second year.The default-free yield on a one-year bond is 10%, and the annualized yield on a two-year bond is also 10%.
-What is the present value of the bank's equity?
A)$1,528.93
B)$1,500.00
C)$1,300.00
D)$1,136.36
E)$392.57

Quizplus · Accepted Answer

The present value (PV) of the bank's obligations is calculated using the given default-free yield rates. For the first period obligation ($750), the PV is calculated using the one-year bond yield of 10%, and for the second period obligation ($550), the PV is calculated using the two-year bond yield of 10%.First, calculate the PV of the obligations:- PV of $750 due in one year = $750 / (1 + 0.10) = $681.82- PV of $550 due in two years = $550 / (1 + 0.10)^2 = $454.55Total PV of obligations = $681.82 + $454.55 = $1,136.37Then, subtract the total PV of obligations from the amount the bank has to invest ($1,528.93):Bank's equity = $1,528.93 - $1,136.37 = $392.56 (rounded to $392.57 for the answer choice).Therefore, the present value of the bank's equity is $392.57.

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