USB Manufacturing Inc. carries a sizeable portfolio of long-term debt in its bal
ID: 2768089 • Letter: U
Question
USB Manufacturing Inc. carries a sizeable portfolio of long-term debt in its balance sheet. The company expects increased volatility in long term interest rates and is concerned about its equity exposure to interest rate risk. The company has decided to pursue an asset-liability management approach where its total equity value will be fully immunized against any unexpected changes in long term interest rates. The USB’s current balance sheet is given below.
Assets Liabilities
Total Firm Value $800,000 Class “A” Bonds $150,000
Yield: 12% Yield: 10%
Duration: 8 Duration: 3
Class “B” Bond 250,000
Yield: 8%
Duration: 6
Equity 400,000
Total 800,000 800,000
a) What is the impact of a 1% increase in the general level of interest rate on USB’s equity value? Show your calculation. (8 marks)
b) What specific asset/liability strategies should the firm undertake to fully immunize (perfect hedge) its equity value against changes in interest rates? Show your calculations. (12 marks)
Explanation / Answer
a)USB’s equity value= Total Firm Value - Class “A” Bonds value- Class “B” Bonds value
change in USB’s equity value= change in Total Firm Value - change in Class “A” Bonds value- change in Class “B” Bonds value
for 1% increase in the general level of interest rate,
change in Total Firm Value=-8*1%*800,000 =-64,000
change in Class “A” Bonds value=-3*1%*150,000=-4,500
change in Class “B” Bonds value=-6*1%*250,000=-15,000
change in USB’s equity value=-64,000 - (-4,500)-(-15,000)
change in USB’s equity value=-64,000+4500+15,000
change in USB’s equity value=-44,500
Therefore the USB’s equity value decreases by $44,500.
Therefore the net duration of the equity=44,500/400,000*1%=11.125
b)
i)to fully immunize (perfect hedge) its equity value against changes in interest rates firm could use futures in Treasury bonds.The futures price is 93-02 or 93.0625 and the duration of the cheapest to deliver bond is 9.2 years for the Treasury bonds futures.
The number of contracts that should be shorted is=400,000*11.125/(93.0625*9.2) =5197.54~5198
Therefore we should short 439919 T-bond futures contracts to immunize equity against the interest rate changes.
SO that the net change in the value of the equity with y% change in interest rate=-11.125*y%*400,000=-44500y
the net change in the value of the futures with y% change in interest rate=5198*9.2*y%=47821.6y
Therefore the net change in equity with y% change in interest rate after considering the profits from the futures with the change in interest rates=47821.6y-44500y=3321.6y
Thus for 1% change in yield the equity value changes by $33.21~0 therefore we have almost perfectly immunized the equity value against changes in interest rates.
ii)We can also use the the interest rate swaps to manage the interest rate risk,under this we pay a fixed interest rate on the notional principal and receive a floating interest rate on the notional principal on a yearly basis.Let the Duration of the swap = -8.5=Duration of floating leg-Duration of fixed leg.
The notional principal required for perfect hedge=400,000*11.125/(8.5)=523529.42
Therefore the notional principal for the swap should be $523529.42 for a perfect hedge.
Here for example if the interest rate rises to 5% from current 3% then the net payoff receive on the interest rate swap=2%*8.5*523529.42 =89000
The net change in equity value=-2%*11.125*400,000=-89000 thus the net equity value after considering the payoff from the swap=89000-89000=0 therefore we perfectly hedged against the interest rate risk.
For any y% change in interest rate
net equity value after considering the payoff from the swap
=y%*8.5*523529.42-y%*11.125*400,000
=4450000y - 4450000y
=0.
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