Question five [ 24 marks ] The financial analysts at Bearings and Nuts Limited a

Question

Question five [ 24 marks ] The financial analysts at Bearings and Nuts Limited a local conglomerate wants hedge the exposure of a variable interest rate loan it negotiated last year. Due to an uncertain economic environment, the fluctuation of local interest rate might affect the total long term obligations on the company’s balance sheet. As a result, the corporate risk manager indicated that the entity could enter into a swap agreement to nullify this potential exposure. Management is also considering mitigating risk by initiating a call option. The stock has a current market value of $60. However, the strike price is $50 and the option is to be exercised in 180 days. The volatility of the stock as measured by standard deviation is 40% and the annualised risk free rate is 4%. Therefore, the following spot curve was obtained with rates up to a maturity date of five years: Maturity (yrs.) Spot Rate (%) 0.5 6.90% 1 6.95% 1.5 7.50% 2 7.75% 2.5 8.17% 3 8.75% 3.5 8.90% 4 9.20% 4.5 9.55% 5 9.85 % Required a. Using the information above, calculate the swap rate that will hedge against the floating rate exposure. [ 10 marks ] b. Calculate the value of the call option [ 10 marks ] c. Use the put-call parity to calculate the value of the put [

Explanation / Answer

a)   = 5* (1-8.17) / (6.90+6.95+7.50+7.75+8.17)

=5*-7.17 / 37.27

=-35.85 / 37.27

= -0.96%

b) Risk free rate= 0.04

Spot Price = 60

Strike Price = 50

Time to maturity days= 180

Volatility= 0.4

So, value of call option is 13.1131

Value of Put option is 2.1231

Template - Black-Scholes Option Value Input Data Stock Price now (P) 60 Exercise Price of Option (EX) 50 Number of periods to Exercise in years (t) 0.5 Compounded Risk-Free Interest Rate (rf) 4.00% Standard Deviation 40.00% Output Data Present Value of Exercise Price (PV(EX)) 49.0099 =++(EX*EXP(-rf*t) s.d.*t^.5 0.2828 =+s.d.*t^0.5 d1 0.8567 =++(LN (P/EX)+(rf+sS.D.*SD/2)*T)/ (SD*t^0.5) d2 0.5739 =d1-s.d.*t^0.5 Delta N(d1) Normal Cumulative Density Function 0.8042 =NORMDIST (d1,0,1,True) Bank Loan N(d2)*PV(EX) 35.1391 =NORMDIST(D2,0,1,True)*(pv(ex)) Value of Call 13.1131 =+Delta N(d1) Normal Cumulative Density Function*P-Bank Loan N(d2)*PV(EX) Value of Put 2.1231 =+ Value of call+(PV(EX)-P

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