Question

Question 5 please!

5. An A-rated company knows it will need to borrow $1M in 4 years, and repay the entire $1M in 5 years. It wishes to lock an interest rate on this loan now, because its CFO is afraid interest rates will increase in the future. The CFO found a bank willing to give the company $1M in 4 years and receive $1M in 5 years, if the company pays the bank $X now. Assume again that the credit spread for bonds rated A is currently constant at 1% for all terms. What is the no-arbitrage value of X? o Home L Clipboard AutoSave OFF Å BESVU - Book3 Q OY Insert Draw Page Layout » Share Comments Share A % e cohereunal Formatting v Format as Table Number Cell Styles • X fx B C D E F G Font Alignment ci A 1 Risk-free rates 2 1Y 3 24 4 3Y 5 5Y 0.18% 0.30% 0.43% 0.87% 1.39% 1.98% 2.73% 3.08% RSITY INIA 6 7Y TOMMERCE bext

Answer 1

Risk free rate for 5 year Bond = 0.87%

Credit Spread = 1%

Hence, Effective rate of borrowing will be = 1%+0.81% = 1.87%

Since the bank is lending $1M to the company in next 4 years with certain amount of "X" receiving upfront from the company. and bank gets it total amount in 5 years.

Hence in case of no arbitrage, X will be difference in present value of $1M in 4 years and 5 years.

Hence X = PV of $1M in 4 years - PV of $1M in 5 years

= $1M/1.87^4 - $1M/1.87^5

= $ 38046