Corporate Bond Market Price Calculation & Credit Default Swap Payout

5.a To calculate the market price of the bond, we can use the formula for the present value of a bond:

Market Price = (Coupon Payment / (1 + Yield to Maturity))^1 + (Coupon Payment / (1 + Yield to Maturity))^2 + ... + (Coupon Payment + Face Value / (1 + Yield to Maturity))^n

Where: Coupon Payment = Annual coupon rate * Face Value Yield to Maturity = Annual yield rate / number of compounding periods n = number of years to maturity * number of compounding periods

In this case, the bond has a 4-year maturity, a 7% coupon rate, and a yield to maturity of 5%. Assuming annual compounding, the market price can be calculated as follows:

Coupon Payment = 7% * Face Value = 0.07 * Face Value Yield to Maturity = 5% / 1 = 0.05 n = 4 * 1 = 4

Market Price = (0.07 * Face Value / (1 + 0.05))^1 + (0.07 * Face Value / (1 + 0.05))^2 + (0.07 * Face Value / (1 + 0.05))^3 + (0.07 * Face Value + Face Value / (1 + 0.05))^4

Simplifying the equation, we get:

Market Price = (0.07 * Face Value / 1.05)^1 + (0.07 * Face Value / 1.05)^2 + (0.07 * Face Value / 1.05)^3 + (1.07 * Face Value / 1.05)^4

Now, you can substitute the value of Face Value into the equation to find the exact market price.

5.b To calculate the cash payout on settlement, we can use the formula:

Cash Payout = (Face Value - Auction Settlement Price) * Notional Amount

In this case, the face value is 100, the auction settlement price is 35, and the notional amount is $20 million. Therefore, the cash payout can be calculated as follows:

Cash Payout = (100 - 35) * $20 million = $65 million * $20 million = $1.3 billion

The cash payout on settlement would be $1.3 billion.