Please show all the steps while providing the answer.

Suppose you are thinking of investing on Shakylandia's bonds with a

significant probability of default. Issue Date: today

Coupon Rate: 8%

Face Value: $1,000

Maturity: 4 years

A US treasury bond with the same maturity yields 3%- Assume that US treasury bond does not have any default chance (it is low enough to be ignored).

a) If Shakylandia did not have any default chance, what would be the price of their bonds today?

b)Now assume that the probability of default exists. Using all the information available, you estimate that in case there is a default, it will happen with 20% chance before the rst coupon payment. Given that the default does not happen in the first year, you calculate that there will be no default going forward!

When a default happens, the country will be able to pay only half of what it promised to pay on the promised dates. (This is called a hair cut)

What is the price of this bond today?

c) Given the default rates in part (b), what should be the coupon rate for this bond to sell at par?