Question

At the end of 2019, Treefern Ltd. had BBB-rated, 5-year bonds outstanding with a yield to maturity of 12.5%. At the time, government bonds with similar maturity had a yield of 2%. Suppose the expected return of the market risk premium is 7% and you believe Treefern Ltd.’s bonds have a beta of 0.60. If the expected loss rate of these bonds in the event of default is 45%. What annual probability of default would be consistent with the yield to maturity of Treefern Ltd.’s bonds at the end of the year 2019?

	A.	20.3%
	B.	14.0%
	C.	19.6%
	D.	16.7%

Answer 1

CORRECT OPTION IS B. 14%

Calculation

As per The Capital Asset Pricing Model (CAPM)

Expected return (R_e)= R_f+beta(Rm-R_f)

Where Rf is Risk free return ie Government bond.

Risk free return are return which contain minimum or no risk ,it can be return on deposits , govt bond etc

( Rm - Rf ) = Risk Premium ie Premium for investing in Risky Instrument instead of Risk free instrument .

R_e=2+0.60(7)

=6.2%

We know are total yield is 12.5%

Expected loss Rate =45%

Again Expected Return = Yield - Probability of Loss

6.2=12.5 - P (45%)

P=(12.5-6.2)/45%

P=14.00%