Final answer:
The promised yield of the bond is 21.11%, calculated using the formula (109 - 90) / 90. The expected yield, considering a 10% default probability and a 41% recovery rate, is 14.56%, found by averaging the outcomes for both scenarios of default and non-default. None of the provided answer choices (a through e) match this correct calculation.
Step-by-step explanation:
To calculate the promised yield and the expected yield of a bond, it's important to first understand what these terms mean. The promised yield is the total return anticipated on a bond if the bond is held until it matures, including all coupon payments and redemption at face value. The expected yield takes into account the probability of default and the recovery rate if default occurs, which adjusts the promised yield to reflect the possibility of not receiving all payments.
For a bond with a face value of £100, price of £90, an annual coupon rate of 9%, a recovery rate of 41%, and a probability of default of 10%, we calculate as follows:
Calculate the coupon payment: £100 (face value) x 9% (annual coupon rate) = £9 per year.
Promised Yield: The investor will receive £9 (annual coupon) + £100 (face value) at maturity. Therefore, the promised yield is (109 - 90) / 90 = 0.2111, or 21.11%.
Expected Yield: We account for the probability of default and the recovery rate here. If the bond defaults, the investor will receive 41% of £100 (face value), which is £41. The total expected cash flow if default occurs is the coupon payment (£9) + recovery rate (£41) = £50.
The expected yield then is a weighted average of the yield if the bond doesn't default and the yield if it does: (90% * (£109 - £90)/£90) + (10% * (£50 - £90)/£90) = 0.19 + (-0.0444) = 0.1456 or 14.56%.
Thus, the correct answer is: Promised Yield = 0.2111 (21.11%), Expected Yield = 0.1456 (14.56%), which is not one of the provided options (a through e).