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i Safari File Edit View History Bookmarks Window Help 60% ! Fri 1 1:10:52 AM Chegg Study Guided Solutions a HW 6 Fantasy Football Yahool Sports Saved Help Save & Exit Submit Check my work 9 a. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 6.2%. Now, with 6 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%, what is the price of the bond now? (Assume semiannual coupon payments.) (Do not round intermediate calculations. Round your answer to 2 decimal places.) 9.09 points Bond price eBook pptx Print b. Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 90% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Yield to maturity Bond HillExplanation / Answer
(a) The bonds were issued at par with a par value of $ 1000. The bonds had a YTM of 6.2 % at issue. As the bonds were issued at par, the bond's coupon rate will be equal to the YTM at maturity. The coupon payments are semi-annual in nature.
Semi-Annual Coupon Payment = 0.062 x 0.5 x 1000 = $ 31
Remaining Tenure = 6 years or 12 half-years
Current YTM = 15 % per annum or 7.5 % per half-year.
The bond's current price will be equal to the total present value of its expected future cash flows (in the form of the bond's remaining semi-annual coupons and face value redemption at maturity).
Therefore, current bond price = 31 x [1/0.075] x [1-{1/(1.075)^(12)}] + 1000 / (1.075)^(12) = $ 659.65
(b) Investors believe that the bond will be able to honour its coupon payment obligations. However, the bond's face value will be repaid only to the extent of 90 % upon maturity.
Therefore, partial face value redemption at maturity = 0.9 x 1000 = $ 900
Current Bond Price = $ 659.65
Let the YTM expected be 2R
Therefore, 659.65 = 31 x (1/R) x [1-{1/(1+R)^(12)}] + 900 / (1+R)^(12)
Using trail and error/ EXCEL's Goal Seek Function to solve the above equation we get:
R = 0.06765 or 6.765 % approximately.
Therefore, Expected YTM = 2 x R = 2 x 6.765 ~ 13.53 % approximately.
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