Question
In: Finance
A firm's bonds have a maturity of 14 years with a $1,000 face value, have an...
A firm's bonds have a maturity of 14 years with a $1,000 face value, have an 11% semiannual coupon, are callable in 7 years at $1,225.17, and currently sell at a price of $1,385.12.
What is their nominal yield to maturity? Do not round
intermediate calculations. Round your answer to two decimal
places.
What is their nominal yield to call? Do not round intermediate
calculations. Round your answer to two decimal places.
Solutions
Expert Solution
| Data given in the question is as follows:- | |||||||||
| a) | Face value | = | $1,000.00 | ||||||
| b) | Current Price | = | $1,385.12 | ||||||
| c) | Call Price | = | $1,225.17 | ||||||
| d) | Years to Maturity | = | 14 years | ||||||
| e) | Years to Call | = | 7 years | ||||||
| f) | Annual coupon rate | = | 11% | Semi-annual | |||||
| Therefore Annual Interest = $ 1,000 x 11%/2 x 2 = $ 110 | |||||||||
| Yield to Maturity (YTM) | = | Annual Interest + ( (Face Value - Current Price) / (Years to Maturity) ) | |||||||
| (Face Value + Current Price) / 2 | |||||||||
| = | $ 110 + ( ( $ 1,000 - $ 1,385.12 ) / ( 14 ) ) | ||||||||
| ( $ 1,000 + $ 1,385.12 ) / 2 | |||||||||
| = | $ 110 - $ 27.5086 | ||||||||
| $ 1,192.56 | |||||||||
| = | $ 81.4914 | ||||||||
| $ 1,192.56 | |||||||||
| YTM | = | 6.9172% | |||||||
| Yield to Call (YTC) | = | Annual Interest + ( (Price to Call - Current Price) / (Years to Call) ) | |||||||
| (Price to Call + Current Price) / 2 | |||||||||
| = | $ 110 + ( ( $ 1,225.17 - $ 1,385.12 ) / ( 7 ) ) | ||||||||
| ( $ 1,225.17 + $ 1,385.12 ) / 2 | |||||||||
| = | $ 110 - $ 22.85 | ||||||||
| $ 1,305.145 | |||||||||
| = | $ 87.15 | ||||||||
| $ 1,305.145 | |||||||||
| YTC | = | 6.6774% | |||||||
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