Question
In: Finance
Cyberdyne Systems is issuing a series of coupon bonds to raise $250M to fund research and...
Cyberdyne Systems is issuing a series of coupon bonds to raise $250M to fund research and development at its Skynet division. Each bond will have a face value of $1,000 and will mature in 10 years. The bonds will pay semi-annual coupons with a coupon rate of 6.5%. The yield to maturity on the bonds is 10%. What is the fair price for one of the bonds?
A) $700.23
B) *$781.91
C) $876.54
D) $933.41
E) $1,000.00
The answer is B, please show the work.
Solutions
Expert Solution
| Since there are semi annual coupon payment so interest rate will be 3.25%, yield will be 5%, number of years to maturity will | |||||
| be 20 years | |||||
| Statement showing Fair price of one bond | |||||
| Particulars | Time | PVf @5% | Amount | PV | |
| Cash Flows (Interest) | 1.00 | 0.9524 | 32.50 | 30.95 | |
| Cash Flows (Interest) | 2.00 | 0.9070 | 32.50 | 29.48 | |
| Cash Flows (Interest) | 3.00 | 0.8638 | 32.50 | 28.07 | |
| Cash Flows (Interest) | 4.00 | 0.8227 | 32.50 | 26.73 | |
| Cash Flows (Interest) | 5.00 | 0.7835 | 32.50 | 25.46 | |
| Cash Flows (Interest) | 6.00 | 0.7462 | 32.50 | 24.25 | |
| Cash Flows (Interest) | 7.00 | 0.7107 | 32.50 | 23.10 | |
| Cash Flows (Interest) | 8.00 | 0.6768 | 32.50 | 22.00 | |
| Cash Flows (Interest) | 9.00 | 0.6446 | 32.50 | 20.95 | |
| Cash Flows (Interest) | 10.00 | 0.6139 | 32.50 | 19.95 | |
| Cash Flows (Interest) | 11.00 | 0.5847 | 32.50 | 19.00 | |
| Cash Flows (Interest) | 12.00 | 0.5568 | 32.50 | 18.10 | |
| Cash Flows (Interest) | 13.00 | 0.5303 | 32.50 | 17.24 | |
| Cash Flows (Interest) | 14.00 | 0.5051 | 32.50 | 16.41 | |
| Cash Flows (Interest) | 15.00 | 0.4810 | 32.50 | 15.63 | |
| Cash Flows (Interest) | 16.00 | 0.4581 | 32.50 | 14.89 | |
| Cash Flows (Interest) | 17.00 | 0.4363 | 32.50 | 14.18 | |
| Cash Flows (Interest) | 18.00 | 0.4155 | 32.50 | 13.50 | |
| Cash Flows (Interest) | 19.00 | 0.3957 | 32.50 | 12.86 | |
| Cash Flows (Interest) | 20.00 | 0.3769 | 32.50 | 12.25 | |
| Cash flows (Maturity Amount) | 20.00 | 0.3769 | 1,000.00 | 376.90 | |
| Fair Price | 781.91 | ||||
| Therefore answer is B) $781.91 | |||||
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