Question
In: Finance
Suppose you purchase a 10-year callable bond issued by ABC Corp. with annual coupons of $20....
Suppose you purchase a 10-year callable bond issued by
ABC Corp. with annual
coupons of $20. Its redemption amount is $100 at the ends of years
2-4, is $80 at
the ends of years 5-7, is $60 at the ends of years 8-10. The market
annual effective
interest rate is i = 5%. In the following, t represents the time
immediately after the
t-th coupon is paid.
(a) Calculate the highest price at time t = 0 guaranteeing a yield
rate no less than
5%.
(b) Calculate the highest price at time t = 6 guaranteeing a yield
rate no less than
5%.
(c) Suppose the bond is called at the end of 8 years (i.e., t = 8).
At t = 8, to replicate
the cash inflows that you would have received at the end of years 9
and 10 (had
the bond not been called earlier), you can purchase zero-coupon
bonds (ZCBs).
Two ZCBs available in the market are (#1) 1-year ZCB and (#2)
10-year ZCB.
Suppose you can purchase each ZCB for any face value that you would
like and
sell them at any time at a price calculated by the yield rate i =
5%. Design two
strategies by using
(i) both ZCBs
(ii) ZCB #2 only
Solutions
Expert Solution
| Bond Price Calculator | |||||||
| Since coupon rate is higher than Interest rate, it is better to invest in the bond | |||||||
| The Value of bond at end of each year will be PV of expected cash inflows in succeeding years | |||||||
| Bond Value at time T=0 | |||||||
| Year | Annual Coupon | Redemption Value if exercised) | Interest rate | cash Inflow to maximise rev | PV factor (1/(1+r)^2) | Cash Inflow from that year | |
| 0 | $ - | $ - | 5% | $ - | 1.00 | $ - | |
| 1 | $ 20 | $ - | 5% | $ 20 | 0.95 | $ 19 | |
| 2 | $ 20 | $ 100 | 5% | $ 20 | 0.91 | $ 18 | |
| 3 | $ 20 | $ 100 | 5% | $ 20 | 0.86 | $ 17 | |
| 4 | $ 20 | $ 100 | 5% | $ 20 | 0.82 | $ 16 | |
| 5 | $ 20 | $ 80 | 5% | $ 20 | 0.78 | $ 16 | |
| 6 | $ 20 | $ 80 | 5% | $ 20 | 0.75 | $ 15 | |
| 7 | $ 20 | $ 80 | 5% | $ 20 | 0.71 | $ 14 | |
| 8 | $ 20 | $ 60 | 5% | $ 20 | 0.68 | $ 14 | |
| 9 | $ 20 | $ 60 | 5% | $ 20 | 0.64 | $ 13 | |
| 10 | $ 20 | $ 60 | 5% | $ 80 | 0.61 | $ 49 | |
| Bond Value at time T=0 | $ 191 | ||||||
| Bond Value at time T=6 | After time T= 6, only 4 coupon payments are left for T=7, 8, 9, 10) | ||||||
| Year | Annual Coupon | Redemption Value if exercised) | Interest rate | cash Inflow to maximise rev | PV factor (1/(1+r)^2) | Cash Inflow from that year | |
| 1 | $ 20 | $ 80 | 5% | $ 20 | 0.95 | $ 19 | |
| 2 | $ 20 | $ 80 | 5% | $ 20 | 0.91 | $ 18 | |
| 3 | $ 20 | $ 60 | 5% | $ 20 | 0.86 | $ 17 | |
| 4 | $ 20 | $ 60 | 5% | $ 20 | 0.82 | $ 16 | |
| Bond Value at time T=6 | $ 71 | ||||||
| C(i) | |||||||
| Buying a 1 year ZCB and 10 year ZCB to get the cash flow | |||||||
| One would have received the following in time T=9 | $20 | ||||||
| One would have received the following in time T=10 | $80 | ||||||
| At T=8 we will get the following table | |||||||
| The cash inflow should be $20 | |||||||
| FV/PV factor=Cost of Bond | |||||||
| Cash Inflow | Amount to be invested | ||||||
| PV factor of ZCB for 1 year bond | 1/(1+5%)^1 | 0.952380952 | $20 | 19.04761905 | |||
| We need to buy a bond whose price will be $80 in 2 years growing at 5% pa | |||||||
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