question archive A 4-year zero coupon bond has a face value of $100 and a price of $85
A 4-year zero coupon bond has a face value of $100 and a price of $85
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A 4-year zero coupon bond has a face value of $100 and a price of $85.480. The table below contains prices, coupons and time to maturity for 3 annual coupon paying bonds that have a face value of $100.
|
Time to Maturity (Years) |
Annual Coupon |
Price |
|
1 |
3.0% |
$99.038 |
|
2 |
8.5% |
$108.487 |
|
3 |
6.5% |
$106.937 |
Please use 3 decimal places in your working.
a) What is the price of a 3-year bond paying annual coupons of 4% and a face value of $100?
b) If you had $1million invested in the 3-year 4% coupon bond, how many of the 4-year zero-coupon bonds would you need to short-sell to hedge your interest rate risk?
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Answer:
Value of 4 year zero coupon bond is equal to the present value today of face value receivable at maturity.
Present value(Bond price)=Face value/(1+r)^n
85.480=100/(1+r)4
(1+r)^4=100/85.480
1+r=1.1698643^(1/4)
r=1.04-1
r=.04
Hence Yield to maturity of the bond is 4%.
We shall check whether the ytm of all bonds is also 4% ?
YTM is can be calculated in excel using irr function as shown below.
We can see that ytm of all bonds is 4%. This means we can earn the annual return of $4 if we invest $100.
2a) At 4% ytm the value of bond shall be 100 itself because rate of earning and earning value is same.See below:
| Year | Cash flow | PV factor @4% | PV |
| 1 | 4 | 0.961538462 | 3.846154 |
| 2 | 4 | 0.924556213 | 3.698225 |
| 3 | 104 | 0.888996359 | 92.45562 |
| 100 |
2b) Amount invested in 3 year 4% coupon bond=1000000
Value of 4 year zero coupon bond=85.480
Number of zero coupon bond to short=1000000/85.480
=11698.64
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