In: Finance
12 percent bond, face value of $1,000 , life of 5 years. return required by the market is 10 percent coupon payments are made once annually.
Figure out price of bond at time of flotation on the market.
end of year three, the market requires a return of 8 percent instead of 10 percent find the market price at this time.
What is the yield of a two year zero coupon bond, when the market price is $970 and a face –value of $1000.
The Price of the bond is the present value of all its future payments.
Given:
Coupon rate = 12%
Face Value = $ 1000
Years until Maturity = 5
Rate of return (ytm) = 10%
Coupon Payments are made annually. Let us now find the coupon payments for 5 years and discount them to the Present Value.
Coupon Payment = Coupon rate * Face Value of the Bond
Coupon Payment = 12% * 1000 = $ 120
Discounting Factor = 1/(1+r)n , where r is the ytm = 10%, n is the corresponding year
PV of Payments = Payments * Discounting Factor of Payment
In the year 5 (Maturity Year), Face value of the Bond is returned, hence 1000 is also considered in the calculations.
Year | Payments | Discounting Factors | PV of Payments |
1 | 120 | 0.9091 | 109.09 |
2 | 120 | 0.8264 | 99.17 |
3 | 120 | 0.7513 | 90.16 |
4 | 120 | 0.6830 | 81.96 |
5 | 1120 | 0.6209 | 695.43 |
Bond Price | 1075.82 |
Bond Price is the sum of all the PV of the Payments.
Bond Price = $ 1,075.82
Given that at the end of year three, the market requires a return of 8 percent instead of 10 percent find the market price at this time.
Here, Tenure of the bond = 5-3 = 2 years
ytm = 8%
Hence, the calculations are as follows:
At the end of two years from now, the Face value of the bond is returned and the coupon payments are made for the next two years.
Here In the discounting factor calculation, r=8% is used instead of 10%.
Year | Payments | Discounting Factors | PV of Payments |
1 | 120 | 0.9259 | 111.11 |
2 | 1120 | 0.8573 | 960.22 |
Bond Price | 1071.33 |
Hence, The Bond Price at the end of 3 years with market rate of return of 8% is $ 1,071.33
Yield of a two year zero coupon bond, when the market price is $970 and a face –value of $1000.
Tenure = 2 years
Market Price = $ 970
Face Value = $ 1,000
Zero coupon bond
Price of a zero coupon bond = M / (1+r)n
(1+r)n = M / Price
1 + r = (M / Price)(1/n)
r = (M / Price)(1/n) -1
Here, M is the Maturity Value = 1000
Price is the Market Price = 970
n is the number of years until maturity = 2
r is the required rate of interest / yield
Upon substituting, r = (1000 / 970)(1/2) -1
r = 0.015346 = 1.53%
Hence Yield = 1.53%