Question

In: Finance

12 percent bond, face value of $1,000 , life of 5 years. return required by the...

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.

Solutions

Expert Solution

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%


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