Question

Bond A has a coupon rate of 10.16 percent, a yield to maturity of 4.87 percent, and a face value of 1000 dollars; matures in 15 years, and pays coupons annually with the next coupon expected in 1 year. What is (X+Y+Z) if X is the present value of any coupon payments expected to remade in 6 years from today, Y is the present value of any coupon payments expected to be made in 8 years from today, and Z is the present value of any coupon payments expected to be made in 18 years from today?

Answer 1

Correct Answer X+Y+Z = 13.6481 Dollars

Working:

The present value of the coupon can be calculated using the formula of the time value of money.

The present value of coupon payment = Coupon Amount (1+ R)^N

Here,

• R is YTM or yield to maturity
• N is the time duration

Now since the coupon rate is 10.16% and face value is 1000 dollars

The coupon that will be paid till maturity(15 years) is Coupon rate X face Value

Thus, Coupon amount = 10.16 % * 1000

Coupon amount = 10.16 % * 1000

Coupon amount = 101.6 dollars

Now, finding the values of

• X

As X is the present value of any coupon payments expected to be made in 6 years

X = 101.6 / (1+0.487)⁶ as YTM in the question is 4.87%

X = 101.6 / (1.487)⁶

X = 101.6 / 10.8109

X = 9.3979 Dollars

Similarly for the value of Y,

• Y

As Y is the present value of any coupon payments expected to be made in 8 years

Y = 101.6 / (1+0.487)⁸ as YTM in the question is 4.87%

Y = 101.6 / (1.487)⁸

Y = 101.6 / 23.9049

Y = 4.25017 Dollars

However, Z is the present value of any coupon payments expected to be made in 18 years, and bond maturity is 15 years. Therefore the value of Z is 0

Therefore, X+Y+Z = 9.3979 + 4.25017 + 0

X+Y+Z = 13.6481 Dollars