Question

1A) Your client is considering the purchase of a bond that is currently selling for $941.03. The client wants to know what annual rate of return can they expect to earn on the bond. The bond has 11 years to maturity, pays a coupon rate of 7.1% (payments made semi-annually), and a face value of $1000. (Round to 100th of a percent and enter your answer as a percentage, e.g., 12.34 for 12.34%)

1B) What is the market price of a bond with a maturity of 19 years, a coupon rate of 4.8% paid semi-annually, a par value of $1000, and a yield to maturity of 5.8%. (Round your answer to the nearest penny.)

1C) What is the most we should pay for a bond with a par value of $1000, coupon rate of 11.6% paid annually, and a remaining life of 17 years? The yield to maturity is 3.8%. Assume annual discounting. (Round your answer to the nearest penny.)

ANSWER

Answer 1

1A)

YTM = {Coupon Amt + (Redemption Amount - Price / Maturity in Periods)} / (Redemption Amt + Price / 2 )

This is an approximate formulae of YTM however you can also calculate it by Interpolation answer will be slightly differ.

Coupon amt = 1000 * 7.1% * 6/12 = 35.5

N = 22 no. of Period

Price = 1000

Redemption Amt = 1000

Therefore = {35.5 + (1000-941.03/22)} / (1000+941.03/2)

= 3.93%

1B)

Market Price is PV of all future cashflow

PVAF present Value Annuity Factor

PVIF present value discounting factor

Coupon = 4.8% of 1000 / 2 = 24

r Rate of Interest required YTM = 5.8/2 = 2.9

n Maturity No. of period = 19*2 = 38

Price = Coupon PVAF(r,n)+ Redemption PVIF (r,n)

= 24 PVAF (2.9%,38) + 1000 PVIF (2.9%,38)

= 24(22.846382) + 1000 ( 0.3374549)

= 548.31 + 337.4549

= 885.75

1C)

Market Price is what we should pay Maximum at Required rate.

Price = Coupon PVAF(r,n)+ Redemption PVIF (r,n)

Market Price is PV of all future cashflow

PVAF present Value Annuity Factor

PVIF present value discounting factor

Coupon = 11.6% of 1000 = 116

r Rate of Interest required YTM = 3.8

n Maturity No. of period = 17

= 116 PVAF (3.8%, 17) + 1000 (3.8%, 17)

= 116(12.35656) + 1000 (0.53045065526)

= 1433.36 + 530.45

= 1963.80

Assuming Redemption at Par in Each Bond.