Question

Suppose you purchase a​ 10-year bond with 6.3% annual coupons. You hold the bond for four years and sell it immediately after receiving the fourth coupon. If the​ bond's yield to maturity was 4.5% when you purchased and sold the​ bond,

a. what cash flows will you pay and receive from your investment in the bond per $100 face​ value?

b. what is the rate of return of your​ investment?

Answer 1

Answer :(a.) Calculation of Cash flows will bond will receive and pay :

Cash Flows to be recived each year for 4 years Coupon Payments of 6.3 (100 * 6.3%) anmd sale value of the bond as showun below .

Purchase Price of the bond can be calculated as :

Price of Bond = (Coupon * PVAF @ Yied for n years ) + (Par value * PVF @ Yied for nth year)

Coupon = Par Value * Coupon Rate

= 100 * 6.3% = 6.3

Yield = 4.5%

n is the number of years to maturity i.e 10

Price of Bond = (6.3 * PVAF @ 4.5% for 10 years ) + (100 * PVF @ 4.5% for 10th year)

= (6.3 * 7.9127181768) + (100 * 0.64392768198)

= 49.8501245138 + 64.392768198

= 114.242892711

Sale Price of the bond can be calculated as :

Price of Bond = (Coupon * PVAF @ Yied for n years ) + (Par value * PVF @ Yied for nth year)

Coupon = Par Value * Coupon Rate

= 100 * 6.3% = 6.3

Yield = 4.5%

n is the number of years to maturity i.e 6 (10 - 4)

Price of Bond = (6.3 * PVAF @ 4.5% for 6 years ) + (100 * PVF @ 4.5% for 6th year)

= (6.3 * 5.15787248259) + (100 * 0.76789573824)

= 32.4945966403 + 76.789573824

= 109.284170464

(b.) Rate of Return = [Sale Price + Coupon for 4 years - Purchase Price] / Purchase Price

= [109.284170464 + (6.3 * 4) - 114.242892711] / 114.242892711

= 17.72%