Question

The 10-year Coupon Bond has a face value of $1,000, the annual coupon rate is 5 percent (out of its face value), the yield to maturity is 10 percent.

(2.a) show me the cash flows of this coupon bond, you can use words or a timeline graph you created.

(2.b) compute the price (present value) of this bond

(2.c) suppose the yield to maturity increases to 20 percent after one year, computes the new price. (remember that as time passed by, the timing of all future cash flows is changed. That is, the first coupon is just paid. You can draw a timeline graph to help your understanding)

(2.d) computes the rate of return in 2.c. That is initially you bought at 10 percent YTM and sold at 20 percent YTM. So, it is the return for holding this bond for one year.

Answer 1

a)

10CM C-50 C-50 C-50 C-50 C-50 -50 C-50 C-50 C-50 C-5-| 小小小小小小小小小小 2345

b)

Face/maturity value of bond=FV=$1000

Coupon=C=1000*5%=$50 per year

No. of coupon payments left=n=10

YTM=i=10%

Fair price of bond=50*(P/A,10%,10)+1000*(P/F,10%,10)

Let us calculate the interest factors

(1+i)" (P/A,,n)=1

1 - (Ρ/Α, 0.10, 10) =- (1+0, 10) 10 - = 6.144567 0.10

(P/F,10%,10)=1/(1+0.10)^10=0.385543

Fair price of bond=50*6.144567+1000*0.385543=$692.77

c)

In this case

Face/maturity value of bond=FV=$1000

Coupon=C=1000*5%=$50 per year

No. of coupon payments left=n=9

YTM=i=20%

Fair price of bond=50*(P/A,20%,10)+1000*(P/F,20%,10)

Let us calculate the interest factors

(1+i)" (P/A,,n)=1

1- (1+0.20 (P/A, 0.20,9) = = – 4.030967 0.20

(P/F,20%,9)=1/(1+0.20)^9=0.193807

Fair price of bond=50*4.030967+1000*0.193807=$395.36

d)

Holding period return=(Final Price-Initial Payment+Coupon)/Initial Payment

Holding period return=(395.36-692.77+50)/692.77=35.71%