Question

Suppose you purchase a​ 10-year bond with 6.4% 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 5.4% 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 annual rate of return of your​ investment?

Answer 1

Face Value = $100

Annual Coupon Rate = 6.40%
Annual Coupon = 6.40% * $100
Annual Coupon = $6.40

At the time of purchase:

Time to Maturity = 10 years
Annual YTM = 5.40%

Price of Bond = $6.40 * PVIFA(5.40%, 10) + $100 * PVIF(5.40%, 10)
Price of Bond = $6.40 * (1 - (1/1.054)^10) / 0.054 + $100 / 1.054^10
Price of Bond = $107.57

At the time of sale:

Time to Maturity = 6 years
Annual YTM = 5.40%

Price of Bond = $6.40 * PVIFA(5.40%, 6) + $100 * PVIF(5.40%, 6)
Price of Bond = $6.40 * (1 - (1/1.054)^6) / 0.054 + $100 / 1.054^6
Price of Bond = $105.01

Answer a.

Cash Flows:

Year 0 = -$107.57
Year 1 = $6.40
Year 2 = $6.40
Year 3 = $6.40
Year 4 = $6.40 + $105.01 = $111.41

Answer b.

Let annual rate of return be i%

$107.57 = $6.40 * PVIFA(i%, 4) + $105.01 * PVIF(i%, 4)

Using financial calculator:
N = 4
PV = -107.57
PMT = 6.40
FV = 105.01

I = 5.40%

Annual Rate of Return = 5.40%