Question

A bond with seven years to maturity pays a 5.5% coupon semiannually. The par value of the bond is $1,000 and the current price is $971.76.

a) If you bought the bond today, what yield to maturity would you earn if you held it to maturity?

b) If you sold it for $986.22 in one year, what would your total return be? Assume you collect both coupon payments.

Answer 1

a) If you bought the bond today, what yield to maturity would you earn if you held it to maturity?

Yield To Maturity(YTM) = (interest per period+ ((Redemption price - Current market price) / life remaining to maturity)) / ((.4*Redemption price)+ (.6*Current market price))

= ((1000*5.5%/2)+(1000-971.76)/(7*2)) / (.4*1000+.6*971.76)

= (27.5+2.01714285714) / 983.056

= 29.5171428571/983.056

= 3.00% per semi annum

= 6.00% per annum

b) If you sold it for $986.22 in one year, what would your total return be?

Investor's total return comprises of 2 elements-capital gain/loss (change in market price) and coupon payment.

Rate of Return = (Sale value - cost of acquisituion + coupon pay) / cost of acquisituion

= (986.22-971.76+55)/971.76

= 69.46/971.76

= 7.15%

Total return in $ = Sale value - cost of acquisituion + coupon pay

= 986.22-971.76+55

= 69.46