Question

please solve with an explanation. thank you!

Cinqua Terra Incorporated issued 10-year bonds three years ago with a coupon rate of 8.00% APR. The bonds pay semi-annual coupons, have a face value of $1,000 each and were issued at par value. Cinqua Terra bonds currently trade at $1,051.00.

Given your answer to the 6-month return, what is the yield to maturity (as an EAR) for holding the bond?

Answer 1

Par value of bond = $1000

Residual Maturity in years = 7

Residual Maturity in semi-annual periods = 7*2 = 14

Coupon Rate = 8%

Semi annual coupon = coupon rate*par value/2 = 8%*1000/2 = $40

Bond price = $1051

Yield to maturity (YTM) can be calculated using the RATE function in spreadsheet

RATE(number of periods, payment per period, present value, future value, when-due, rate guess)

Where, number of periods = no.of semi annual periods = 14

payment per period = Semi annual coupon = $40

present value = price of bond = $1051

future value = par vaue = $1000

when-due = when is the coupon payment made each semi-annual period = end = 0

rate guess = a guess of the YTM = 3.5%

Yield to maturity (YTM) = RATE(14, 40, -1051, 1000, 0, 3.5%) = 3.5320%

This is the semi-annual YTM

Annualised yield to maturity = (1+semi-annual YTM)²-1 = (1+3.5320%)²-1 = 7.1887%

Yield to maturity (as an EAR) = 7.1887%