Question

A bond has 10 years until maturity, carries a coupon rate of 9%, and sells for $1,100. Interest is paid
annually.
a/ If the bond has a yield to maturity of 9% 1 year from now, what will its price be at that time?
b/ What will be the rate of return on the bond?
c/ Now assume that interest is paid semiannually. What will be the rate of return on the bond?
d/ If the inflation rate during the year is 3%, what is the real rate of return on the bond? (Assume
annual interest payments.)

Please carefully at question c), where I think the formula is Rate of return= (Annual coupon + Price change)/ Investment, then the answer should be

Rate of return= [(45x2) + (1000-1100)]/1100= -.909% , which is the same to question b)

Answer 1

Part (a)

If the bond has a yield to maturity of 9% = annual coupon rate 1 year from now, its price will be same as its par value at that time. Hence, the price 1 year from now = Par value = $ 1,000

Part (b)

the rate of return on the bond = (C + P1) / P0 - 1 = (9% x 1000 + 1,000) / 1,100 - 1 = -0.9091%

Part (c)

The first coupon can be reinvested for the next 6 months. Reinvestment rate = YTM

YTM can be found using the RATE function of excel. Since coupon payment is half yearly, hence,

Half yearly YTM, y = RATE (Nper, PMT, PV, FV) = RATE (2 x 10, 9%/2 x 1000, -1100, 1000) = 3.7785%

Hence, the total proceeds at the end of year 1 = P1 + C1 x (1 + y) + C2

where C1 = C2 = Half yarly coupon payment = 9%/2 x 1,000 = 45

Hence, total proceeds at the end of year 1 = 1,000 + 45 x (1 + 3.7785%) + 45 = 1,091.70

Hence, the rate of return on the bond = 1,091.70/1100 - 1 = - 0.7545%

Part (d)

the real rate of return = (1 + r) / (1 + i) - 1 = (1 - 0.9091%) / (1 + 3%) - 1 = - 3.7952%