Question

Consider a five-year bond with a face value of $500,000 and semi-annual coupon of $19,000. The market yield is 7.00% p.a.

(a) What is the price of the bond?

(b) We hold the bond for 1.5 years and then sell it at a yield of 7.50% p.a. What is the selling price and what is the holding period yield p.a. on this investment? (Show all your workings and round off your result to two decimals)

Answer 1

a]

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 7%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 5 * 2 (5 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 19000 (semiannual coupon payment)

fv = 500000 (face value receivable on maturity)

PV is calculated to be $512,474.91

b]

Selling price is calculated using PV function in Excel :

rate = 7.5%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 3.5 * 2 (3.5 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 19000 (semiannual coupon payment)

fv = 500000 (face value receivable on maturity)

PV is calculated to be $501,514.48

Holding period yield = (selling price - purchase price + total semiannual payments received during holding period) / purchase price

Holding period yield = ($501,514.48 - $512,474.91 + ($19,000 * 3)) / $512,474.91

Holding period yield = 8.98%

Holding period yield (per annum) = (1 + 8.98%)^1/1.5 - 1

Holding period yield (per annum) = 5.90%