Question

14. Suppose that you buy a semi-annual coupon bond with coupon rate of 10%;
the market price of $1,120, and the time to maturity of 17 years. Seven years from now,
the YTM on your bond is expected to decline by 2%, and you plan to sell. What is the
holding period yield (HPY) on your investment?

Could you explain the question in detail with formula plz! I don't understand others poster answers.

Answer 1

Holding Period Yeild = {(Income Received) + (End Value - Beginning Value) } / Beginning Value

Income Received ( in form of dividends in 7 years) = $50 semiannualy for 14 periods = 50*14 = $700

Beginning Value = $1120

Ending Value = ?? ( We have to find out) i.e the price at which we sold the bond at the end of 7 Years.

From the question we can infer that, the Yield to Maturity declined by 2% from the year "0".

So lets calculate the YTM at Year "0" and reduce it by 2% (for YTM at end of year seven)

Using Excel Sheet , Rate Formula, YTM is calulated as below:

	(IN Rs.)
CURRENT BOND VALUE	-1120
NO. OF PERIODS	34
FACE VALUE OF BOND	1000
SEMI ANNUAL PAYMENT AMOUNT	50
		YTM Formula
YIELD TO MATURITY (YTM) for 17 Years	4.320%	RATE(34,50,-1120,1000)

We can observe that the YTM for 17 Year Period if we bought bond at price of $1120 is 4.320%

We plan to sell the bond in year seven, when the YTM on bond will be 2.320% (4.320%-2%) for a person who buys the bond in year seven.

So, Bond Price in year seven @ YTM of 4.320% and 10 Years leftover maturity time (i.e 20 payments leftover) is calculated as below:

Using Excel Calcultate Bond value using PV function

=PV(2.32%,20,50,1000) = $1424.98

So Ending Bond Value = $1424.98

If we sell in year seven, we will sell the bond at a premium of $304.98 (i.e 1424.98-1120) and we would already have received $700 as coupon amount in seven years.

Therefore, total yeild at the time we sell is

Holding Period Yeild = { 700 + (1424.98 - 1120) } / 1120 } *100 = 89.73%