Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a. Suppose that today you buy a bond with an annual coupon of 6 percent for $1,010. The bond has 15 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000.

b. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for?

c. What is the HPY on your investment?

Answer 1

Yield to maturity is the rate of return the investor will get if he/she hold the bold till maturity period

So YTM is like Internal rate of return, if we discount all the cash inflow from the bond using YTM, the present value will be equal to the bond current price.

YTM is calculated using Excel, the function used is (IRR)

Pls refer below table

Year	Cash flow	Amount
0	Bod price (Outflow)	-1010
1	Coupon (Inflow)	60
2	Coupon (Inflow)	60
3	Coupon (Inflow)	60
4	Coupon (Inflow)	60
5	Coupon (Inflow)	60
6	Coupon (Inflow)	60
7	Coupon (Inflow)	60
8	Coupon (Inflow)	60
9	Coupon (Inflow)	60
10	Coupon (Inflow)	60
11	Coupon (Inflow)	60
12	Coupon (Inflow)	60
13	Coupon (Inflow)	60
14	Coupon (Inflow)	60
15	Coupon (Inflow)	1060
	YTM	5.90%
	Formula	=IRR(G44:G64)

So YTM of the bond is 5.9%

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Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 8%

                YTM or Required rate = 4.9%

                Time to maturity (n) = 13 years

                Annual coupon C = $80

Let's put all the values in the formula to find the bond current value

P = 80* [{1 - (1 + 0.049) ^ -13}/ (0.049)] + [1000/ (1 + 0.049) ^13]

P = 80* [{1 - (1.049) ^ -13}/ (0.049)] + [1000/ (1.049) ^13]

P = 80* [{1 - 0.53693}/ 0.049] + [1000/ 1.86244]

P = 80* [0.46307/ 0.049] + [536.93005]

P = 80* 9.45041 + 536.93005

P = 756.0328 + 536.93005

P = 1292.96285

So price of the bond is $1292.96

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Holding period return = [120 (1292.96 – 1010)]/1010

Pls note we need to add the two couppon payment

                                         = (120 + 282.96)/1010

                                          = 402.96/1010

= .39897 or 39.89 % or 39.9% or 40%

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Hope that helps.

Feel free to comment if you need further assistance J