Question

Suppose a​ ten-year, $ 1000 bond with an 8.5 % coupon rate and semiannual coupons is trading for $ 1035.41.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to 9.1 % ​APR, what will be the​ bond's price?

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)	-1035.41
1	Coupon (Inflow)	42.5
2	Coupon (Inflow)	42.5
3	Coupon (Inflow)	42.5
4	Coupon (Inflow)	42.5
5	Coupon (Inflow)	42.5
6	Coupon (Inflow)	42.5
7	Coupon (Inflow)	42.5
8	Coupon (Inflow)	42.5
9	Coupon (Inflow)	42.5
10	Coupon (Inflow)	42.5
11	Coupon (Inflow)	42.5
12	Coupon (Inflow)	42.5
13	Coupon (Inflow)	42.5
14	Coupon (Inflow)	42.5
15	Coupon (Inflow)	42.5
16	Coupon (Inflow)	42.5
17	Coupon (Inflow)	42.5
18	Coupon (Inflow)	42.5
19	Coupon (Inflow)	42.5
20	Par + Coupon (Inflow	1042.5
	YTM	3.99%
	Formula	=IRR(G44:G64)

Annual YTM = 3.99* 2 = 7.98% or 8% per year

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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 = 8.5%

                YTM or Required rate = 9.1%

                Time to maturity (n) = 10 years

                Annual coupon C = $85

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

P = 85* [{1 - (1 + 0.091) ^ -10}/ (0.091)] + [1000/ (1 + 0.091) ^10]

P = 85* [{1 - (1.091) ^ -10}/ (0.091)] + [1000/ (1.091) ^10]

P = 85* [{1 - 0.41855}/ 0.091] + [1000/ 2.38917]

P = 85* [0.58145/ 0.091] + [418.5554]

P = 85* 6.38956 + 418.5554

P = 543.1126 + 418.5554

P = 961.668

So price of the bond is $961.67

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