Question

You own a 20-year, $1,000 par value bond paying 6 percent interest annually. The market price of the bond is $750, and your required rate of return is 10 percent.

a. Compute the bond's expected rate of return.

b. Determine the value of the bond to you, given your required rate of return.

c. Should you sell the bond or continue to own it?

Answer 1

In first question we need to find the required rate, we can use excel to find the rate of return using IRR function

Year	Cash flow	Amount
0	Bond price	-750
1	Coupon	60
2	Coupon	60
3	Coupon	60
4	Coupon	60
5	Coupon	60
6	Coupon	60
7	Coupon	60
8	Coupon	60
9	Coupon	60
10	Coupon	60
11	Coupon	60
12	Coupon	60
13	Coupon	60
14	Coupon	60
15	Coupon	60
16	Coupon	60
17	Coupon	60
18	Coupon	60
19	Coupon	60
20	Par + coupon	1060
	Return	8.68%
	Formula	=IRR(C2:C22)

So the return you will get on the bond is 8.68%

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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 = 0.06

                YTM or Required rate = 0.1

                Time to maturity (n) = 20 years

                Annual coupon C = $60

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

P = 60* [{1 - (1 + 0.1) ^ -20}/ (0.1)] + [1000/ (1 + 0.1) ^20]

P = 60* [{1 - (1.1) ^ -20}/ (0.1)] + [1000/ (1.1) ^20]

P = 60* [{1 - 0.14864}/ 0.1] + [1000/ 6.7275]

P = 60* [0.85136/ 0.1] + [148.64363]

P = 60* 8.5136 + 148.64363

P = 510.816 + 148.64363

P = 659.45963

So price of the bond is $659.46

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The bond is overvalued, its price should be (659.46) at the 10% required rate of return, however it s priced at 750, so you should sell the bond.

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Hope this answer your query.

Feel free to comment if you need further assistance. J