Question

Assume semiannual compo a coupon rate of 49 12. Valuing Bonds Mycroft Corp. has a $2.000 par value bond outstanding with a cou percent paid semiannually and 13 years to maturity. The yield to maturity of the bo What is the dollar price of the bond? t paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 e outstanding with a coupon rate of 3.7 net

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Answer 1

Bond is a fixed income financial instrument which may issue at par, premium or discount and redeemed at par normally on maturity. Bond pays periodically fixed coupon to bondholder till maturity of bond except in case of zero coupon bond.

Yield to maturity (YTM) is the rate at which Present value all the future cash inflows of bond equals to Price of the Bond.

Thus,

Price of the Bond (B₀) -

$B_{0} = \sum_{y=1}^{n}\frac{C}{(1+y)^n} + \frac{MV}{(1+y)^n}$

Where,

C = coupon

y = yield rate

n = maturity period

MV = Maturity value(par value)

Following information provided in question -

Par Value = $ 2000

Coupon rate = 4.9%

Yield rate = 3.8%

maturity = 13 years

Coupon semi-annually payable

Thus, for semi annual,

Coupon rate = 2.45%

Yield rate = 3.8/2 = 1.9%

Maturity = 13*2 = 26

Please refer below spreadsheet for calculation of Price of Bond -

D10 Bond Par Value 2000 2.45% 1.90% 26 Coupon rate (semi Yield semi 4 Maturity (semi) Period Cash Flows Present Value 49 1-26 26 998.01 1,226.03 2,224.04 2000 $ 10 Price of Bond (B0) 12

Formula reference -

Function Library Defined Names D10 Bond Par Value 2000 0.0245 0.019 26 Coupon rate (semi Yield semi 4 Maturity (semi) Period Cash Flows Present Value -C2 C3 PV(C4,26,-C8,,0 1-26 26 10 Price of Bond (BO SUM(D8:D9)

Thus, Price of Bond is $ 2,224.04

Please note -

Price of Bond is inversely related to yield rate which means when yield rate increase then Bond price fall and vice versa.

Relationship between coupon, yield and Price of bond -

Yield = Coupon, then Price of Bond is equal to Par value.

Yield > Coupon, then Price of Bond is less than Par value.

Yield < Coupon , the Price of Bond is greater than Par value

We can confirm this relationship in our solution, In above situation, Yield < Coupon, that's why Price of Bond is greater than its Par value.