Question

Microhard has issued a bond with the following characteristics:

Par: $1,000

Time to maturity: 13 years

Coupon rate: 8 percent

Semiannual payments

Calculate the price of this bond if the YTM is (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.):

8%-

10%

^%-

Answer 1

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Price of this bond if the YTM = 8%

The bond will trade at par as YTM=coupon rate.

Current Market Price of Bonds = $1,000

Price of this bond if the YTM = 10%

Prima facie, the bond will trade at discount as YTM>coupon rate

Year	Cash flow	PVAF/PVF@5%	Present Value (Cashflow*PVAF/PVF)
1-26	40	14.3752*	575.01
26	1000	0.2812**	281.24

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 575.01+281.24

= $856.25

Note : Since the bond makes semiannual interest payments, total no. of period is 26 (13*2), cashflow per period is 40(1000*8%/2) and cashflows are discounted at 5% (10/2).

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n

Price of this bond if the YTM = 6%

Prima facie, the bond will trade at Premium as YTM<coupon rate

Year	Cash flow	PVAF/PVF@3%	Present Value (Cashflow*PVAF/PVF)
1-26	40	17.8768	715.07
26	1000	0.4637	463.69

Current Market Price of Bonds = Cashflow*PVAF/PVF

= 715.07+463.69

= $1178.77

Note : Since the bond makes semiannual interest payments, total no. of period is 26 (13*2), cashflow per period is 40(1000*8%/2) and cashflows are discounted at 3% (6/2).

*PVAF = (1-(1+r)^-n)/r

**PVF = 1 / (1+r)^n