Question

Microhard has issued a bond with the following characteristics:

Par: $1,000

Time to maturity: 20 years

Coupon rate: 8 percent

Semiannual payments

Calculate the price of this bond if the YTM is:

a. 10 percent

b. 8 percent

c. 6 percent

Bond yields are quoted as APRs.

For part a, use 3 methods to calculate the bond price:

1. PV of future cash flows;

2. Bond price formula;

3. Excel built-in function “PRICE”.

For parts b and c, use excel.

Answer 1

Coupons=8%*1000/2=40
Face value=Par=1000
Years to maturity=20
Periods to maturity=20*2=40
Hence, there will be 40 cash flows of coupon=40 and 1 cash flow of 1000

a)

1.
Coupons are in the form of an annuity
PV of coupons=Coupons/periodic rate*(1-1/(1+periodic rate)^n)

Face value is a lumps um in future
PV of face value=Face value/(1+periodic rate)^n

PV of future cash flows=PV of coupons+PV of face value=40/5%*(1-1/1.05^40)+1000/1.05^40=828.4091365

2.

=40/1.05+40/1.05^2+40/1.05^3....40/1.05^40+1000/1.05^40

=828.4091365

3.

=PRICE(DATE(2001,1,1),DATE(2021,1,1),8%,10%,100,2)/100*1000

=828.4091365

Alternatively

=PV(10%/2,20*2,-8%*1000/2,-1000)

=828.4091365

b)

=PRICE(DATE(2001,1,1),DATE(2021,1,1),8%,8%,100,2)/100*1000

=1000

c)

=PRICE(DATE(2001,1,1),DATE(2021,1,1),8%,6%,100,2)/100*1000

=1231.14772