Question

Bond Valuation Assignment A $1,000 par value bond, with a coupon interest rate of 8.4 percent per year paid semiannually, matures in 24 years. Complete the table below by filling in the prices and YTM's that correspond to the given YTM's and prices respectively. You must show ALL WORK in part C (PVA, and PV calculations) and ALL calculator menu inputs in part D for full credit. PRICE YTM 0% b)$1.000 10% $598.139

Answer 1

Coupon amount =8.4%/2 * 1000 =$42

Total no of coupon payments = 24*2 = 48

a) Price P = 42/(1+0) + 42/(1+0)^2 + ... + 42/(1+0)^48 + 1000/(1+0)^48

=(42+42+...+42)+ 1000

= 2016 + 1000 = $3016

b) Let the six monthly YTM be y

1000 = 42/(1+y) + 42/(1+y)^2 + ... + 42/(1+y)^48 + 1000/(1+y)^48

As the Bond price =$1000 = par value

Six monthly YTM = six montly Coupon rate = 4.2%

So, YTM = 4.2% *2 = 8.4%

c) Six monthly YTM =10%/2 = 0.05

Price P = 42/(1+0.05) + 42/(1+0.05)^2 + ... + 42/(1+0.05)^48 + 1000/(1+0.05)^48

= 42* PVA(5%, 48) + 1000 *PV(5%,48)

= 42/0.05* (1-1/1.05^48) + 1000 * 1/1.05^48

=$855.38

d) Let the six monthly YTM be y

598.139 = 42/(1+y) + 42/(1+y)^2 + ... + 42/(1+y)^48 + 1000/(1+y)^48

Using hit and trial method

Putting y = 0.1 makes Right hand side of above equation =  425.98

Putting y = 0.08 makes Right hand side of above equation =  536.81

Putting y = 0.075 makes Right hand side of above equation =  573.67

Putting y = 0.07 makes Right hand side of above equation =  615.55

So, y lies between 0.07 and 0.075

Putting y = 0.072 makes Right hand side of above equation =  598.139

So, YTM = six monthly YTM * 2 = 0.072*2 = 14.4%