Question

What is the price of a junk bond that makes quarterly coupon payments of $10 until maturity? Maturity date is in ten years. Face value is $1,000. Market rate for junk bonds is 10%. 10 What is the price of the junk bond if expected inflation increases by 4 percentage points?

Answer 1

Calculating price of bond today

Face value = $1000, Quarterly coupon payments = $10, Market rate = 10%

No of quarters to maturity = 4 x no of years to maturity = 4 x 10 = 40

Quarterly discount rate = Market rate / 4 = 10% / 4 = 2.50%

We know that price of bond is equal to present value of future cash flows, Future cash flows consist of quarterly coupon payments and face value payment at maturity. We can find the present value of future cash flows or price of bond using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt,-fv)

Using PV function in excel, we get price of junk bond = $623.4583

Price of Junk bond = $623.4583

If the expected inflation increases by 4%, then interest rates for all maturities will increase by 4%

So New market rate = 10% + 4% = 14%

New quarterly rate = New market rate / 4 = 14% / 4 = 3.5%

Similar to above we can find the price of junk bond using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt,-fv)

Using PV function in excel, we get price of junk bond when expected inflation increases by 4% = $466.1231

Hence Price of bond when expected inflation increases by 4% = $466.1231