A $5,000 bond with a coupon rate of 5.7% paid semiannually has four years to maturity...
A $5,000 bond with a coupon rate of 5.7% paid semiannually has four years to maturity and a yield to maturity of 6.8%.
If interest rates fall and the yield to maturity decreases by 0.8%, what will happen to the price of the bond?
Homework Answers
Calculating Price of bond when Yield to maturity is 6.8%
Face value = $5000,
As coupons are paid semi annually, therefore
Semi annual coupon payment = (Coupon rate x Face value) / 2 = (5.7% x 5000) / 2 = 285 / 2 =$142.50
No of half years to maturity = 2 x no of years to maturity = 2 x 4 = 8
Semi annual yield to maturity = Yield to maturity / 2 = 6.8% / 2 = 3.4%
Price of a bond can be found out finding present value of semi annual coupon payments and face value payment by discounting at semi annual yield to maturity. We can find the present value or price 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 bond when Yield to maturity is 6.8% = $4810.1747
Calculating Price of bond when Yield to maturity decreases by 0.8%
New Yield to maturity = 6.8% - 0.8% = 6.0%
New Semi annual Yield to maturity = New Yield to maturity / 2 = 6% / 2 = 3%
Now we can use PV function in excel to calculate new price of bond
Formula to be used in excel: =PV(rate,nper,-pmt,-fv)
Using PV function in excel, we get new price of bond = $4947.3523
We can see that due decrease in Yield to maturity or interest rates, price of bond rises
Increase in Price of bond = New price - Old price = 4947.3523 - 4810.1747 = 137.1776 = $137.18
Answer: Price of bond will rise by $137.18
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