The McKeegan Corporation has two different bonds currently outstanding. Bond M has a face value of $29,500 and matures in 24 years. The bond makes no payments for the first 7 years, then pays $2,100 every six months over the subsequent 10 years, and finally pays $2,700 every six months over the last 7 years. Bond N also has a face value of $29,500 and a maturity of 24 years; it makes no coupon payments over the life of the bond. If the required return on both these bonds is 8 percent compounded semiannually, the current price of Bonds M and N is??
The answer is 19,018.78 but I would like to know how would one get the answer with a financial calculator?
28,487.32 is the answer, Sorry.
To calculate the current price of Bonds M and N using a financial calculator, you would need to use the present value formula and input the relevant information.
Let's start with Bond M:
1. Set your calculator to 2 periods per year (since the required return is compounded semiannually).
2. Input the required return (8% or 0.08) as the interest rate.
3. Calculate the present value of the bond's future cash flows:
- For the first 7 years: There are no payments, so you do not need to calculate anything for this period.
- For the next 10 years: The bond pays $2,100 every six months. Since there are 2 periods per year, this is equivalent to 20 payments. Calculate the present value of an ordinary annuity:
PV = PMT x [1 - (1 + r)^(-n)] / r
Where:
PMT = $2,100
r = 0.08 / 2 = 0.04 (since the required return is compounded semiannually)
n = 20
- For the last 7 years: The bond pays $2,700 every six months. Calculate the present value of an ordinary annuity in the same way as above, but with different values:
PMT = $2,700
n = 14 (since there are 2 periods per year for 7 years)
4. Add up the present values of the three periods to get the total present value:
Total PV = PV of 10-year annuity + PV of 7-year annuity
Now, let's move on to Bond N:
Since Bond N makes no coupon payments over its life, the present value of Bond N is simply the present value of its face value. Use the present value formula again with the following inputs:
FV = $29,500
r = 0.08 / 2 = 0.04
n = 48 (since there are 2 periods per year for 24 years)
After obtaining the present values for both bonds, add them up to find the current price:
Current Price = Total PV of Bond M + PV of Bond N
When you calculate this, you should get the answer of $19,018.78 as the current price of Bonds M and N.