Question

Calculate the fair present values of the following bonds, all of which pay interest semiannually, have...

Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of,\$1000, have 5 years remaining to maturity, and have a required rate of return of 10 percent

1. the bond has a 6 percent coupon rate.
2. the bond has a 8 percent coupon rate.
3. the bond has a 10 percent coupon rate.
4. what do your answers to parts (a) through (c) say about the relation between coupon rates and present values

Value of a bond is present value of future cash flows discounted at YTM

1)

When coupon = 6%

periodic coupons = 1000*6%/2 = \$30

Number of periods = 5* 2 = 10

Required return = 10% / 2 = 5%

Present value= 30*PVIFA(r=5% ;n=10) +1000*PVF(r=5%;n=10)

Present value = 30*7.72173 + 1000*0.6139 = \$845.57

2)

Here everything remains same except

Coupon = 1000*8%/2 = 40

Present value = 40*PVIFA(r = 5% ; n = 10)

+ 1000*PVF(r = 5% ; n = 10)

Present value = \$922.78

3)

When coupon rate = required return , present value of bond will be par value

So present value of bond = \$1000

conclusion:

when coupon rate increases present value of the bond increases

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