Question

6. Assuming that the current interest rate is 3 percent, compute the present value of a five-year, 5 percent coupon bond with a face value of $1,000. What happens when the interest rate goes to 4 percent

Answer 1

Answer:

Part (a) $1,091.60

Part (b) $1,044.52

Explanation:

Part (a)

Face Value = FV = $1,000

N = 5 Years

r = YTM = 3%

Coupon Rate = 5%

C = Coupon Payment = 5% x $1,000 = $50

PV = ?? We have to calculate the Present Value

PV = C $[\frac{1-\frac{1}{(1+r)^{N} } }{r}]$ + $\frac{FV}{(1+r)^{N} }$

PV = 50 $[\frac{1-\frac{1}{(1+0.03)^{5} } }{0.03}]$ + $\frac{1000}{(1+0.03)^{5} }$ = $1,091.60

Part (b)

Now the interest rate changes to 4%

r = 4%

PV = C $[\frac{1-\frac{1}{(1+r)^{N} } }{r}]$ + $\frac{FV}{(1+r)^{N} }$

PV = 50 $[\frac{1-\frac{1}{(1+0.04)^{5} } }{0.04}]$ + $\frac{1000}{(1+0.04)^{5} }$ = $1,044.52