A private, for profit clinic has a bond issue outstanding with a coupon rate of

Question

A private, for profit clinic has a bond issue outstanding with a coupon rate of 8 percent and five years remaining until maturity. The par value of the bond is $1000, and the bond pays interest annually.

What is the current value of the bond if present market conditions justify a 16% required rate of return?

Now suppose the center’s five-year bond had semiannual coupon payments. What is its current value? (assume an 8% semiannual required rate of return. But the actual rate would be slightly less than 8% because a semiannual coupon bond is slightly less risky than an annual coupon bond).

Now assume that the center’s bond had a semiannual coupon but 30 years remaining to maturity. What is the current value under these conditions? (assume an 8% semiannual required rate of return. But the actual rate would be slightly greater than 7% because of increased price risk).

Please show all work. and formula used.

Explanation / Answer

The present value of a bond is obtained by using the excel formula =pv(rate,nper,pmt,fv) where rate is the yield, nper is the number of periods, pmt is the coupon payment, abd fv is the face value

a. rate = 16% = 0.16, nper = 5 years, pmt = 8% of 1000 = $80 annually, fv =1000

=pv(0.16,5,80,1000) = $738.06 ; Hence value of the bond is 738.06

b. Now the 8% coupon is paid semi annual. Therefore, the semi-annual rate is 4% twice a yera

rate =0.16/2 = 0.08, nper = 10 (because semi annual), pmt = 40, fv =1000

=pv(0.08,10,40,1000) = $731.06. Hence the value of the bond is $731.06

c. When number of years becomes 30 years

rate =0.08, nper = 60 (30 *2 because semi annual), pmt 40, fv=1000

=pv(0.08,60,40,1000) = $504.94. The bond value reduces to $504.94

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