A tax-exempt bond was recently issued at an annual 12 percent coupon rate and ma

ID: 2761028 • Letter: A

Question

A tax-exempt bond was recently issued at an annual 12 percent coupon rate and matures twenty years from today. The par value of the bond is $1,000.

A. If required market rates are 12 percent, what is the market price of the bond?

B. If required market rates fall to 6 percent, what is the market price of the bond?

C. If required market rates rise to 18 percent, what is the market price of the bond.

D. At what required market rate (6 percent, 12 percent, or 18 percent) does the above bond sell at a discount? At a premium?

Solution:

Market Price of the Bond as on today = Interest x PVIFA (Required Rate of Return, Year) + Maturity Value x PVIF (Required Rate of Return, Year)

Coupon Interest = $1,000 x 12% = $120

Maturity period = 20 years

A. Required Rate of Return 12%

Market Price of the Bond as on today = Interest x PVIFA (12%, 20) + Maturity Value x PVIF (20%, 20)

= ($120 x 7.4694) + ($1,000 x 0.10366) = $896 + $103.66 = $999.66 or $1,000

B. Required Rate of Return 6%

Market Price of the Bond as on today = Interest x PVIFA (6%, 20) + Maturity Value x PVIF (6%, 20)

= ($120 x 11.4699) + ($1,000 x 0.3118) = $1,376.39 + $311.80 = $1,688.19 or $1,688

C. Required Rate of Return 18%

Market Price of the Bond as on today = Interest x PVIFA (18%, 20) + Maturity Value x PVIF (18%, 20)

= ($120 x 5.3527) + ($1,000 x 0.0365) = $642.33 + $36.50 = $678.83 or $679

D. At what required market rate (6 percent, 12 percent, or 18 percent) does the above bond sell at a discount? At a premium?

At 18% --- bond sell at discount (i.e. Market Value as on today is less than par value)

At 6% --- bond sell at Premium (i.e. Market Value of bond as on today is higher than par value)

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