Question

A 4.75 percent coupon municipal bond has 20 years left to maturity and has a price quote of 101.30. The bond can be called in eight years. The call premium is one year of coupon payments. (Assume interest payments are semiannual and a par value of $5,000.)
Compute the bond’s current yield. (Round your answer to 2 decimal places.)
Compute the yield to maturity. (Round your answer to 2 decimal places.)
Compute the taxable equivalent yield (for an investor in the 36 percent marginal tax bracket). (Round your answer to 2 decimal places.)

Answer 1

Answer:

Answer is given below.

Explanation:

Par value of bond = $ 5000

Coupon rate = 4.75% * 6 / 12 = 2.375% Per period

Term = 20Years *2 = 40 Periods

Current price of bond = Par value * 101.30% = $5,000 * 101.30% = $5,065

Callable price = Par value + Call premium = $5,000 + $5,000 * 4.75% = S5,237.5

Callableterm = 8 Years * 2 = 16  Periods

Couponamountperperiod =Parvalue • Couponrate = $5000*2.375% = $118.75

Current yield = Coupon amount /Current price = $118.75/$5,065 = 0.023445212 = 2.345%Per period Rounded)

Currentyield = 2.345%Perperiod *2 = 4.69%Perannum

YTM = [Coupon amount + (Maturity value - Current price ) / Term] / [(Current price + Maturity value ) /2]

= [$118.75+($5,000-$5,065)/40]/[($5,065+S5,000)/2]

= $117.125 / $5032.5

= 0.023273721 = 2.33%Perperiod

YTM = 2.33% * 2 = 4.66% Per annum

Tax rate = 36%

After tax equivalent yield YTM (1 -Tax rate) = 4.66%(1-36%) = 2.9824% Per annum

Yield to call (YTC) = [Couponamount+(Call price - Current price)/Callable Term/ [(Current price+Call price)/2]

= [$118.75 + ($5,237.5 - $5,065)/16 ] / [($5,065 + $5,237.5)/ 2]

= $129.53125/ $5151.25

= 0.025145596 = 2.515%Per period (Rounded)

YTC = 2.515%2 = 5.03%Per annum (Rounded)

Answer 2

Answer:

Compute the bond’s current yield.

• 4.69%

Compute the yield to maturity.

• 4.65%

Compute the taxable equivalent yield (for an investor in the 36 percent marginal tax bracket).

• 7.27%

Explanation:

par value of bond = $5,000

total semiannual coupon paid = $118.75

semiannual interest rate = 4.75% / 2 = 2.375%

market value of coupon = $5,000 x 1.013 = $5,065

1) bond's current yield = ($118.75 / $5,065) x 2 = 4.69%

2) YTM = {C + [(F - P) / n]} / [(F + P) / 2]

= {$118.75 + [($5,000 -$5,065) / 40]} / [($5,000 + $5,065) / 2]

= ($118.75 - $1.625) / $5,032.50 = 0.02327 x 2 = 0.046547 or 4.65%

3) 4.65% = X (1 - 36%)

4.65% = 0.64X

X = 4.65% / 0.64 = 7.2656% ≈ 7.27%