6) A 10-year municipal bond has a coupon rate of 4.5% and just sold today for 104.56. It matures on December 1, 2023. What is its tax-equivalent yield? Assume a marginal tax rate of 40% and interest is paid June 1 and December 1. 

 

7. Which of the following is true about duration and modified duration?

I.          The Macaulay duration calculates the weighted average time before a bondholder would receive the bond's cash flows.
II.         Modified duration measures price sensitivity of a bond to changes in YTM by adjusting duration with a factor based on current yield.
III.        The value of duration and modified duration are usually very close, but duration is almost always a larger number.

IV.        Duration is important to banks when they try to assess the risk of bond portfolios on their balance sheet.

A. Only I and II are true. B. All but IV are true. C. Only II and III are true. D.All are true.

 

8. A bond has a current price of $800, a maturity value of $1,000 (matures in 5 years). If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond's annual coupon rate?

 

9. Another bond was issued on 6/1/2018 and has a 4% coupon rate, with interest paid semi-annually, and a maturity value of $1,000, and matures on 6/1/2043. However, it is callable after 6/1/2023 with a call premium of 7.5%. If the bond is currently priced to yield 3.75%, what is the bond's yield to call if you bought it on 3/1/2022?

 

10. This last bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price of $1,200. What is the its yield-to-maturity?

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- A tax-equivalent yield is the return that a taxable bond needs to earn to match the equivalent tax-free bond.

- Tax equivalent yield = Tax free yield / (1 - tax rate) = (0.045 / 2) / (1 - 0.40) = 0.0225 / 0.60 = 0.0375

- Tax free yield is the tax free return earned on a municipal bond. Since this particular municipal bond pays tax free returns semi-annually, that is twice a year, the tax free yield in the calculation is divided by 2.

Step-by-step explanation

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Tax equivalent yield = Tax free yield / (1 - tax rate)

= (0.045/2)/(1-0.40)

= 0.0225/0.60

= 0.0375

= 3.75%

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Modified duration

Let's say I am a stockist of winter clothes such as sweaters and mufflers. In anticipation of a good winter, I have stocked clothes in excess. My biggest concern is whether I will be able to sell all these before the onset of summer Let's say if the summer steps in earlier than expected, then what do I do? Naturally to clear the stock I will have to lower its price. Contrary, if for some reason the winter gets more severe and prolonged, then what could happen? In such a situation I will charge a premium for the goods that I have in stock and since I have a large supply, I would therefore make more money.

Thus, the behavior of an external factor seems to be having a major impact on the prices I charge in the market. Now keep this in mind as I attempt to explain "modified duration" for debt products.

Modified Duration by definition expresses the sensitivity of the price of a bond to a change in interest rate.

OPTION = B

All but IV are true

Explanation

I.The Macaulay duration calculates the weighted average time before a
bondholder would receive the bond's cash flows.
II. Modified duration measures price sensitivity of a bond to changes in YTM by
adjusting duration with a factor based on current yield.
III. The value of duration and modified duration are usually very close, but duration
is almost always a larger number.

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Semi-annual Coupon can be calculated using PMT function on a calculator

N = 5 x 2 = 10, PV = -800, FV = 1000, I/Y = 8%/2 = 4%

=> Compute PMT = $15.34

Coupon Rate = 15.34 x 2 / 1000 = 3.07%

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Given: Here, Issue Date of Bond is 6/1/2018 Maturity Date of Bond is 6/1/2043 Call Date is 6/1/2023 Purchase Date is 6/1/2022 Coupon Rate is 4% Compounding Period of Coupon is Semi Annual i.e. 2 Maturity Value is $1,000 Call Value is 7.5% call premium YTM is 3.75% Calculation of Yield to Call: Calculation of Yield to Call is as follows: Workings: Issue Date 43252 Maturity Date (Maturity) 52383 Purchase Date (Settlement) 44713 Coupon Rate (Rate 0.04 Face Value of Bond (Redemption) 1000 6 Yeild to Maturity (Yld) 0.0375 Compounding Period (Frequency) 2 00 Price of Bond =PRICE(B3,B2,B4,B6,100,2)*10 9 Callable Date (Maturity) 45078 10 Call Value Premium 0.075 11 Call Value (Redemption) =B5*(1+B10) 12 Yield to Call =YIELD(B3,B9,B4,BS/10,B11/10,2)

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Book1 - Excel - X FILE HOME INSERT PAGE LAYOUT FORMULAS DATA REVIEW VIEW Sign in X Cut AutoSum Calibri - 11 - A A Be Wrap Text General AY H BB Copy Fill Sort & Find & Paste 4.0 Insert Delete Format Format Painter BIU . Merge & Center . $ - % " Conditional Format as Cell Formatting Table Styles Clear Filter * Select Clipboard G Font Alignment G Number G Styles Cells Editing B14 X A B C D E F G H J K L M N O P 2 Let us assume Face value of bond 1000 Current price 1200 Interest rate 8% 5 Semi annual interest rate 4.00% B5/2 6 Semi annual coupon payment 40 B3*B6 7 Years to maturity 5 (2035-2021) 8 No. of semi annual periods 10 B8*2 9 10 Yield 3.5940930789% RATE(B9,-B7,B4,-B3,0)*2 11 13 14 15 16 17 18 19 20 21 22 23 24 Sheet1 Sheet2 Sheet3 Sheet4 Sheet5 Sheet6 + + READY 100% 8:04 AM W 30-Mar-21