A zero-coupon bond matures in 15 years. At a market discount rate of 4.5% per ye

Question

A zero-coupon bond matures in 15 years. At a market discount rate of 4.5% per year and assuming semi-annual compounding, what is the price of the bond?

You sold the zero-coupon bond in the question above with exactly 7 years left to maturity when the market discount rate for such a security is 3.5%, what is the taxable gain for this bond?

Analyze the following Treasury note & bond quotes from April 10, 2014.

0.250

a. Plot the yield vs. price curve for each (best done in Excel).

b. Which bond has lowest price sensitivity? Which has the highest?

c. Which bond would you purchase if you thought the yield curve would increase by 100bps within the next year?

SIDENOTE: another source answered question 1 like this but i dont know if this correct if true continue to rest . . .The price of the zero-coupon bond is closest to 51.67. The price is determined in the following manner:

PV=100(1+r)N

where:

PV = present value, or the price of the bond

r = market discount rate, or required rate of return per period

N = number of evenly spaced periods to maturity

PV=100(1+0.045)15

PV = 51.67

Maturity(yrs) Coupon Bid Asked Change Asked Yield 1

0.250

100.0391 100.0547 -0.0156 0.037 5 1.125 98.4609 98.4766 -0.0625 1.439 10 6.875 146.0859 146.1016 +0.0469 1.935 30 2.500 98.2813 98.3125 +0.2109 2.582

Explanation / Answer

Part 1)

Price of 15 years zero coupon bond

= Maturity Value/ [(1+rate od discount/interest)^number of compounding periods]

Here bond is semi-annually compounded, so rate semi-annually = 4.5/2 = 2.25%, and n = 15*2 = 30 periods

Price today = 100/(1.0225)^30 = 51.298

Part 2)

Now if we sell this bond exactly when 7 years are left to maturity:

Price of the bond at that time:

new rate of interest = 3.5% annually = 1.75% semi annual, n = 7*2 = 14 periods

Price of bond = 100/[(1.0175)^14] = 78.436

Gain on sale of bond = 78.436 -51.289 = 27.147 per bond.

PS: Question 2 is separate from question 1, please ask it as a separate question. Thanks.

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