Answer:
Task a: $102.74
Task b: 2.73%
Task c: $100.44
Task d: $101.84
Explanation:
<u>a.At what price will the bond sell?
</u>
<u>Solution:</u>
The price of the bond = Coupon payment for year 1 / (1+ YTM on 1-year zero-coupon bonds) + (Coupon payment for year 2 + maturity Value) / (1+ YTM on 2-year zero-coupon bonds) ^2
= $10/ (1+7.5%) + ($10 + $100)/ (1+8.5%) ^2
=$9.30 +$93.44
=$102.74
<u>b. What will the yield to maturity on the bond be?</u>
<u>Solution:</u>
We have following formula for calculation of bond’s yield to maturity (YTM)
Bond price P0 = C/ (1+YTM) + (M+C) / (1+YTM) ^2
Where,
P0 = the current market price of bond =$102.74
C = coupon payment = 10% of $100 = $10
YTM = interest rate, or yield to maturity =?
M = value at maturity, or par value = $ 100
Now we have,
$102.74 = $10/ (1+YTM) + $110 / (1+YTM) ^2
YTM = 2.73%
<u>(c) If the expectations theory of the yield curve is correct, what is the market expectation of the price that the bond will sell for next year?
</u>
<u>Solution
</u>
Under expectation theory
ft = E(rt )
Therefore (1+ ft) = (1.085) ^ 2 / 1.075 = 1.0951
Or ft = E(rt )= 1.0951 -1 = 0.0951 or 9.51%
By using this theory the bond price on year,
P = $110/1.0951 = $100.44
<u>(d) Recalculate your answer to (c) if you believe in the liquidity preference theory and you believe that the liquidity premium is 1.5%.</u>
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<u>Solution</u>
If the liquidity premium is 1.5%,
Then ft = E (rt) + L
Where L is liquidity premium = 1.5%
Therefore,
E(rt) = ft - L = 9.51% - 1.5% = 8.01%
And price of the bond
P = $110/1.0801 = $101.84
