John invests $100,000 in a newly issued 3 year bond. The bond is issued at par on 1 Jan 2007.The coupon rate is 4%. Interest is paid on each 30 Jun and 31 Dec. On 1 Jan 2008, John finds that the stock market provides better return. Therefore, John sells the bond on 1 Jan 2008. Yield-to-maturity is 4.2% on 1 Jan 2008. All sale proceeds are invested in a stock at $190 per share. During 2008, a dividend of $2 per share is received by John. On 31 Dec 2008, John sells all stock at $195 per share.
a) What is the Yield-to-maturity on 1 Jan 2007 ? Briefly explain why.
b) What are the sale proceeds from disposing the bond on 1 Jan 2008 ?
c) What is the return from investment in the bond in 2007 ?
d) What is the dividend income received by John in 2008 ?
e) What is the return from investment in the share in 2008 ?
f) What is the geometric average return for the 2007 and 2008 investment period?
Elain, Ming, Wong: We don't do homework for you. If you show thinking or work, we will generally critique it.
a) To find the yield-to-maturity on 1 Jan 2007, we need to calculate the yield-to-maturity formula using the bond's details.
The yield-to-maturity (YTM) is the total return anticipated on a bond if it is held until it matures. It is expressed as an annual percentage rate. The formula for YTM is:
YTM = (C + (F - P) / n) / ((F + P) / 2)
Where:
C = coupon payment
F = face value of the bond
P = purchase price of the bond
n = number of periods until maturity
In this case:
Coupon payment (C) = $4,000 (4% of $100,000)
Face value (F) = $100,000
Purchase price (P) = $100,000
Number of periods until maturity (n) = 2 (since it's a 3-year bond and we are calculating the YTM on 1 Jan 2007)
Plugging these values into the formula:
YTM = ($4,000 + ($100,000 - $100,000) / 2) / (($100,000 + $100,000) / 2)
YTM = (4,000 + 0) / (200,000 / 2)
YTM = 4,000 / 100,000
YTM = 0.04 or 4%
Therefore, the Yield-to-maturity on 1 Jan 2007 is 4%.
b) To calculate the sale proceeds from disposing the bond on 1 Jan 2008, we need to find the present value of the bond's future cash flows using the yield-to-maturity on 1 Jan 2008.
The present value (PV) of the bond's future cash flows can be calculated using the formula:
PV = (C / (1 + r)^t) + (C / (1 + r)^(t+1)) + ... + (C + F) / (1 + r)^(t+n)
Where:
PV = present value
C = coupon payment
r = yield-to-maturity
t = number of periods elapsed (in this case, 1 year)
n = number of periods remaining (in this case, 2 years)
Plugging in the values:
PV = (4,000 / (1 + 0.042)^1) + (4,000 / (1 + 0.042)^2) + (100,000 / (1 + 0.042)^3)
PV = 3,846.15 + 3,699.42 + 92,479.34
PV = 99,024.91
Therefore, the sale proceeds from disposing the bond on 1 Jan 2008 are $99,024.91.
c) The return from investment in the bond in 2007 can be calculated by subtracting the initial investment from the sale proceeds and dividing by the initial investment.
Return from bond investment in 2007 = (Sale proceeds - Initial investment) / Initial investment
Return from bond investment in 2007 = ($99,024.91 - $100,000) / $100,000
Return from bond investment in 2007 = -$975.09 / $100,000
Return from bond investment in 2007 = -0.00975 or -0.975%
Therefore, the return from investment in the bond in 2007 is -0.975%.
d) The dividend income received by John in 2008 is given as $2 per share. However, the number of shares bought by John is not specified in the question. It is needed to calculate the exact dividend income.
e) To calculate the return from investment in the share in 2008, we need to find the change in value and divide it by the initial investment, then convert it to a percentage.
Return from share investment in 2008 = (Sale proceeds - Initial investment) / Initial investment
Return from share investment in 2008 = ($195 - $190) / $190
Return from share investment in 2008 = $5 / $190
Return from share investment in 2008 ≈ 0.0263 or 2.63%
Therefore, the return from investment in the share in 2008 is approximately 2.63%.
f) The geometric average return for the 2007 and 2008 investment period can be calculated using the formula:
Geometric average return = ((1 + Return1) * (1 + Return2))^(1/n) - 1
Where:
Return1 = return from bond investment in 2007
Return2 = return from share investment in 2008
n = number of investment periods (in this case, 2)
Plugging in the values:
Geometric average return = ((1 + (-0.00975)) * (1 + 0.0263))^(1/2) - 1
Geometric average return = ((0.99025) * (1.0263))^(1/2) - 1
Geometric average return = 1.016695 - 1
Geometric average return ≈ 0.0167 or 1.67%
Therefore, the geometric average return for the 2007 and 2008 investment period is approximately 1.67%.