Lorenzo can purchase a $4,000 bond for $3,800. If the bond pays quarterly dividends at 8% (stated annual inte

Question

Lorenzo can purchase a $4,000 bond for $3,800. If the bond pays quarterly dividends at 8% (stated annual interest rate) and the bond will mature in 6.5 years, what is the actual rate of return Lorenzo would get on this investment?

Answer 1

A quarterly dividend at an annual interest rate of of 8% means that Lorenzo gets 2% every three months, or 0.25 years. In 6.5 years, he receives this dividend 6.5*4 = 26 times. I'm not sure, but it looks like that dividend is paid on the initial investment of $3800, meaning he receives $3800*0.02*26 = $1976. And then, at the end, the bond itself becomes worth $4000, meaning the total value is $5976, and the return rate is ($5976 - $3800) / $3800 = 0.57 = 57%. This question is confusing, though, because bonds do not usually pay a regular dividend. Thus, I'm not sure if the dividend is meant to be paid out to you, or paid into the bond account. I assumed the former. If the latter, then the value of the dividends is not $3800*0.02*26, but instead $3800*(1.02)^26 - $3800 = $2,558.98, for a total final value of $6,558.98 at maturity and a return rate of ($6,559 - $3800) / $3800 = 0.73 = 73%.

Answer 2

Lorenzo's bond earns him $320/year. In 6.5 years he will have earned $2080. At maturity, he will have received $2080 + $200 = $2280 on a $3800 investment for 6.5 years.

That works out to an average annual return of 8.1759%

(Bond interest is paid out, not compounded, on a coupon bond. A zero coupon bond interest is effectively compounded. Bonds and CD's pay differently and different calculations are used.)

Answer 3

Present value of bond is present value of coupons (you call them dividends) plus
present value of par value of bond at maturity.

Dividends of 8% of 4000 = 320. (I assume the 320 is quarterly)
6.5 years equals 26 quarters.
PV of dividends: 320*(1-v^26)/i, where v=1/(1+i)
PV of par value: 4000*(v^26)

3800=320*(1-v^26)/i + 4000*(v^26)
320*(1-v^26)/i + 4000*(v^26) - 3800 = 0

By trial and error, i=.085 approximately.