Question

In March 2015, Daniela Motor Financing (DMF), offered some securities for sale to the public. Under the terms of the deal, DMF promised to repay the owner of one of these securities $2,000 in March 2040, but investors would receive nothing until then. Investors paid DMF $740 for each of these securities; so they gave up $740 in March 2015, for the promise of a $2,000 payment 25 years later.
Required:
a. Assuming you purchased the bond for $740, what rate of return would you earn if you held the bond for 25 years until it matured with a value $2,000?
b. Suppose under the terms of the bond you could redeem the bond in 2023. DMF agreed to pay an annual interest rate of 1.4 percent until that date. How much would the bond be worth at that time?
c. In 2023, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2040. What annual rate of return will you earn over the last 17 years?

Answer 1

Answer:

a. 4.06%

b. $827.06

c. 5.33%

Explanation:

a. Assuming you purchased the bond for $740, what rate of return would you earn if you held the bond for 25 years until it matured with a value $2,000?

Rate of return = [(Promised payment / Bond purchase price)^(1 / 25)] - 1 = [(2,000 / 740)^(1/25)] - 1 = 1.0406 = 0.0406 = 4.06%

Therefore, the rate of return that you would earn is 4.06%.

b. Suppose under the terms of the bond you could redeem the bond in 2023. DMF agreed to pay an annual interest rate of 1.4 percent until that date. How much would the bond be worth at that time?

Since 2015 to 2023 is 8 years, the worth of the bond after 8 years at 1.4 percent can be computed as follows:

Worth after 8 years = Bond purchase price * (1 + r)^n

Where;

r = annual interest rate = 1.40%, or 0.014

n = number years after = 8

Therefore, we have:

Worth after 8 years = 740 * (1 + 0.014)^8 = $827.06

c. In 2023, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2040. What annual rate of return will you earn over the last 17 years?

Return in last 17 years = [(Bond purchase price / Worth after 8 years)^(1/17)] - 1 = [(2,000 / 827.06)^(1/17)] - 1 = 1.0533 - 1 = 0.0533 = 5.33%