In March 2015, Daniela Motor Financing (DMF), offered some securities for sale t

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 2045, but investors would receive nothing until then. Investors paid DMF $790 for each of these securities; so they gave up $790 in March 2015, for the promise of a $2,000 payment 30 years later.
  
a. Assuming you purchased the bond for $790, what rate of return would you earn if you held the bond for 30 years until it matured with a value $2,000

b. Suppose under the terms of the bond you could redeem the bond in 2026. DMF agreed to pay an annual interest rate of .9 percent until that date. How much would the bond be worth at that time?

c. In 2026, instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in 2045. What annual rate of return will you earn over the last 19 years?

Explanation / Answer

a. Rate of return earnbed is given by:

rate=(future value/present value)1/time - 1

=(2,000/790)1/30 - 1

=2.53161/30-1

=1.0475-1

=0.0475 or 4.75%

b) Promised interest till 2026 that is another 11 years is at 0.9%.

So value of the bond in 2026=790(1+0.009)11=790*1.1036=$871.84

c) If we do not encash the bond in 2026 and hold it till maturity in 2045, then return earned is:

rate= (2,000/871.84)1/19 - 1

=2.29391/19-1

=1.0447-1

=0.0447 or 4.47%

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